id	sid	tid	token	lemma	pos
ejpam-4931	1	1	european	european	PROPN
ejpam-4931	1	2	journal	journal	PROPN
ejpam-4931	1	3	of	of	ADP
ejpam-4931	1	4	pure	pure	ADJ
ejpam-4931	1	5	and	and	CCONJ
ejpam-4931	1	6	applied	apply	VERB
ejpam-4931	1	7	mathematics	mathematic	NOUN
ejpam-4931	1	8	vol	vol	NOUN
ejpam-4931	1	9	.	.	PUNCT
ejpam-4931	2	1	16	16	NUM
ejpam-4931	2	2	,	,	PUNCT
ejpam-4931	2	3	no	no	INTJ
ejpam-4931	2	4	.	.	NOUN
ejpam-4931	2	5	4	4	NUM
ejpam-4931	2	6	,	,	PUNCT
ejpam-4931	2	7	2023	2023	NUM
ejpam-4931	2	8	,	,	PUNCT
ejpam-4931	2	9	2247	2247	NUM
ejpam-4931	2	10	-	-	SYM
ejpam-4931	2	11	2285	2285	NUM
ejpam-4931	2	12	issn	issn	PROPN
ejpam-4931	2	13	1307	1307	NUM
ejpam-4931	2	14	-	-	SYM
ejpam-4931	2	15	5543	5543	NUM
ejpam-4931	2	16	–	–	PUNCT
ejpam-4931	3	1	ejpam.com	ejpam.com	X
ejpam-4931	3	2	published	publish	VERB
ejpam-4931	3	3	by	by	ADP
ejpam-4931	3	4	new	new	PROPN
ejpam-4931	3	5	york	york	PROPN
ejpam-4931	3	6	business	business	PROPN
ejpam-4931	3	7	global	global	ADJ
ejpam-4931	3	8	global	global	ADJ
ejpam-4931	3	9	existence	existence	NOUN
ejpam-4931	3	10	of	of	ADP
ejpam-4931	3	11	weak	weak	ADJ
ejpam-4931	3	12	solutions	solution	NOUN
ejpam-4931	3	13	to	to	ADP
ejpam-4931	3	14	3d	3d	PROPN
ejpam-4931	3	15	compressible	compressible	ADJ
ejpam-4931	3	16	primitive	primitive	ADJ
ejpam-4931	3	17	equations	equation	NOUN
ejpam-4931	3	18	of	of	ADP
ejpam-4931	3	19	atmospheric	atmospheric	ADJ
ejpam-4931	3	20	dynamics	dynamic	NOUN
ejpam-4931	3	21	with	with	ADP
ejpam-4931	3	22	degenerate	degenerate	ADJ
ejpam-4931	3	23	viscosity	viscosity	NOUN
ejpam-4931	3	24	jules	jule	NOUN
ejpam-4931	3	25	ouya1	ouya1	ADJ
ejpam-4931	3	26	,	,	PUNCT
ejpam-4931	3	27	arouna	arouna	PROPN
ejpam-4931	3	28	ouédraogo1,∗	ouédraogo1,∗	PROPN
ejpam-4931	3	29	1	1	NUM
ejpam-4931	3	30	département	département	PROPN
ejpam-4931	3	31	de	de	X
ejpam-4931	3	32	mathématiques	mathématiques	PROPN
ejpam-4931	3	33	,	,	PUNCT
ejpam-4931	3	34	laboratoire	laboratoire	PROPN
ejpam-4931	3	35	de	de	X
ejpam-4931	3	36	mathématiques	mathématiques	PROPN
ejpam-4931	3	37	,	,	PUNCT
ejpam-4931	3	38	informatique	informatique	PROPN
ejpam-4931	3	39	et	et	NOUN
ejpam-4931	3	40	applications	application	NOUN
ejpam-4931	3	41	(	(	PUNCT
ejpam-4931	3	42	l@mia	l@mia	NOUN
ejpam-4931	3	43	)	)	PUNCT
ejpam-4931	3	44	,	,	PUNCT
ejpam-4931	3	45	université	université	ADJ
ejpam-4931	3	46	norbert	norbert	PROPN
ejpam-4931	3	47	zongo	zongo	PROPN
ejpam-4931	3	48	,	,	PUNCT
ejpam-4931	3	49	koudougou	koudougou	PROPN
ejpam-4931	3	50	,	,	PUNCT
ejpam-4931	3	51	burkina	burkina	PROPN
ejpam-4931	3	52	faso	faso	PROPN
ejpam-4931	3	53	abstract	abstract	NOUN
ejpam-4931	3	54	.	.	PUNCT
ejpam-4931	4	1	in	in	ADP
ejpam-4931	4	2	this	this	DET
ejpam-4931	4	3	work	work	NOUN
ejpam-4931	4	4	,	,	PUNCT
ejpam-4931	4	5	we	we	PRON
ejpam-4931	4	6	show	show	VERB
ejpam-4931	4	7	the	the	DET
ejpam-4931	4	8	existence	existence	NOUN
ejpam-4931	4	9	of	of	ADP
ejpam-4931	4	10	global	global	ADJ
ejpam-4931	4	11	weak	weak	ADJ
ejpam-4931	4	12	solutions	solution	NOUN
ejpam-4931	4	13	to	to	ADP
ejpam-4931	4	14	the	the	DET
ejpam-4931	4	15	three	three	NUM
ejpam-4931	4	16	-	-	PUNCT
ejpam-4931	4	17	dimensional	dimensional	ADJ
ejpam-4931	4	18	compressible	compressible	ADJ
ejpam-4931	4	19	primitive	primitive	ADJ
ejpam-4931	4	20	equations	equation	NOUN
ejpam-4931	4	21	of	of	ADP
ejpam-4931	4	22	atmospheric	atmospheric	ADJ
ejpam-4931	4	23	dynamics	dynamic	NOUN
ejpam-4931	4	24	with	with	ADP
ejpam-4931	4	25	degenerate	degenerate	ADJ
ejpam-4931	4	26	viscosity	viscosity	NOUN
ejpam-4931	4	27	density	density	NOUN
ejpam-4931	4	28	-	-	PUNCT
ejpam-4931	4	29	dependent	dependent	ADJ
ejpam-4931	4	30	for	for	ADP
ejpam-4931	4	31	large	large	ADJ
ejpam-4931	4	32	initial	initial	ADJ
ejpam-4931	4	33	data	datum	NOUN
ejpam-4931	4	34	.	.	PUNCT
ejpam-4931	5	1	with	with	ADP
ejpam-4931	5	2	a	a	DET
ejpam-4931	5	3	pressure	pressure	NOUN
ejpam-4931	5	4	law	law	NOUN
ejpam-4931	5	5	of	of	ADP
ejpam-4931	5	6	the	the	DET
ejpam-4931	5	7	form	form	NOUN
ejpam-4931	5	8	ρ2	ρ2	NOUN
ejpam-4931	5	9	,	,	PUNCT
ejpam-4931	5	10	we	we	PRON
ejpam-4931	5	11	represent	represent	VERB
ejpam-4931	5	12	the	the	DET
ejpam-4931	5	13	vertical	vertical	ADJ
ejpam-4931	5	14	velocity	velocity	NOUN
ejpam-4931	5	15	as	as	ADP
ejpam-4931	5	16	a	a	DET
ejpam-4931	5	17	function	function	NOUN
ejpam-4931	5	18	of	of	ADP
ejpam-4931	5	19	the	the	DET
ejpam-4931	5	20	density	density	NOUN
ejpam-4931	5	21	and	and	CCONJ
ejpam-4931	5	22	the	the	DET
ejpam-4931	5	23	horizontal	horizontal	ADJ
ejpam-4931	5	24	one	one	NOUN
ejpam-4931	5	25	which	which	PRON
ejpam-4931	5	26	will	will	AUX
ejpam-4931	5	27	be	be	AUX
ejpam-4931	5	28	important	important	ADJ
ejpam-4931	5	29	in	in	ADP
ejpam-4931	5	30	using	use	VERB
ejpam-4931	5	31	faedo	faedo	ADJ
ejpam-4931	5	32	-	-	PUNCT
ejpam-4931	5	33	galerkin	galerkin	ADJ
ejpam-4931	5	34	method	method	NOUN
ejpam-4931	5	35	to	to	PART
ejpam-4931	5	36	obtain	obtain	VERB
ejpam-4931	5	37	the	the	DET
ejpam-4931	5	38	global	global	ADJ
ejpam-4931	5	39	existence	existence	NOUN
ejpam-4931	5	40	of	of	ADP
ejpam-4931	5	41	the	the	DET
ejpam-4931	5	42	approximate	approximate	ADJ
ejpam-4931	5	43	solutions	solution	NOUN
ejpam-4931	5	44	.	.	PUNCT
ejpam-4931	6	1	in	in	ADP
ejpam-4931	6	2	analogy	analogy	NOUN
ejpam-4931	6	3	with	with	ADP
ejpam-4931	6	4	the	the	DET
ejpam-4931	6	5	cases	case	NOUN
ejpam-4931	6	6	in	in	ADP
ejpam-4931	6	7	[	[	X
ejpam-4931	6	8	17–19	17–19	NUM
ejpam-4931	6	9	]	]	PUNCT
ejpam-4931	6	10	,	,	PUNCT
ejpam-4931	6	11	we	we	PRON
ejpam-4931	6	12	prove	prove	VERB
ejpam-4931	6	13	that	that	SCONJ
ejpam-4931	6	14	the	the	DET
ejpam-4931	6	15	weak	weak	ADJ
ejpam-4931	6	16	solutions	solution	NOUN
ejpam-4931	6	17	satisfy	satisfy	VERB
ejpam-4931	6	18	the	the	DET
ejpam-4931	6	19	basic	basic	ADJ
ejpam-4931	6	20	energy	energy	NOUN
ejpam-4931	6	21	inequality	inequality	NOUN
ejpam-4931	6	22	and	and	CCONJ
ejpam-4931	6	23	the	the	DET
ejpam-4931	6	24	breschdesjardins	breschdesjardin	NOUN
ejpam-4931	6	25	entropy	entropy	PROPN
ejpam-4931	6	26	inequality	inequality	PROPN
ejpam-4931	6	27	.	.	PUNCT
ejpam-4931	7	1	based	base	VERB
ejpam-4931	7	2	on	on	ADP
ejpam-4931	7	3	these	these	DET
ejpam-4931	7	4	estimates	estimate	NOUN
ejpam-4931	7	5	and	and	CCONJ
ejpam-4931	7	6	using	use	VERB
ejpam-4931	7	7	compactness	compactness	NOUN
ejpam-4931	7	8	arguments	argument	NOUN
ejpam-4931	7	9	,	,	PUNCT
ejpam-4931	7	10	we	we	PRON
ejpam-4931	7	11	prove	prove	VERB
ejpam-4931	7	12	the	the	DET
ejpam-4931	7	13	global	global	ADJ
ejpam-4931	7	14	existence	existence	NOUN
ejpam-4931	7	15	of	of	ADP
ejpam-4931	7	16	weak	weak	ADJ
ejpam-4931	7	17	solutions	solution	NOUN
ejpam-4931	7	18	of	of	ADP
ejpam-4931	7	19	(	(	PUNCT
ejpam-4931	7	20	1	1	NUM
ejpam-4931	7	21	)	)	PUNCT
ejpam-4931	7	22	by	by	ADP
ejpam-4931	7	23	vanishing	vanish	VERB
ejpam-4931	7	24	the	the	DET
ejpam-4931	7	25	parameters	parameter	NOUN
ejpam-4931	7	26	in	in	ADP
ejpam-4931	7	27	our	our	PRON
ejpam-4931	7	28	approximate	approximate	ADJ
ejpam-4931	7	29	system	system	NOUN
ejpam-4931	7	30	step	step	NOUN
ejpam-4931	7	31	by	by	ADP
ejpam-4931	7	32	step	step	NOUN
ejpam-4931	7	33	.	.	PUNCT
ejpam-4931	8	1	2020	2020	NUM
ejpam-4931	8	2	mathematics	mathematic	NOUN
ejpam-4931	8	3	subject	subject	NOUN
ejpam-4931	8	4	classifications	classification	NOUN
ejpam-4931	8	5	:	:	PUNCT
ejpam-4931	8	6	35q30	35q30	NUM
ejpam-4931	8	7	,	,	PUNCT
ejpam-4931	8	8	35b40	35b40	NUM
ejpam-4931	8	9	,	,	PUNCT
ejpam-4931	8	10	76d05	76d05	NUM
ejpam-4931	8	11	,	,	PUNCT
ejpam-4931	8	12	34c35	34c35	NUM
ejpam-4931	8	13	key	key	ADJ
ejpam-4931	8	14	words	word	NOUN
ejpam-4931	8	15	and	and	CCONJ
ejpam-4931	8	16	phrases	phrase	NOUN
ejpam-4931	8	17	:	:	PUNCT
ejpam-4931	8	18	compressible	compressible	VERB
ejpam-4931	8	19	primitive	primitive	ADJ
ejpam-4931	8	20	equations	equation	NOUN
ejpam-4931	8	21	,	,	PUNCT
ejpam-4931	8	22	global	global	ADJ
ejpam-4931	8	23	weak	weak	ADJ
ejpam-4931	8	24	solutions	solution	NOUN
ejpam-4931	8	25	,	,	PUNCT
ejpam-4931	8	26	degenerate	degenerate	ADJ
ejpam-4931	8	27	viscosity	viscosity	NOUN
ejpam-4931	8	28	density	density	NOUN
ejpam-4931	8	29	-	-	PUNCT
ejpam-4931	8	30	dependent	dependent	ADJ
ejpam-4931	8	31	1	1	NUM
ejpam-4931	8	32	.	.	PUNCT
ejpam-4931	9	1	introduction	introduction	NOUN
ejpam-4931	9	2	we	we	PRON
ejpam-4931	9	3	are	be	AUX
ejpam-4931	9	4	interested	interested	ADJ
ejpam-4931	9	5	in	in	ADP
ejpam-4931	9	6	the	the	DET
ejpam-4931	9	7	study	study	NOUN
ejpam-4931	9	8	of	of	ADP
ejpam-4931	9	9	equations	equation	NOUN
ejpam-4931	9	10	of	of	ADP
ejpam-4931	9	11	type	type	NOUN
ejpam-4931	9	12	primitive	primitive	ADJ
ejpam-4931	9	13	compressible	compressible	ADJ
ejpam-4931	9	14	equations	equation	NOUN
ejpam-4931	9	15	,	,	PUNCT
ejpam-4931	9	16	cpes	cpe	NOUN
ejpam-4931	9	17	.	.	PUNCT
ejpam-4931	10	1	these	these	PRON
ejpam-4931	10	2	are	be	AUX
ejpam-4931	10	3	the	the	DET
ejpam-4931	10	4	equations	equation	NOUN
ejpam-4931	10	5	governing	govern	VERB
ejpam-4931	10	6	the	the	DET
ejpam-4931	10	7	motions	motion	NOUN
ejpam-4931	10	8	of	of	ADP
ejpam-4931	10	9	the	the	DET
ejpam-4931	10	10	dynamics	dynamic	NOUN
ejpam-4931	10	11	of	of	ADP
ejpam-4931	10	12	the	the	DET
ejpam-4931	10	13	atmosphere	atmosphere	NOUN
ejpam-4931	10	14	.	.	PUNCT
ejpam-4931	11	1	they	they	PRON
ejpam-4931	11	2	belong	belong	VERB
ejpam-4931	11	3	to	to	ADP
ejpam-4931	11	4	the	the	DET
ejpam-4931	11	5	class	class	NOUN
ejpam-4931	11	6	of	of	ADP
ejpam-4931	11	7	geophysical	geophysical	ADJ
ejpam-4931	11	8	fluid	fluid	NOUN
ejpam-4931	11	9	dynamics	dynamic	NOUN
ejpam-4931	11	10	equations	equation	NOUN
ejpam-4931	11	11	.	.	PUNCT
ejpam-4931	12	1	more	more	ADV
ejpam-4931	12	2	precisely	precisely	ADV
ejpam-4931	12	3	,	,	PUNCT
ejpam-4931	12	4	in	in	ADP
ejpam-4931	12	5	the	the	DET
ejpam-4931	12	6	hierarchy	hierarchy	NOUN
ejpam-4931	12	7	of	of	ADP
ejpam-4931	12	8	models	model	NOUN
ejpam-4931	12	9	,	,	PUNCT
ejpam-4931	12	10	the	the	DET
ejpam-4931	12	11	cpes	cpe	NOUN
ejpam-4931	12	12	are	be	AUX
ejpam-4931	12	13	situated	situate	VERB
ejpam-4931	12	14	between	between	ADP
ejpam-4931	12	15	the	the	DET
ejpam-4931	12	16	non	non	ADJ
ejpam-4931	12	17	-	-	ADJ
ejpam-4931	12	18	hydrostatic	hydrostatic	ADJ
ejpam-4931	12	19	equations	equation	NOUN
ejpam-4931	12	20	and	and	CCONJ
ejpam-4931	12	21	the	the	DET
ejpam-4931	12	22	saint	saint	NOUN
ejpam-4931	12	23	-	-	PUNCT
ejpam-4931	12	24	venant	venant	NOUN
ejpam-4931	12	25	equations	equation	NOUN
ejpam-4931	12	26	.	.	PUNCT
ejpam-4931	13	1	the	the	DET
ejpam-4931	13	2	primitive	primitive	ADJ
ejpam-4931	13	3	equations	equation	NOUN
ejpam-4931	13	4	are	be	AUX
ejpam-4931	13	5	derived	derive	VERB
ejpam-4931	13	6	from	from	ADP
ejpam-4931	13	7	the	the	DET
ejpam-4931	13	8	said	say	VERB
ejpam-4931	13	9	hydrostatic	hydrostatic	ADJ
ejpam-4931	13	10	approximation	approximation	NOUN
ejpam-4931	13	11	in	in	ADP
ejpam-4931	13	12	which	which	PRON
ejpam-4931	13	13	,	,	PUNCT
ejpam-4931	13	14	the	the	DET
ejpam-4931	13	15	conservation	conservation	NOUN
ejpam-4931	13	16	of	of	ADP
ejpam-4931	13	17	vertical	vertical	ADJ
ejpam-4931	13	18	momentum	momentum	NOUN
ejpam-4931	13	19	is	be	AUX
ejpam-4931	13	20	replaced	replace	VERB
ejpam-4931	13	21	by	by	ADP
ejpam-4931	13	22	the	the	DET
ejpam-4931	13	23	hydrostatic	hydrostatic	ADJ
ejpam-4931	13	24	equation	equation	NOUN
ejpam-4931	13	25	.	.	PUNCT
ejpam-4931	14	1	in	in	ADP
ejpam-4931	14	2	general	general	ADJ
ejpam-4931	14	3	,	,	PUNCT
ejpam-4931	14	4	the	the	DET
ejpam-4931	14	5	cpes	cpe	NOUN
ejpam-4931	14	6	are	be	AUX
ejpam-4931	14	7	obtained	obtain	VERB
ejpam-4931	14	8	from	from	ADP
ejpam-4931	14	9	the	the	DET
ejpam-4931	14	10	full	full	ADJ
ejpam-4931	14	11	navier	navier	NOUN
ejpam-4931	14	12	-	-	PUNCT
ejpam-4931	14	13	stokes	stoke	NOUN
ejpam-4931	14	14	equations	equation	NOUN
ejpam-4931	14	15	for	for	ADP
ejpam-4931	14	16	modeling	model	VERB
ejpam-4931	14	17	the	the	DET
ejpam-4931	14	18	atmosphere	atmosphere	NOUN
ejpam-4931	14	19	with	with	ADP
ejpam-4931	14	20	an	an	DET
ejpam-4931	14	21	anisotropic	anisotropic	NOUN
ejpam-4931	14	22	viscosity	viscosity	NOUN
ejpam-4931	14	23	tensor	tensor	NOUN
ejpam-4931	14	24	.	.	PUNCT
ejpam-4931	15	1	taking	take	VERB
ejpam-4931	15	2	advantage	advantage	NOUN
ejpam-4931	15	3	of	of	ADP
ejpam-4931	15	4	the	the	DET
ejpam-4931	15	5	difference	difference	NOUN
ejpam-4931	15	6	between	between	ADP
ejpam-4931	15	7	the	the	DET
ejpam-4931	15	8	horizontal	horizontal	ADJ
ejpam-4931	15	9	and	and	CCONJ
ejpam-4931	15	10	vertical	vertical	ADJ
ejpam-4931	15	11	dimensions	dimension	NOUN
ejpam-4931	15	12	of	of	ADP
ejpam-4931	15	13	the	the	DET
ejpam-4931	15	14	atmosphere	atmosphere	NOUN
ejpam-4931	15	15	(	(	PUNCT
ejpam-4931	15	16	10	10	NUM
ejpam-4931	15	17	to	to	PART
ejpam-4931	15	18	20	20	NUM
ejpam-4931	15	19	kilometers	kilometer	NOUN
ejpam-4931	15	20	for	for	ADP
ejpam-4931	15	21	altitude	altitude	NOUN
ejpam-4931	15	22	versus	versus	ADP
ejpam-4931	15	23	thousands	thousand	NOUN
ejpam-4931	15	24	of	of	ADP
ejpam-4931	15	25	kilometers	kilometer	NOUN
ejpam-4931	15	26	for	for	ADP
ejpam-4931	15	27	length	length	NOUN
ejpam-4931	15	28	)	)	PUNCT
ejpam-4931	15	29	,	,	PUNCT
ejpam-4931	15	30	we	we	PRON
ejpam-4931	15	31	obtain	obtain	VERB
ejpam-4931	15	32	the	the	DET
ejpam-4931	15	33	following	following	ADJ
ejpam-4931	15	34	hydrostatic	hydrostatic	ADJ
ejpam-4931	15	35	model	model	NOUN
ejpam-4931	15	36	:	:	PUNCT
ejpam-4931	15	37	∗corresponding	∗corresponde	VERB
ejpam-4931	15	38	author	author	NOUN
ejpam-4931	15	39	.	.	PUNCT
ejpam-4931	16	1	doi	doi	NOUN
ejpam-4931	16	2	:	:	PUNCT
ejpam-4931	16	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4931	https://doi.org/10.29020/nybg.ejpam.v16i4.4931	ADJ
ejpam-4931	16	4	email	email	NOUN
ejpam-4931	16	5	addresses	address	NOUN
ejpam-4931	16	6	:	:	PUNCT
ejpam-4931	16	7	ouyajules6@gmail.com	ouyajules6@gmail.com	X
ejpam-4931	16	8	(	(	PUNCT
ejpam-4931	16	9	j.	j.	PROPN
ejpam-4931	16	10	ouya	ouya	PROPN
ejpam-4931	16	11	)	)	PUNCT
ejpam-4931	16	12	,	,	PUNCT
ejpam-4931	16	13	arounaoued2002@yahoo.fr	arounaoued2002@yahoo.fr	PROPN
ejpam-4931	16	14	(	(	PUNCT
ejpam-4931	16	15	a.	a.	NOUN
ejpam-4931	16	16	ouédraogo	ouédraogo	PROPN
ejpam-4931	16	17	)	)	PUNCT
ejpam-4931	16	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4931	16	19	2247	2247	NUM
ejpam-4931	17	1	©	©	ADP
ejpam-4931	17	2	2023	2023	NUM
ejpam-4931	17	3	ejpam	ejpam	NOUN
ejpam-4931	17	4	all	all	DET
ejpam-4931	17	5	rights	right	NOUN
ejpam-4931	17	6	reserved	reserve	VERB
ejpam-4931	17	7	.	.	PUNCT
ejpam-4931	18	1	j.	j.	PROPN
ejpam-4931	18	2	ouya	ouya	PROPN
ejpam-4931	18	3	,	,	PUNCT
ejpam-4931	18	4	a.	a.	NOUN
ejpam-4931	18	5	ouédraogo	ouédraogo	PROPN
ejpam-4931	18	6	/	/	SYM
ejpam-4931	18	7	eur	eur	PROPN
ejpam-4931	18	8	.	.	PUNCT
ejpam-4931	19	1	j.	j.	PROPN
ejpam-4931	19	2	pure	pure	PROPN
ejpam-4931	19	3	appl	appl	PROPN
ejpam-4931	19	4	.	.	PROPN
ejpam-4931	19	5	math	math	PROPN
ejpam-4931	19	6	,	,	PUNCT
ejpam-4931	19	7	16	16	NUM
ejpam-4931	19	8	(	(	PUNCT
ejpam-4931	19	9	4	4	NUM
ejpam-4931	19	10	)	)	PUNCT
ejpam-4931	19	11	(	(	PUNCT
ejpam-4931	19	12	2023	2023	NUM
ejpam-4931	19	13	)	)	PUNCT
ejpam-4931	19	14	,	,	PUNCT
ejpam-4931	19	15	2247	2247	NUM
ejpam-4931	19	16	-	-	SYM
ejpam-4931	19	17	2285	2285	NUM
ejpam-4931	19	18	2248	2248	NUM
ejpam-4931	19	19			X
ejpam-4931	19	20	∂tρ+	∂tρ+	VERB
ejpam-4931	19	21	divx(ρu	divx(ρu	PROPN
ejpam-4931	19	22	)	)	PUNCT
ejpam-4931	19	23	+	+	PUNCT
ejpam-4931	19	24	∂y(ρv	∂y(ρv	NUM
ejpam-4931	19	25	)	)	PUNCT
ejpam-4931	19	26	=	=	SYM
ejpam-4931	19	27	0	0	NUM
ejpam-4931	19	28	,	,	PUNCT
ejpam-4931	19	29	∂t(ρu	∂t(ρu	PROPN
ejpam-4931	19	30	)	)	PUNCT
ejpam-4931	20	1	+	+	CCONJ
ejpam-4931	20	2	divx(ρu⊗	divx(ρu⊗	PROPN
ejpam-4931	20	3	u	u	NOUN
ejpam-4931	20	4	)	)	PUNCT
ejpam-4931	20	5	+	+	SYM
ejpam-4931	20	6	∂y(ρuv	∂y(ρuv	NOUN
ejpam-4931	20	7	)	)	PUNCT
ejpam-4931	21	1	+	+	PUNCT
ejpam-4931	21	2	∇xp(ρ	∇xp(ρ	NOUN
ejpam-4931	21	3	)	)	PUNCT
ejpam-4931	21	4	+	+	CCONJ
ejpam-4931	21	5	rρ|u|u	rρ|u|u	NOUN
ejpam-4931	21	6	=	=	SYM
ejpam-4931	21	7	divx	divx	PROPN
ejpam-4931	21	8	(	(	PUNCT
ejpam-4931	21	9	2ν1dx(u	2ν1dx(u	NUM
ejpam-4931	21	10	)	)	PUNCT
ejpam-4931	21	11	)	)	PUNCT
ejpam-4931	22	1	+	+	CCONJ
ejpam-4931	22	2	∂y(ν2∂yu	∂y(ν2∂yu	NOUN
ejpam-4931	22	3	)	)	PUNCT
ejpam-4931	22	4	,	,	PUNCT
ejpam-4931	22	5	∂yp(ρ	∂yp(ρ	PROPN
ejpam-4931	22	6	)	)	PUNCT
ejpam-4931	22	7	=	=	PUNCT
ejpam-4931	23	1	−gρ	−gρ	PROPN
ejpam-4931	23	2	.	.	PUNCT
ejpam-4931	24	1	(	(	PUNCT
ejpam-4931	24	2	1	1	X
ejpam-4931	24	3	)	)	PUNCT
ejpam-4931	24	4	here	here	ADV
ejpam-4931	24	5	,	,	PUNCT
ejpam-4931	24	6	t	t	PROPN
ejpam-4931	24	7	>	>	X
ejpam-4931	24	8	0	0	PROPN
ejpam-4931	24	9	,	,	PUNCT
ejpam-4931	24	10	x	x	SYM
ejpam-4931	24	11	=	=	SYM
ejpam-4931	24	12	(	(	PUNCT
ejpam-4931	24	13	x1	x1	PROPN
ejpam-4931	24	14	,	,	PUNCT
ejpam-4931	24	15	x2	x2	PROPN
ejpam-4931	24	16	)	)	PUNCT
ejpam-4931	24	17	and	and	CCONJ
ejpam-4931	24	18	y	y	PROPN
ejpam-4931	24	19	are	be	AUX
ejpam-4931	24	20	respectively	respectively	ADV
ejpam-4931	24	21	the	the	DET
ejpam-4931	24	22	temporal	temporal	ADJ
ejpam-4931	24	23	,	,	PUNCT
ejpam-4931	24	24	horizontal	horizontal	ADJ
ejpam-4931	24	25	and	and	CCONJ
ejpam-4931	24	26	vertical	vertical	ADJ
ejpam-4931	24	27	variables	variable	NOUN
ejpam-4931	24	28	.	.	PUNCT
ejpam-4931	25	1	(	(	PUNCT
ejpam-4931	25	2	x	x	X
ejpam-4931	25	3	,	,	PUNCT
ejpam-4931	25	4	y	y	NOUN
ejpam-4931	25	5	)	)	PUNCT
ejpam-4931	25	6	∈	∈	PROPN
ejpam-4931	25	7	ω	ω	X
ejpam-4931	25	8	=	=	SYM
ejpam-4931	25	9	ωx×	ωx×	X
ejpam-4931	25	10	(	(	PUNCT
ejpam-4931	25	11	0	0	NUM
ejpam-4931	25	12	,	,	PUNCT
ejpam-4931	25	13	1	1	NUM
ejpam-4931	25	14	)	)	PUNCT
ejpam-4931	25	15	,	,	PUNCT
ejpam-4931	25	16	with	with	ADP
ejpam-4931	25	17	ωx	ωx	PROPN
ejpam-4931	25	18	=	=	PUNCT
ejpam-4931	25	19	t2	t2	VERB
ejpam-4931	25	20	the	the	DET
ejpam-4931	25	21	two	two	NUM
ejpam-4931	25	22	-	-	PUNCT
ejpam-4931	25	23	dimensional	dimensional	ADJ
ejpam-4931	25	24	torus.the	torus.the	DET
ejpam-4931	25	25	functions	function	NOUN
ejpam-4931	25	26	ρ	ρ	NOUN
ejpam-4931	25	27	and	and	CCONJ
ejpam-4931	25	28	p	p	PROPN
ejpam-4931	25	29	represent	represent	VERB
ejpam-4931	25	30	respectively	respectively	ADV
ejpam-4931	25	31	the	the	DET
ejpam-4931	25	32	density	density	NOUN
ejpam-4931	25	33	and	and	CCONJ
ejpam-4931	25	34	the	the	DET
ejpam-4931	25	35	pressure	pressure	NOUN
ejpam-4931	25	36	of	of	ADP
ejpam-4931	25	37	the	the	DET
ejpam-4931	25	38	medium	medium	NOUN
ejpam-4931	25	39	.	.	PUNCT
ejpam-4931	26	1	they	they	PRON
ejpam-4931	26	2	each	each	PRON
ejpam-4931	26	3	depend	depend	VERB
ejpam-4931	26	4	on	on	ADP
ejpam-4931	26	5	x	x	PROPN
ejpam-4931	26	6	,	,	PUNCT
ejpam-4931	26	7	y	y	PROPN
ejpam-4931	26	8	and	and	CCONJ
ejpam-4931	26	9	t.	t.	NOUN
ejpam-4931	26	10	the	the	DET
ejpam-4931	26	11	vector	vector	NOUN
ejpam-4931	26	12	u	u	NOUN
ejpam-4931	26	13	=	=	PUNCT
ejpam-4931	26	14	(	(	PUNCT
ejpam-4931	26	15	u	u	NOUN
ejpam-4931	26	16	=	=	PUNCT
ejpam-4931	26	17	(	(	PUNCT
ejpam-4931	26	18	u1	u1	PROPN
ejpam-4931	26	19	,	,	PUNCT
ejpam-4931	26	20	u2	u2	PROPN
ejpam-4931	26	21	)	)	PUNCT
ejpam-4931	26	22	,	,	PUNCT
ejpam-4931	26	23	v	v	NOUN
ejpam-4931	26	24	)	)	PUNCT
ejpam-4931	26	25	is	be	AUX
ejpam-4931	26	26	the	the	DET
ejpam-4931	26	27	velocity	velocity	NOUN
ejpam-4931	26	28	of	of	ADP
ejpam-4931	26	29	the	the	DET
ejpam-4931	26	30	flow	flow	NOUN
ejpam-4931	26	31	(	(	PUNCT
ejpam-4931	26	32	where	where	SCONJ
ejpam-4931	26	33	u	u	NOUN
ejpam-4931	26	34	is	be	AUX
ejpam-4931	26	35	the	the	DET
ejpam-4931	26	36	horizontal	horizontal	ADJ
ejpam-4931	26	37	velocity	velocity	NOUN
ejpam-4931	26	38	and	and	CCONJ
ejpam-4931	26	39	v	v	ADP
ejpam-4931	26	40	the	the	DET
ejpam-4931	26	41	vertical	vertical	ADJ
ejpam-4931	26	42	velocity	velocity	NOUN
ejpam-4931	26	43	)	)	PUNCT
ejpam-4931	26	44	.	.	PUNCT
ejpam-4931	27	1	u⊗u	u⊗u	PROPN
ejpam-4931	27	2	is	be	AUX
ejpam-4931	27	3	the	the	DET
ejpam-4931	27	4	matrix	matrix	NOUN
ejpam-4931	27	5	with	with	ADP
ejpam-4931	27	6	components	component	NOUN
ejpam-4931	27	7	uiuj	uiuj	PROPN
ejpam-4931	27	8	,	,	PUNCT
ejpam-4931	27	9	divx	divx	X
ejpam-4931	28	1	=	=	PUNCT
ejpam-4931	28	2	∂x1	∂x1	NOUN
ejpam-4931	28	3	+	+	NOUN
ejpam-4931	28	4	∂x2	∂x2	NOUN
ejpam-4931	28	5	is	be	AUX
ejpam-4931	28	6	the	the	DET
ejpam-4931	28	7	divergence	divergence	NOUN
ejpam-4931	28	8	operator	operator	NOUN
ejpam-4931	28	9	and	and	CCONJ
ejpam-4931	28	10	dx	dx	PROPN
ejpam-4931	28	11	is	be	AUX
ejpam-4931	28	12	the	the	DET
ejpam-4931	28	13	strain	strain	NOUN
ejpam-4931	28	14	tensor	tensor	NOUN
ejpam-4931	28	15	with	with	ADP
ejpam-4931	28	16	dx(u	dx(u	NUM
ejpam-4931	28	17	)	)	PUNCT
ejpam-4931	29	1	=	=	SYM
ejpam-4931	29	2	∇xu+	∇xu+	PROPN
ejpam-4931	29	3	(	(	PUNCT
ejpam-4931	29	4	∇xu	∇xu	PROPN
ejpam-4931	29	5	)	)	PUNCT
ejpam-4931	29	6	t	t	NOUN
ejpam-4931	29	7	2	2	NUM
ejpam-4931	29	8	along	along	ADP
ejpam-4931	29	9	the	the	DET
ejpam-4931	29	10	horizontal	horizontal	ADJ
ejpam-4931	29	11	directions	direction	NOUN
ejpam-4931	29	12	.	.	PUNCT
ejpam-4931	30	1	the	the	DET
ejpam-4931	30	2	term	term	NOUN
ejpam-4931	30	3	rρ|u|u	rρ|u|u	NOUN
ejpam-4931	30	4	,	,	PUNCT
ejpam-4931	30	5	with	with	ADP
ejpam-4931	30	6	r	r	NOUN
ejpam-4931	30	7	>	>	X
ejpam-4931	30	8	0	0	NUM
ejpam-4931	30	9	a	a	DET
ejpam-4931	30	10	positive	positive	ADJ
ejpam-4931	30	11	constant	constant	NOUN
ejpam-4931	30	12	,	,	PUNCT
ejpam-4931	30	13	comes	come	VERB
ejpam-4931	30	14	from	from	ADP
ejpam-4931	30	15	the	the	DET
ejpam-4931	30	16	quadratic	quadratic	ADJ
ejpam-4931	30	17	friction	friction	NOUN
ejpam-4931	30	18	source	source	NOUN
ejpam-4931	30	19	and	and	CCONJ
ejpam-4931	30	20	is	be	AUX
ejpam-4931	30	21	useful	useful	ADJ
ejpam-4931	30	22	for	for	SCONJ
ejpam-4931	30	23	the	the	DET
ejpam-4931	30	24	mathematical	mathematical	ADJ
ejpam-4931	30	25	study	study	NOUN
ejpam-4931	30	26	(	(	PUNCT
ejpam-4931	30	27	see	see	VERB
ejpam-4931	30	28	[	[	X
ejpam-4931	30	29	3	3	NUM
ejpam-4931	30	30	]	]	NUM
ejpam-4931	30	31	)	)	PUNCT
ejpam-4931	30	32	.	.	PUNCT
ejpam-4931	31	1	ν1	ν1	NOUN
ejpam-4931	31	2	and	and	CCONJ
ejpam-4931	31	3	ν2	ν2	NOUN
ejpam-4931	31	4	are	be	AUX
ejpam-4931	31	5	the	the	DET
ejpam-4931	31	6	turbulence	turbulence	NOUN
ejpam-4931	31	7	viscosities	viscosity	NOUN
ejpam-4931	31	8	in	in	ADP
ejpam-4931	31	9	the	the	DET
ejpam-4931	31	10	horizontal	horizontal	ADJ
ejpam-4931	31	11	and	and	CCONJ
ejpam-4931	31	12	vertical	vertical	ADJ
ejpam-4931	31	13	direction	direction	NOUN
ejpam-4931	31	14	respectively	respectively	ADV
ejpam-4931	31	15	.	.	PUNCT
ejpam-4931	32	1	they	they	PRON
ejpam-4931	32	2	depend	depend	VERB
ejpam-4931	32	3	on	on	ADP
ejpam-4931	32	4	the	the	DET
ejpam-4931	32	5	density	density	NOUN
ejpam-4931	32	6	ρ	ρ	PROPN
ejpam-4931	32	7	.	.	PUNCT
ejpam-4931	33	1	in	in	ADP
ejpam-4931	33	2	(	(	PUNCT
ejpam-4931	33	3	1	1	NUM
ejpam-4931	33	4	)	)	PUNCT
ejpam-4931	33	5	,	,	PUNCT
ejpam-4931	33	6	the	the	DET
ejpam-4931	33	7	first	first	ADJ
ejpam-4931	33	8	equation	equation	NOUN
ejpam-4931	33	9	expresses	express	VERB
ejpam-4931	33	10	the	the	DET
ejpam-4931	33	11	conservation	conservation	NOUN
ejpam-4931	33	12	of	of	ADP
ejpam-4931	33	13	mass	mass	PROPN
ejpam-4931	33	14	,	,	PUNCT
ejpam-4931	33	15	the	the	DET
ejpam-4931	33	16	second	second	ADJ
ejpam-4931	33	17	,	,	PUNCT
ejpam-4931	33	18	the	the	DET
ejpam-4931	33	19	evolution	evolution	NOUN
ejpam-4931	33	20	of	of	ADP
ejpam-4931	33	21	the	the	DET
ejpam-4931	33	22	momentum	momentum	NOUN
ejpam-4931	33	23	and	and	CCONJ
ejpam-4931	33	24	the	the	DET
ejpam-4931	33	25	last	last	ADJ
ejpam-4931	33	26	equation	equation	NOUN
ejpam-4931	33	27	,	,	PUNCT
ejpam-4931	33	28	∂yp(ρ	∂yp(ρ	PROPN
ejpam-4931	33	29	)	)	PUNCT
ejpam-4931	33	30	=	=	PUNCT
ejpam-4931	34	1	−gρ	−gρ	PROPN
ejpam-4931	34	2	,	,	PUNCT
ejpam-4931	34	3	is	be	AUX
ejpam-4931	34	4	from	from	ADP
ejpam-4931	34	5	the	the	DET
ejpam-4931	34	6	hydrostatic	hydrostatic	ADJ
ejpam-4931	34	7	approximation	approximation	NOUN
ejpam-4931	34	8	with	with	ADP
ejpam-4931	34	9	g	g	PROPN
ejpam-4931	34	10	>	>	X
ejpam-4931	34	11	0	0	NUM
ejpam-4931	35	1	the	the	DET
ejpam-4931	35	2	free	free	ADJ
ejpam-4931	35	3	fall	fall	NOUN
ejpam-4931	35	4	acceleration	acceleration	NOUN
ejpam-4931	35	5	.	.	PUNCT
ejpam-4931	36	1	in	in	ADP
ejpam-4931	36	2	order	order	NOUN
ejpam-4931	36	3	to	to	PART
ejpam-4931	36	4	close	close	VERB
ejpam-4931	36	5	the	the	DET
ejpam-4931	36	6	system	system	NOUN
ejpam-4931	36	7	,	,	PUNCT
ejpam-4931	36	8	we	we	PRON
ejpam-4931	36	9	assume	assume	VERB
ejpam-4931	36	10	that	that	SCONJ
ejpam-4931	36	11	the	the	DET
ejpam-4931	36	12	fluid	fluid	NOUN
ejpam-4931	36	13	is	be	AUX
ejpam-4931	36	14	newtonian	newtonian	ADJ
ejpam-4931	36	15	.	.	PUNCT
ejpam-4931	37	1	f.	f.	PROPN
ejpam-4931	37	2	wang	wang	PROPN
ejpam-4931	37	3	et	et	PROPN
ejpam-4931	37	4	al	al	PROPN
ejpam-4931	37	5	.	.	PROPN
ejpam-4931	37	6	,	,	PUNCT
ejpam-4931	37	7	in	in	ADP
ejpam-4931	37	8	[	[	X
ejpam-4931	37	9	19	19	NUM
ejpam-4931	37	10	]	]	PUNCT
ejpam-4931	37	11	,	,	PUNCT
ejpam-4931	37	12	investigated	investigate	VERB
ejpam-4931	37	13	the	the	DET
ejpam-4931	37	14	global	global	ADJ
ejpam-4931	37	15	existence	existence	NOUN
ejpam-4931	37	16	of	of	ADP
ejpam-4931	37	17	weak	weak	ADJ
ejpam-4931	37	18	solutions	solution	NOUN
ejpam-4931	37	19	to	to	ADP
ejpam-4931	37	20	cpe	cpe	PROPN
ejpam-4931	37	21	(	(	PUNCT
ejpam-4931	37	22	1	1	NUM
ejpam-4931	37	23	)	)	PUNCT
ejpam-4931	37	24	in	in	ADP
ejpam-4931	37	25	which	which	PRON
ejpam-4931	37	26	the	the	DET
ejpam-4931	37	27	pressure	pressure	NOUN
ejpam-4931	37	28	is	be	AUX
ejpam-4931	37	29	assumed	assume	VERB
ejpam-4931	37	30	to	to	PART
ejpam-4931	37	31	be	be	AUX
ejpam-4931	37	32	p	p	X
ejpam-4931	37	33	(	(	PUNCT
ejpam-4931	37	34	ρ	ρ	NOUN
ejpam-4931	37	35	)	)	PUNCT
ejpam-4931	37	36	=	=	SYM
ejpam-4931	37	37	c2ρ	c2ρ	PROPN
ejpam-4931	37	38	.	.	PUNCT
ejpam-4931	38	1	in	in	ADP
ejpam-4931	38	2	[	[	X
ejpam-4931	38	3	11	11	NUM
ejpam-4931	38	4	]	]	PUNCT
ejpam-4931	38	5	,	,	PUNCT
ejpam-4931	38	6	liu	liu	PROPN
ejpam-4931	38	7	and	and	CCONJ
ejpam-4931	38	8	titi	titi	PROPN
ejpam-4931	38	9	have	have	AUX
ejpam-4931	38	10	studied	study	VERB
ejpam-4931	38	11	problem	problem	NOUN
ejpam-4931	38	12	(	(	PUNCT
ejpam-4931	38	13	1	1	NUM
ejpam-4931	38	14	)	)	PUNCT
ejpam-4931	38	15	with	with	ADP
ejpam-4931	38	16	p	p	PROPN
ejpam-4931	38	17	(	(	PUNCT
ejpam-4931	38	18	ρ	ρ	NOUN
ejpam-4931	38	19	)	)	PUNCT
ejpam-4931	38	20	=	=	PRON
ejpam-4931	38	21	ργ	ργ	NOUN
ejpam-4931	38	22	,	,	PUNCT
ejpam-4931	38	23	γ	γ	X
ejpam-4931	38	24	>	>	X
ejpam-4931	38	25	1	1	NUM
ejpam-4931	38	26	,	,	PUNCT
ejpam-4931	38	27	without	without	ADP
ejpam-4931	38	28	buoyancy	buoyancy	NOUN
ejpam-4931	38	29	(	(	PUNCT
ejpam-4931	38	30	no	no	DET
ejpam-4931	38	31	gravity	gravity	NOUN
ejpam-4931	38	32	)	)	PUNCT
ejpam-4931	38	33	.	.	PUNCT
ejpam-4931	39	1	the	the	DET
ejpam-4931	39	2	main	main	ADJ
ejpam-4931	39	3	aim	aim	NOUN
ejpam-4931	39	4	of	of	ADP
ejpam-4931	39	5	this	this	DET
ejpam-4931	39	6	paper	paper	NOUN
ejpam-4931	39	7	is	be	AUX
ejpam-4931	39	8	to	to	PART
ejpam-4931	39	9	extend	extend	VERB
ejpam-4931	39	10	the	the	DET
ejpam-4931	39	11	result	result	NOUN
ejpam-4931	39	12	of	of	ADP
ejpam-4931	39	13	[	[	X
ejpam-4931	39	14	11	11	NUM
ejpam-4931	39	15	,	,	PUNCT
ejpam-4931	39	16	19	19	NUM
ejpam-4931	39	17	]	]	PUNCT
ejpam-4931	39	18	for	for	ADP
ejpam-4931	39	19	a	a	DET
ejpam-4931	39	20	pressure	pressure	NOUN
ejpam-4931	39	21	law	law	NOUN
ejpam-4931	39	22	of	of	ADP
ejpam-4931	39	23	the	the	DET
ejpam-4931	39	24	form	form	NOUN
ejpam-4931	39	25	p(ρ	p(ρ	NOUN
ejpam-4931	39	26	)	)	PUNCT
ejpam-4931	39	27	=	=	SYM
ejpam-4931	39	28	aργ	aργ	NOUN
ejpam-4931	39	29	,	,	PUNCT
ejpam-4931	39	30	with	with	ADP
ejpam-4931	39	31	constant	constant	ADJ
ejpam-4931	39	32	γ	γ	X
ejpam-4931	39	33	>	>	SYM
ejpam-4931	39	34	1	1	NUM
ejpam-4931	39	35	and	and	CCONJ
ejpam-4931	39	36	a	a	DET
ejpam-4931	39	37	>	>	X
ejpam-4931	39	38	0	0	PUNCT
ejpam-4931	39	39	a	a	DET
ejpam-4931	39	40	given	give	VERB
ejpam-4931	39	41	positive	positive	ADJ
ejpam-4931	39	42	constant	constant	NOUN
ejpam-4931	39	43	.	.	PUNCT
ejpam-4931	40	1	this	this	PRON
ejpam-4931	40	2	is	be	AUX
ejpam-4931	40	3	one	one	NUM
ejpam-4931	40	4	of	of	ADP
ejpam-4931	40	5	the	the	DET
ejpam-4931	40	6	perspectives	perspective	NOUN
ejpam-4931	40	7	put	put	VERB
ejpam-4931	40	8	forward	forward	ADV
ejpam-4931	40	9	by	by	ADP
ejpam-4931	40	10	timak	timak	NOUN
ejpam-4931	40	11	ngom	ngom	ADV
ejpam-4931	40	12	in	in	ADP
ejpam-4931	40	13	his	his	PRON
ejpam-4931	40	14	thesis	thesis	NOUN
ejpam-4931	40	15	defended	defend	VERB
ejpam-4931	40	16	in	in	ADP
ejpam-4931	40	17	2010	2010	NUM
ejpam-4931	40	18	[	[	X
ejpam-4931	40	19	3	3	NUM
ejpam-4931	40	20	]	]	PUNCT
ejpam-4931	40	21	.	.	PUNCT
ejpam-4931	41	1	but	but	CCONJ
ejpam-4931	41	2	we	we	PRON
ejpam-4931	41	3	will	will	AUX
ejpam-4931	41	4	consider	consider	VERB
ejpam-4931	41	5	the	the	DET
ejpam-4931	41	6	particular	particular	ADJ
ejpam-4931	41	7	case	case	NOUN
ejpam-4931	41	8	γ	γ	X
ejpam-4931	41	9	=	=	SYM
ejpam-4931	41	10	2	2	NUM
ejpam-4931	41	11	,	,	PUNCT
ejpam-4931	41	12	in	in	ADP
ejpam-4931	41	13	which	which	PRON
ejpam-4931	41	14	the	the	DET
ejpam-4931	41	15	density	density	NOUN
ejpam-4931	41	16	can	can	AUX
ejpam-4931	41	17	not	not	PART
ejpam-4931	41	18	longer	long	ADV
ejpam-4931	41	19	be	be	AUX
ejpam-4931	41	20	written	write	VERB
ejpam-4931	41	21	,	,	PUNCT
ejpam-4931	41	22	ρ(t	ρ(t	NUM
ejpam-4931	41	23	,	,	PUNCT
ejpam-4931	41	24	x	x	NOUN
ejpam-4931	41	25	,	,	PUNCT
ejpam-4931	41	26	y	y	NOUN
ejpam-4931	41	27	)	)	PUNCT
ejpam-4931	41	28	=	=	SYM
ejpam-4931	41	29	ξ(t	ξ(t	NOUN
ejpam-4931	41	30	,	,	PUNCT
ejpam-4931	41	31	x)e	x)e	PUNCT
ejpam-4931	41	32	−g	−g	NOUN
ejpam-4931	41	33	c2	c2	PROPN
ejpam-4931	41	34	y	y	PROPN
ejpam-4931	41	35	as	as	ADP
ejpam-4931	41	36	in	in	ADP
ejpam-4931	41	37	[	[	X
ejpam-4931	41	38	19	19	NUM
ejpam-4931	41	39	]	]	PUNCT
ejpam-4931	41	40	.	.	PUNCT
ejpam-4931	42	1	however	however	ADV
ejpam-4931	42	2	,	,	PUNCT
ejpam-4931	42	3	using	use	VERB
ejpam-4931	42	4	the	the	DET
ejpam-4931	42	5	hydrostatic	hydrostatic	ADJ
ejpam-4931	42	6	equation	equation	NOUN
ejpam-4931	42	7	it	it	PRON
ejpam-4931	42	8	can	can	AUX
ejpam-4931	42	9	take	take	VERB
ejpam-4931	42	10	the	the	DET
ejpam-4931	42	11	following	follow	VERB
ejpam-4931	42	12	form	form	NOUN
ejpam-4931	42	13	ρ(t	ρ(t	NUM
ejpam-4931	42	14	,	,	PUNCT
ejpam-4931	42	15	x	x	NOUN
ejpam-4931	42	16	,	,	PUNCT
ejpam-4931	42	17	y	y	NOUN
ejpam-4931	42	18	)	)	PUNCT
ejpam-4931	42	19	=	=	SYM
ejpam-4931	42	20	ξ(t	ξ(t	NOUN
ejpam-4931	42	21	,	,	PUNCT
ejpam-4931	42	22	x	x	PRON
ejpam-4931	42	23	)	)	PUNCT
ejpam-4931	42	24	+	+	CCONJ
ejpam-4931	42	25	ϕ(y	ϕ(y	PROPN
ejpam-4931	42	26	)	)	PUNCT
ejpam-4931	42	27	,	,	PUNCT
ejpam-4931	42	28	(	(	PUNCT
ejpam-4931	42	29	2	2	X
ejpam-4931	42	30	)	)	PUNCT
ejpam-4931	42	31	where	where	SCONJ
ejpam-4931	42	32	ϕ(y	ϕ(y	NUM
ejpam-4931	42	33	)	)	PUNCT
ejpam-4931	43	1	=	=	SYM
ejpam-4931	43	2	g	g	ADP
ejpam-4931	43	3	2a	2a	NUM
ejpam-4931	43	4	(	(	PUNCT
ejpam-4931	43	5	1−	1−	NUM
ejpam-4931	43	6	y	y	NOUN
ejpam-4931	43	7	)	)	PUNCT
ejpam-4931	43	8	and	and	CCONJ
ejpam-4931	43	9	(	(	PUNCT
ejpam-4931	43	10	t	t	PROPN
ejpam-4931	43	11	,	,	PUNCT
ejpam-4931	43	12	x	x	NOUN
ejpam-4931	43	13	)	)	PUNCT
ejpam-4931	43	14	∈	∈	PROPN
ejpam-4931	44	1	[	[	X
ejpam-4931	44	2	0	0	NUM
ejpam-4931	44	3	;	;	PUNCT
ejpam-4931	44	4	+	+	PROPN
ejpam-4931	44	5	∞[×t2	∞[×t2	PROPN
ejpam-4931	44	6	,	,	PUNCT
ejpam-4931	44	7	ξ(t	ξ(t	PROPN
ejpam-4931	44	8	,	,	PUNCT
ejpam-4931	44	9	x	x	X
ejpam-4931	44	10	)	)	PUNCT
ejpam-4931	44	11	≥	≥	NOUN
ejpam-4931	44	12	0	0	NUM
ejpam-4931	44	13	,	,	PUNCT
ejpam-4931	44	14	the	the	DET
ejpam-4931	44	15	new	new	ADJ
ejpam-4931	44	16	densities	density	NOUN
ejpam-4931	44	17	.	.	PUNCT
ejpam-4931	45	1	for	for	ADP
ejpam-4931	45	2	simplicity	simplicity	NOUN
ejpam-4931	45	3	and	and	CCONJ
ejpam-4931	45	4	without	without	ADP
ejpam-4931	45	5	lost	lose	VERB
ejpam-4931	45	6	of	of	ADP
ejpam-4931	45	7	generality	generality	NOUN
ejpam-4931	45	8	,	,	PUNCT
ejpam-4931	45	9	we	we	PRON
ejpam-4931	45	10	take	take	VERB
ejpam-4931	45	11	a	a	DET
ejpam-4931	45	12	=	=	SYM
ejpam-4931	45	13	1	1	NUM
ejpam-4931	45	14	and	and	CCONJ
ejpam-4931	45	15	ν1(ρ	ν1(ρ	PROPN
ejpam-4931	45	16	)	)	PUNCT
ejpam-4931	45	17	=	=	SYM
ejpam-4931	45	18	ν2(ρ	ν2(ρ	NOUN
ejpam-4931	45	19	)	)	PUNCT
ejpam-4931	45	20	=	=	SYM
ejpam-4931	45	21	ξ(t	ξ(t	NOUN
ejpam-4931	45	22	,	,	PUNCT
ejpam-4931	45	23	x	x	PRON
ejpam-4931	45	24	)	)	PUNCT
ejpam-4931	45	25	+	+	CCONJ
ejpam-4931	45	26	ϕ(y	ϕ(y	PROPN
ejpam-4931	45	27	)	)	PUNCT
ejpam-4931	45	28	.	.	PUNCT
ejpam-4931	46	1	(	(	PUNCT
ejpam-4931	46	2	3	3	X
ejpam-4931	46	3	)	)	PUNCT
ejpam-4931	46	4	then	then	ADV
ejpam-4931	46	5	,	,	PUNCT
ejpam-4931	46	6	for	for	ADP
ejpam-4931	46	7	ξ	ξ	PROPN
ejpam-4931	46	8	>	>	SYM
ejpam-4931	46	9	0	0	NUM
ejpam-4931	46	10	the	the	DET
ejpam-4931	46	11	system	system	NOUN
ejpam-4931	46	12	(	(	PUNCT
ejpam-4931	46	13	1	1	X
ejpam-4931	46	14	)	)	PUNCT
ejpam-4931	46	15	becomes	becomes	NOUN
ejpam-4931	46	16	∂t	∂t	PROPN
ejpam-4931	46	17	(	(	PUNCT
ejpam-4931	46	18	ξ(1	ξ(1	PROPN
ejpam-4931	46	19	+	+	CCONJ
ejpam-4931	46	20	ϕ	ϕ	PROPN
ejpam-4931	46	21	ξ	ξ	PROPN
ejpam-4931	46	22	)	)	PUNCT
ejpam-4931	46	23	)	)	PUNCT
ejpam-4931	47	1	+	+	CCONJ
ejpam-4931	47	2	divx	divx	PROPN
ejpam-4931	47	3	(	(	PUNCT
ejpam-4931	47	4	ξ(1	ξ(1	PROPN
ejpam-4931	47	5	+	+	CCONJ
ejpam-4931	47	6	ϕ	ϕ	PROPN
ejpam-4931	47	7	ξ	ξ	PROPN
ejpam-4931	47	8	)	)	PUNCT
ejpam-4931	47	9	u	u	NOUN
ejpam-4931	47	10	)	)	PUNCT
ejpam-4931	47	11	+	+	CCONJ
ejpam-4931	47	12	∂y	∂y	SYM
ejpam-4931	47	13	(	(	PUNCT
ejpam-4931	47	14	ξ(1	ξ(1	PROPN
ejpam-4931	47	15	+	+	CCONJ
ejpam-4931	47	16	ϕ	ϕ	PROPN
ejpam-4931	47	17	ξ	ξ	PROPN
ejpam-4931	47	18	)	)	PUNCT
ejpam-4931	47	19	v	v	NOUN
ejpam-4931	47	20	)	)	PUNCT
ejpam-4931	47	21	=	=	SYM
ejpam-4931	47	22	0	0	NUM
ejpam-4931	47	23	,	,	PUNCT
ejpam-4931	47	24	∂t	∂t	PROPN
ejpam-4931	47	25	(	(	PUNCT
ejpam-4931	47	26	ξ(1	ξ(1	PROPN
ejpam-4931	47	27	+	+	CCONJ
ejpam-4931	47	28	ϕ	ϕ	PROPN
ejpam-4931	47	29	ξ	ξ	PROPN
ejpam-4931	47	30	)	)	PUNCT
ejpam-4931	47	31	u	u	NOUN
ejpam-4931	47	32	)	)	PUNCT
ejpam-4931	47	33	+	+	CCONJ
ejpam-4931	47	34	divx	divx	PROPN
ejpam-4931	47	35	(	(	PUNCT
ejpam-4931	47	36	ξ(1	ξ(1	PROPN
ejpam-4931	47	37	+	+	CCONJ
ejpam-4931	47	38	ϕ	ϕ	PROPN
ejpam-4931	47	39	ξ	ξ	PROPN
ejpam-4931	47	40	)	)	PUNCT
ejpam-4931	47	41	u⊗	u⊗	PROPN
ejpam-4931	47	42	u	u	PROPN
ejpam-4931	47	43	)	)	PUNCT
ejpam-4931	48	1	+	+	CCONJ
ejpam-4931	48	2	∂y	∂y	SYM
ejpam-4931	48	3	(	(	PUNCT
ejpam-4931	48	4	ξ(1	ξ(1	PROPN
ejpam-4931	48	5	+	+	CCONJ
ejpam-4931	48	6	ϕ	ϕ	PROPN
ejpam-4931	48	7	ξ	ξ	PROPN
ejpam-4931	48	8	)	)	PUNCT
ejpam-4931	48	9	uv	uv	NOUN
ejpam-4931	48	10	)	)	PUNCT
ejpam-4931	49	1	+	+	CCONJ
ejpam-4931	49	2	rξ(1	rξ(1	X
ejpam-4931	49	3	+	+	X
ejpam-4931	49	4	ϕ	ϕ	X
ejpam-4931	49	5	ξ	ξ	PROPN
ejpam-4931	49	6	)	)	PUNCT
ejpam-4931	49	7	|u|u	|u|u	ADP
ejpam-4931	50	1	+	+	PUNCT
ejpam-4931	50	2	∇x	∇x	NOUN
ejpam-4931	50	3	(	(	PUNCT
ejpam-4931	50	4	ξ(1	ξ(1	PROPN
ejpam-4931	50	5	+	+	CCONJ
ejpam-4931	50	6	ϕ	ϕ	PROPN
ejpam-4931	50	7	ξ	ξ	PROPN
ejpam-4931	50	8	)	)	PUNCT
ejpam-4931	50	9	)	)	PUNCT
ejpam-4931	50	10	2	2	NUM
ejpam-4931	50	11	=	=	SYM
ejpam-4931	50	12	divx	divx	X
ejpam-4931	50	13	(	(	PUNCT
ejpam-4931	50	14	2ξ(1	2ξ(1	X
ejpam-4931	50	15	+	+	CCONJ
ejpam-4931	50	16	ϕ	ϕ	X
ejpam-4931	50	17	ξ	ξ	PROPN
ejpam-4931	50	18	)	)	PUNCT
ejpam-4931	50	19	dx(u	dx(u	NUM
ejpam-4931	50	20	)	)	PUNCT
ejpam-4931	50	21	)	)	PUNCT
ejpam-4931	51	1	+	+	CCONJ
ejpam-4931	51	2	∂y	∂y	SYM
ejpam-4931	51	3	(	(	PUNCT
ejpam-4931	51	4	ξ(1	ξ(1	PROPN
ejpam-4931	51	5	+	+	CCONJ
ejpam-4931	51	6	ϕ	ϕ	PROPN
ejpam-4931	51	7	ξ	ξ	PROPN
ejpam-4931	51	8	)	)	PUNCT
ejpam-4931	51	9	∂yu	∂yu	PROPN
ejpam-4931	51	10	)	)	PUNCT
ejpam-4931	51	11	,	,	PUNCT
ejpam-4931	51	12	(	(	PUNCT
ejpam-4931	51	13	4	4	X
ejpam-4931	51	14	)	)	PUNCT
ejpam-4931	51	15	j.	j.	PROPN
ejpam-4931	51	16	ouya	ouya	PROPN
ejpam-4931	51	17	,	,	PUNCT
ejpam-4931	51	18	a.	a.	NOUN
ejpam-4931	51	19	ouédraogo	ouédraogo	PROPN
ejpam-4931	51	20	/	/	SYM
ejpam-4931	51	21	eur	eur	PROPN
ejpam-4931	51	22	.	.	PUNCT
ejpam-4931	52	1	j.	j.	PROPN
ejpam-4931	52	2	pure	pure	PROPN
ejpam-4931	52	3	appl	appl	PROPN
ejpam-4931	52	4	.	.	PROPN
ejpam-4931	52	5	math	math	PROPN
ejpam-4931	52	6	,	,	PUNCT
ejpam-4931	52	7	16	16	NUM
ejpam-4931	52	8	(	(	PUNCT
ejpam-4931	52	9	4	4	NUM
ejpam-4931	52	10	)	)	PUNCT
ejpam-4931	52	11	(	(	PUNCT
ejpam-4931	52	12	2023	2023	NUM
ejpam-4931	52	13	)	)	PUNCT
ejpam-4931	52	14	,	,	PUNCT
ejpam-4931	52	15	2247	2247	NUM
ejpam-4931	52	16	-	-	SYM
ejpam-4931	52	17	2285	2285	NUM
ejpam-4931	52	18	2249	2249	NUM
ejpam-4931	52	19	where	where	SCONJ
ejpam-4931	52	20	(	(	PUNCT
ejpam-4931	52	21	x	x	NOUN
ejpam-4931	52	22	,	,	PUNCT
ejpam-4931	52	23	y	y	NOUN
ejpam-4931	52	24	)	)	PUNCT
ejpam-4931	52	25	∈	∈	PROPN
ejpam-4931	52	26	ω	ω	PROPN
ejpam-4931	52	27	and	and	CCONJ
ejpam-4931	52	28	t	t	PROPN
ejpam-4931	52	29	≥	≥	NUM
ejpam-4931	52	30	0	0	NUM
ejpam-4931	52	31	.	.	PUNCT
ejpam-4931	53	1	we	we	PRON
ejpam-4931	53	2	state	state	VERB
ejpam-4931	53	3	the	the	DET
ejpam-4931	53	4	asymptotic	asymptotic	ADJ
ejpam-4931	53	5	regime	regime	NOUN
ejpam-4931	53	6	uj	uj	NOUN
ejpam-4931	53	7	=	=	NOUN
ejpam-4931	53	8	∑	∑	PROPN
ejpam-4931	53	9	i≥0	i≥0	PROPN
ejpam-4931	53	10	εiuij	εiuij	PROPN
ejpam-4931	53	11	,	,	PUNCT
ejpam-4931	53	12	j	j	PROPN
ejpam-4931	53	13	=	=	SYM
ejpam-4931	53	14	1	1	NUM
ejpam-4931	53	15	,	,	PUNCT
ejpam-4931	53	16	2	2	NUM
ejpam-4931	53	17	,	,	PUNCT
ejpam-4931	53	18	v	v	NOUN
ejpam-4931	53	19	=	=	SYM
ejpam-4931	53	20	∑	∑	PROPN
ejpam-4931	53	21	i≥0	i≥0	PROPN
ejpam-4931	53	22	εivi	εivi	NOUN
ejpam-4931	53	23	,	,	PUNCT
ejpam-4931	53	24	ρ	ρ	PROPN
ejpam-4931	53	25	=	=	PUNCT
ejpam-4931	53	26	∑	∑	PUNCT
ejpam-4931	53	27	i≥0	i≥0	PROPN
ejpam-4931	53	28	εiρi	εiρi	VERB
ejpam-4931	53	29	=	=	SYM
ejpam-4931	53	30	∑	∑	PUNCT
ejpam-4931	53	31	i≥0	i≥0	PROPN
ejpam-4931	53	32	εiξi	εiξi	PROPN
ejpam-4931	53	33	(	(	PUNCT
ejpam-4931	53	34	1	1	NUM
ejpam-4931	53	35	+	+	CCONJ
ejpam-4931	53	36	ϕi	ϕi	ADP
ejpam-4931	53	37	ξi	ξi	NOUN
ejpam-4931	53	38	)	)	PUNCT
ejpam-4931	53	39	,	,	PUNCT
ejpam-4931	53	40	where	where	SCONJ
ejpam-4931	53	41	ε	ε	PROPN
ejpam-4931	53	42	=	=	SYM
ejpam-4931	53	43	ϕ0	ϕ0	PROPN
ejpam-4931	53	44	ξ0	ξ0	NOUN
ejpam-4931	53	45	.	.	PUNCT
ejpam-4931	54	1	we	we	PRON
ejpam-4931	54	2	introduce	introduce	VERB
ejpam-4931	54	3	the	the	DET
ejpam-4931	54	4	asymptotic	asymptotic	ADJ
ejpam-4931	54	5	development	development	NOUN
ejpam-4931	54	6	at	at	ADP
ejpam-4931	54	7	the	the	DET
ejpam-4931	54	8	main	main	ADJ
ejpam-4931	54	9	order	order	NOUN
ejpam-4931	54	10	ε0	ε0	NOUN
ejpam-4931	54	11	in	in	ADP
ejpam-4931	54	12	(	(	PUNCT
ejpam-4931	54	13	4	4	NUM
ejpam-4931	54	14	)	)	PUNCT
ejpam-4931	54	15	and	and	CCONJ
ejpam-4931	54	16	omit	omit	VERB
ejpam-4931	54	17	the	the	DET
ejpam-4931	54	18	powers	power	NOUN
ejpam-4931	54	19	”	"	PUNCT
ejpam-4931	54	20	0	0	NUM
ejpam-4931	54	21	”	"	PUNCT
ejpam-4931	54	22	to	to	ADP
ejpam-4931	54	23	obtain	obtain	PROPN
ejpam-4931	54	24	∂tξ	∂tξ	PROPN
ejpam-4931	54	25	+	+	CCONJ
ejpam-4931	54	26	divx(ξu	divx(ξu	NOUN
ejpam-4931	54	27	)	)	PUNCT
ejpam-4931	55	1	+	+	CCONJ
ejpam-4931	55	2	∂y	∂y	SYM
ejpam-4931	55	3	(	(	PUNCT
ejpam-4931	55	4	ξv	ξv	NOUN
ejpam-4931	55	5	)	)	PUNCT
ejpam-4931	55	6	=	=	SYM
ejpam-4931	55	7	0	0	NUM
ejpam-4931	55	8	,	,	PUNCT
ejpam-4931	55	9	∂t(ξu	∂t(ξu	X
ejpam-4931	55	10	)	)	PUNCT
ejpam-4931	55	11	+	+	CCONJ
ejpam-4931	55	12	divx(ξu⊗	divx(ξu⊗	NOUN
ejpam-4931	55	13	u	u	NOUN
ejpam-4931	55	14	)	)	PUNCT
ejpam-4931	55	15	+	+	CCONJ
ejpam-4931	55	16	∂y(ξuv	∂y(ξuv	X
ejpam-4931	55	17	)	)	PUNCT
ejpam-4931	56	1	+	+	X
ejpam-4931	56	2	∇xξ	∇xξ	PROPN
ejpam-4931	56	3	2	2	NUM
ejpam-4931	56	4	+	+	CCONJ
ejpam-4931	56	5	rξ|u|u	rξ|u|u	NOUN
ejpam-4931	56	6	=	=	SYM
ejpam-4931	56	7	divx	divx	PROPN
ejpam-4931	56	8	(	(	PUNCT
ejpam-4931	56	9	2ξdx(u	2ξdx(u	NUM
ejpam-4931	56	10	)	)	PUNCT
ejpam-4931	56	11	)	)	PUNCT
ejpam-4931	57	1	+	+	CCONJ
ejpam-4931	57	2	∂y	∂y	SYM
ejpam-4931	57	3	(	(	PUNCT
ejpam-4931	57	4	ξ∂yu	ξ∂yu	PROPN
ejpam-4931	57	5	)	)	PUNCT
ejpam-4931	57	6	,	,	PUNCT
ejpam-4931	57	7	∂yξ	∂yξ	PROPN
ejpam-4931	57	8	=	=	SYM
ejpam-4931	57	9	0	0	X
ejpam-4931	57	10	.	.	PUNCT
ejpam-4931	57	11	(	(	PUNCT
ejpam-4931	57	12	5	5	X
ejpam-4931	57	13	)	)	PUNCT
ejpam-4931	57	14	the	the	DET
ejpam-4931	57	15	boundary	boundary	ADJ
ejpam-4931	57	16	conditions	condition	NOUN
ejpam-4931	57	17	on	on	ADP
ejpam-4931	57	18	∂ω	∂ω	PROPN
ejpam-4931	57	19	are	be	AUX
ejpam-4931	57	20	expressed	express	VERB
ejpam-4931	57	21	as	as	ADP
ejpam-4931	57	22	periodic	periodic	ADJ
ejpam-4931	57	23	conditions	condition	NOUN
ejpam-4931	57	24	on	on	ADP
ejpam-4931	57	25	∂ωx:v	∂ωx:v	NOUN
ejpam-4931	57	26	/	/	SYM
ejpam-4931	57	27	y=0	y=0	X
ejpam-4931	57	28	=	=	SYM
ejpam-4931	57	29	v	v	NOUN
ejpam-4931	57	30	/	/	SYM
ejpam-4931	57	31	y=1	y=1	NOUN
ejpam-4931	57	32	=	=	SYM
ejpam-4931	57	33	0	0	NUM
ejpam-4931	57	34	,	,	PUNCT
ejpam-4931	57	35	∂yu	∂yu	NOUN
ejpam-4931	57	36	/	/	SYM
ejpam-4931	57	37	y=0	y=0	X
ejpam-4931	57	38	=	=	SYM
ejpam-4931	57	39	∂yu	∂yu	PROPN
ejpam-4931	57	40	/	/	SYM
ejpam-4931	57	41	y=1	y=1	X
ejpam-4931	58	1	=	=	SYM
ejpam-4931	58	2	0	0	X
ejpam-4931	58	3	.	.	PUNCT
ejpam-4931	59	1	(	(	PUNCT
ejpam-4931	59	2	6	6	NUM
ejpam-4931	59	3	)	)	PUNCT
ejpam-4931	59	4	the	the	DET
ejpam-4931	59	5	initial	initial	ADJ
ejpam-4931	59	6	data	datum	NOUN
ejpam-4931	59	7	are	be	AUX
ejpam-4931	59	8	written	write	VERB
ejpam-4931	59	9	ρ|t=0	ρ|t=0	PUNCT
ejpam-4931	59	10	=	=	SYM
ejpam-4931	59	11	ξ0(x	ξ0(x	PROPN
ejpam-4931	59	12	)	)	PUNCT
ejpam-4931	59	13	,	,	PUNCT
ejpam-4931	59	14	ρu|t=0	ρu|t=0	PROPN
ejpam-4931	59	15	=	=	SYM
ejpam-4931	59	16	ξ0u0	ξ0u0	PROPN
ejpam-4931	59	17	=	=	SYM
ejpam-4931	59	18	m0(x	m0(x	PROPN
ejpam-4931	59	19	,	,	PUNCT
ejpam-4931	59	20	y	y	PROPN
ejpam-4931	59	21	)	)	PUNCT
ejpam-4931	59	22	,	,	PUNCT
ejpam-4931	59	23	(	(	PUNCT
ejpam-4931	59	24	7	7	X
ejpam-4931	59	25	)	)	PUNCT
ejpam-4931	59	26	with	with	ADP
ejpam-4931	59	27	ξ0	ξ0	PROPN
ejpam-4931	59	28	≥	≥	NOUN
ejpam-4931	59	29	0	0	NUM
ejpam-4931	59	30	a.e	a.e	NOUN
ejpam-4931	59	31	in	in	ADP
ejpam-4931	59	32	ωx	ωx	PRON
ejpam-4931	59	33	a	a	DET
ejpam-4931	59	34	bounded	bounded	ADJ
ejpam-4931	59	35	non	non	ADJ
ejpam-4931	59	36	-	-	ADJ
ejpam-4931	59	37	negative	negative	ADJ
ejpam-4931	59	38	function	function	NOUN
ejpam-4931	59	39	,	,	PUNCT
ejpam-4931	59	40	i.e.	i.e.	X
ejpam-4931	59	41	,	,	PUNCT
ejpam-4931	59	42	there	there	PRON
ejpam-4931	59	43	exists	exist	VERB
ejpam-4931	59	44	a	a	DET
ejpam-4931	59	45	positive	positive	ADJ
ejpam-4931	59	46	number	number	NOUN
ejpam-4931	59	47	m	m	VERB
ejpam-4931	59	48	such	such	ADJ
ejpam-4931	59	49	that	that	SCONJ
ejpam-4931	59	50	0	0	NUM
ejpam-4931	59	51	≤	≤	ADJ
ejpam-4931	59	52	ξ0	ξ0	ADJ
ejpam-4931	59	53	≤m	≤m	NOUN
ejpam-4931	59	54	<	<	X
ejpam-4931	59	55	+	+	PROPN
ejpam-4931	59	56	∞.	∞.	PROPN
ejpam-4931	59	57	(	(	PUNCT
ejpam-4931	59	58	8)	8)	NUM
ejpam-4931	59	59	furthermore	furthermore	ADV
ejpam-4931	59	60	,	,	PUNCT
ejpam-4931	59	61	we	we	PRON
ejpam-4931	59	62	assume	assume	VERB
ejpam-4931	59	63	that	that	SCONJ
ejpam-4931	59	64	the	the	DET
ejpam-4931	59	65	initial	initial	ADJ
ejpam-4931	59	66	data	data	NOUN
ejpam-4931	59	67	satisfies:	satisfies:	PROPN
ejpam-4931	59	68	u0	u0	ADJ
ejpam-4931	59	69	=	=	PROPN
ejpam-4931	59	70	m0	m0	PROPN
ejpam-4931	59	71	ξ0	ξ0	PROPN
ejpam-4931	59	72	if	if	SCONJ
ejpam-4931	59	73	ξ0	ξ0	PROPN
ejpam-4931	59	74	̸=	̸=	PROPN
ejpam-4931	59	75	0	0	NUM
ejpam-4931	59	76	and	and	CCONJ
ejpam-4931	59	77	u0	u0	ADJ
ejpam-4931	59	78	=	=	NOUN
ejpam-4931	59	79	0	0	NUM
ejpam-4931	59	80	elsewhere	elsewhere	ADV
ejpam-4931	59	81	,	,	PUNCT
ejpam-4931	59	82	|m0|2	|m0|2	NUM
ejpam-4931	59	83	ξ0	ξ0	NOUN
ejpam-4931	59	84	=	=	SYM
ejpam-4931	59	85	0	0	NUM
ejpam-4931	59	86	,	,	PUNCT
ejpam-4931	60	1	a.e	a.e	NOUN
ejpam-4931	60	2	on	on	ADP
ejpam-4931	60	3	{	{	PUNCT
ejpam-4931	60	4	(	(	PUNCT
ejpam-4931	60	5	x	x	NOUN
ejpam-4931	60	6	,	,	PUNCT
ejpam-4931	60	7	y	y	NOUN
ejpam-4931	60	8	)	)	PUNCT
ejpam-4931	60	9	∈	∈	PROPN
ejpam-4931	60	10	ω	ω	NOUN
ejpam-4931	60	11	:	:	PUNCT
ejpam-4931	60	12	ξ0(x	ξ0(x	NOUN
ejpam-4931	60	13	)	)	PUNCT
ejpam-4931	60	14	=	=	SYM
ejpam-4931	60	15	0	0	X
ejpam-4931	60	16	}	}	PUNCT
ejpam-4931	60	17	(	(	PUNCT
ejpam-4931	60	18	9	9	NUM
ejpam-4931	60	19	)	)	PUNCT
ejpam-4931	60	20	and	and	CCONJ
ejpam-4931	60	21			NUM
ejpam-4931	60	22	ξ0	ξ0	PROPN
ejpam-4931	60	23	∈	∈	PROPN
ejpam-4931	60	24	l1(ω	l1(ω	PROPN
ejpam-4931	60	25	)	)	PUNCT
ejpam-4931	60	26	∩	∩	NOUN
ejpam-4931	60	27	l2(ω	l2(ω	NOUN
ejpam-4931	60	28	)	)	PUNCT
ejpam-4931	60	29	,	,	PUNCT
ejpam-4931	60	30	∇x	∇x	NOUN
ejpam-4931	60	31	√	√	ADP
ejpam-4931	60	32	ξ0	ξ0	PROPN
ejpam-4931	60	33	∈	∈	PROPN
ejpam-4931	60	34	l2(ω	l2(ω	PROPN
ejpam-4931	60	35	)	)	PUNCT
ejpam-4931	60	36	,	,	PUNCT
ejpam-4931	60	37	m0	m0	PROPN
ejpam-4931	60	38	∈	∈	PROPN
ejpam-4931	60	39	l	l	NOUN
ejpam-4931	60	40	4	4	NUM
ejpam-4931	60	41	3	3	NUM
ejpam-4931	60	42	(	(	PUNCT
ejpam-4931	60	43	ω	ω	NOUN
ejpam-4931	60	44	)	)	PUNCT
ejpam-4931	60	45	,	,	PUNCT
ejpam-4931	60	46	m0u0	m0u0	PROPN
ejpam-4931	60	47	=	=	PROPN
ejpam-4931	60	48	m2	m2	PROPN
ejpam-4931	60	49	0	0	NUM
ejpam-4931	60	50	ξ0	ξ0	PROPN
ejpam-4931	60	51	∈	∈	PROPN
ejpam-4931	60	52	l1(ω	l1(ω	PROPN
ejpam-4931	60	53	)	)	PUNCT
ejpam-4931	60	54	.	.	PUNCT
ejpam-4931	61	1	(	(	PUNCT
ejpam-4931	61	2	10	10	NUM
ejpam-4931	61	3	)	)	PUNCT
ejpam-4931	61	4	the	the	DET
ejpam-4931	61	5	factor	factor	NOUN
ejpam-4931	61	6	1	1	NUM
ejpam-4931	61	7	+	+	CCONJ
ejpam-4931	61	8	ϕ	ϕ	X
ejpam-4931	61	9	ξ	ξ	PROPN
ejpam-4931	61	10	is	be	AUX
ejpam-4931	61	11	approximately	approximately	ADV
ejpam-4931	61	12	equal	equal	ADJ
ejpam-4931	61	13	to	to	ADP
ejpam-4931	61	14	1	1	NUM
ejpam-4931	61	15	,	,	PUNCT
ejpam-4931	61	16	meaning	mean	VERB
ejpam-4931	61	17	that	that	SCONJ
ejpam-4931	61	18	the	the	DET
ejpam-4931	61	19	difference	difference	NOUN
ejpam-4931	61	20	between	between	ADP
ejpam-4931	61	21	the	the	DET
ejpam-4931	61	22	vertical	vertical	ADJ
ejpam-4931	61	23	and	and	CCONJ
ejpam-4931	61	24	horizontal	horizontal	ADJ
ejpam-4931	61	25	components	component	NOUN
ejpam-4931	61	26	of	of	ADP
ejpam-4931	61	27	the	the	DET
ejpam-4931	61	28	density	density	NOUN
ejpam-4931	61	29	is	be	AUX
ejpam-4931	61	30	small	small	ADJ
ejpam-4931	61	31	.	.	PUNCT
ejpam-4931	62	1	in	in	ADP
ejpam-4931	62	2	general	general	ADJ
ejpam-4931	62	3	,	,	PUNCT
ejpam-4931	62	4	in	in	ADP
ejpam-4931	62	5	certain	certain	ADJ
ejpam-4931	62	6	fluid	fluid	ADJ
ejpam-4931	62	7	dynamics	dynamic	NOUN
ejpam-4931	62	8	problems	problem	NOUN
ejpam-4931	62	9	,	,	PUNCT
ejpam-4931	62	10	density	density	NOUN
ejpam-4931	62	11	can	can	AUX
ejpam-4931	62	12	influence	influence	VERB
ejpam-4931	62	13	fluid	fluid	ADJ
ejpam-4931	62	14	velocity	velocity	NOUN
ejpam-4931	62	15	.	.	PUNCT
ejpam-4931	63	1	the	the	DET
ejpam-4931	63	2	factor	factor	NOUN
ejpam-4931	63	3	1	1	NUM
ejpam-4931	63	4	+	+	NUM
ejpam-4931	63	5	ϕ	ϕ	X
ejpam-4931	63	6	ξ	ξ	PROPN
ejpam-4931	63	7	,	,	PUNCT
ejpam-4931	63	8	close	close	ADV
ejpam-4931	63	9	to	to	ADP
ejpam-4931	63	10	1	1	NUM
ejpam-4931	63	11	,	,	PUNCT
ejpam-4931	63	12	suggests	suggest	VERB
ejpam-4931	63	13	j.	j.	PROPN
ejpam-4931	63	14	ouya	ouya	PROPN
ejpam-4931	63	15	,	,	PUNCT
ejpam-4931	63	16	a.	a.	NOUN
ejpam-4931	63	17	ouédraogo	ouédraogo	PROPN
ejpam-4931	63	18	/	/	SYM
ejpam-4931	63	19	eur	eur	PROPN
ejpam-4931	63	20	.	.	PUNCT
ejpam-4931	64	1	j.	j.	PROPN
ejpam-4931	64	2	pure	pure	PROPN
ejpam-4931	64	3	appl	appl	PROPN
ejpam-4931	64	4	.	.	PROPN
ejpam-4931	64	5	math	math	PROPN
ejpam-4931	64	6	,	,	PUNCT
ejpam-4931	64	7	16	16	NUM
ejpam-4931	64	8	(	(	PUNCT
ejpam-4931	64	9	4	4	NUM
ejpam-4931	64	10	)	)	PUNCT
ejpam-4931	64	11	(	(	PUNCT
ejpam-4931	64	12	2023	2023	NUM
ejpam-4931	64	13	)	)	PUNCT
ejpam-4931	64	14	,	,	PUNCT
ejpam-4931	64	15	2247	2247	NUM
ejpam-4931	64	16	-	-	SYM
ejpam-4931	64	17	2285	2285	NUM
ejpam-4931	64	18	2250	2250	NUM
ejpam-4931	64	19	that	that	SCONJ
ejpam-4931	64	20	the	the	DET
ejpam-4931	64	21	variation	variation	NOUN
ejpam-4931	64	22	in	in	ADP
ejpam-4931	64	23	vertical	vertical	ADJ
ejpam-4931	64	24	density	density	NOUN
ejpam-4931	64	25	has	have	VERB
ejpam-4931	64	26	a	a	DET
ejpam-4931	64	27	negligible	negligible	ADJ
ejpam-4931	64	28	effect	effect	NOUN
ejpam-4931	64	29	on	on	ADP
ejpam-4931	64	30	fluid	fluid	ADJ
ejpam-4931	64	31	velocity	velocity	NOUN
ejpam-4931	64	32	,	,	PUNCT
ejpam-4931	64	33	indicating	indicate	VERB
ejpam-4931	64	34	that	that	SCONJ
ejpam-4931	64	35	other	other	ADJ
ejpam-4931	64	36	forces	force	NOUN
ejpam-4931	64	37	or	or	CCONJ
ejpam-4931	64	38	factors	factor	NOUN
ejpam-4931	64	39	are	be	AUX
ejpam-4931	64	40	predominant	predominant	ADJ
ejpam-4931	64	41	in	in	ADP
ejpam-4931	64	42	determining	determine	VERB
ejpam-4931	64	43	velocity	velocity	NOUN
ejpam-4931	64	44	.	.	PUNCT
ejpam-4931	65	1	in	in	ADP
ejpam-4931	65	2	particular	particular	ADJ
ejpam-4931	65	3	,	,	PUNCT
ejpam-4931	65	4	for	for	ADP
ejpam-4931	65	5	a	a	DET
ejpam-4931	65	6	fluid	fluid	NOUN
ejpam-4931	65	7	in	in	ADP
ejpam-4931	65	8	hydrostatic	hydrostatic	ADJ
ejpam-4931	65	9	equilibrium	equilibrium	NOUN
ejpam-4931	65	10	the	the	DET
ejpam-4931	65	11	vertical	vertical	ADJ
ejpam-4931	65	12	pressure	pressure	NOUN
ejpam-4931	65	13	difference	difference	NOUN
ejpam-4931	65	14	is	be	AUX
ejpam-4931	65	15	balanced	balance	VERB
ejpam-4931	65	16	by	by	ADP
ejpam-4931	65	17	the	the	DET
ejpam-4931	65	18	vertical	vertical	ADJ
ejpam-4931	65	19	density	density	NOUN
ejpam-4931	65	20	difference	difference	NOUN
ejpam-4931	65	21	,	,	PUNCT
ejpam-4931	65	22	so	so	CCONJ
ejpam-4931	65	23	the	the	DET
ejpam-4931	65	24	factor	factor	NOUN
ejpam-4931	65	25	1	1	NUM
ejpam-4931	65	26	+	+	CCONJ
ejpam-4931	65	27	ϕ	ϕ	X
ejpam-4931	65	28	ξ	ξ	X
ejpam-4931	65	29	close	close	ADV
ejpam-4931	65	30	to	to	PART
ejpam-4931	65	31	1	1	NUM
ejpam-4931	65	32	,	,	PUNCT
ejpam-4931	65	33	indicates	indicate	VERB
ejpam-4931	65	34	that	that	SCONJ
ejpam-4931	65	35	the	the	DET
ejpam-4931	65	36	vertical	vertical	ADJ
ejpam-4931	65	37	density	density	NOUN
ejpam-4931	65	38	variation	variation	NOUN
ejpam-4931	65	39	has	have	VERB
ejpam-4931	65	40	a	a	DET
ejpam-4931	65	41	negligible	negligible	ADJ
ejpam-4931	65	42	effect	effect	NOUN
ejpam-4931	65	43	on	on	ADP
ejpam-4931	65	44	the	the	DET
ejpam-4931	65	45	pressure	pressure	NOUN
ejpam-4931	65	46	balance	balance	NOUN
ejpam-4931	65	47	,	,	PUNCT
ejpam-4931	65	48	suggesting	suggest	VERB
ejpam-4931	65	49	that	that	SCONJ
ejpam-4931	65	50	the	the	DET
ejpam-4931	65	51	fluid	fluid	NOUN
ejpam-4931	65	52	is	be	AUX
ejpam-4931	65	53	mainly	mainly	ADV
ejpam-4931	65	54	balanced	balance	VERB
ejpam-4931	65	55	by	by	ADP
ejpam-4931	65	56	the	the	DET
ejpam-4931	65	57	horizontal	horizontal	ADJ
ejpam-4931	65	58	density	density	NOUN
ejpam-4931	65	59	variation	variation	NOUN
ejpam-4931	65	60	.	.	PUNCT
ejpam-4931	66	1	in	in	ADP
ejpam-4931	66	2	the	the	DET
ejpam-4931	66	3	case	case	NOUN
ejpam-4931	66	4	of	of	ADP
ejpam-4931	66	5	the	the	DET
ejpam-4931	66	6	atmosphere	atmosphere	NOUN
ejpam-4931	66	7	,	,	PUNCT
ejpam-4931	66	8	air	air	NOUN
ejpam-4931	66	9	density	density	NOUN
ejpam-4931	66	10	can	can	AUX
ejpam-4931	66	11	influence	influence	VERB
ejpam-4931	66	12	fluid	fluid	ADJ
ejpam-4931	66	13	velocity	velocity	NOUN
ejpam-4931	66	14	.	.	PUNCT
ejpam-4931	67	1	in	in	ADP
ejpam-4931	67	2	the	the	DET
ejpam-4931	67	3	atmosphere	atmosphere	NOUN
ejpam-4931	67	4	,	,	PUNCT
ejpam-4931	67	5	vertical	vertical	ADJ
ejpam-4931	67	6	density	density	NOUN
ejpam-4931	67	7	variation	variation	NOUN
ejpam-4931	67	8	due	due	ADP
ejpam-4931	67	9	to	to	ADP
ejpam-4931	67	10	temperature	temperature	NOUN
ejpam-4931	67	11	(	(	PUNCT
ejpam-4931	67	12	and	and	CCONJ
ejpam-4931	67	13	therefore	therefore	ADV
ejpam-4931	67	14	pressure	pressure	NOUN
ejpam-4931	67	15	)	)	PUNCT
ejpam-4931	67	16	variations	variation	NOUN
ejpam-4931	67	17	is	be	AUX
ejpam-4931	67	18	an	an	DET
ejpam-4931	67	19	important	important	ADJ
ejpam-4931	67	20	factor	factor	NOUN
ejpam-4931	67	21	contributing	contribute	VERB
ejpam-4931	67	22	to	to	ADP
ejpam-4931	67	23	atmospheric	atmospheric	ADJ
ejpam-4931	67	24	circulation	circulation	NOUN
ejpam-4931	67	25	,	,	PUNCT
ejpam-4931	67	26	including	include	VERB
ejpam-4931	67	27	convective	convective	ADJ
ejpam-4931	67	28	movements	movement	NOUN
ejpam-4931	67	29	and	and	CCONJ
ejpam-4931	67	30	meteorological	meteorological	ADJ
ejpam-4931	67	31	phenomena	phenomenon	NOUN
ejpam-4931	67	32	such	such	ADJ
ejpam-4931	67	33	as	as	ADP
ejpam-4931	67	34	updrafts	updraft	NOUN
ejpam-4931	67	35	and	and	CCONJ
ejpam-4931	67	36	downdrafts	downdraft	NOUN
ejpam-4931	67	37	.	.	PUNCT
ejpam-4931	68	1	however	however	ADV
ejpam-4931	68	2	,	,	PUNCT
ejpam-4931	68	3	in	in	ADP
ejpam-4931	68	4	some	some	DET
ejpam-4931	68	5	situations	situation	NOUN
ejpam-4931	68	6	where	where	SCONJ
ejpam-4931	68	7	other	other	ADJ
ejpam-4931	68	8	forces	force	NOUN
ejpam-4931	68	9	or	or	CCONJ
ejpam-4931	68	10	factors	factor	NOUN
ejpam-4931	68	11	are	be	AUX
ejpam-4931	68	12	predominant	predominant	ADJ
ejpam-4931	68	13	,	,	PUNCT
ejpam-4931	68	14	the	the	DET
ejpam-4931	68	15	factor	factor	NOUN
ejpam-4931	68	16	1	1	NUM
ejpam-4931	68	17	+	+	CCONJ
ejpam-4931	68	18	ϕ	ϕ	X
ejpam-4931	68	19	ξ	ξ	X
ejpam-4931	68	20	may	may	AUX
ejpam-4931	68	21	be	be	AUX
ejpam-4931	68	22	close	close	ADJ
ejpam-4931	68	23	to	to	ADP
ejpam-4931	68	24	1	1	NUM
ejpam-4931	68	25	,	,	PUNCT
ejpam-4931	68	26	suggesting	suggest	VERB
ejpam-4931	68	27	that	that	SCONJ
ejpam-4931	68	28	the	the	DET
ejpam-4931	68	29	variation	variation	NOUN
ejpam-4931	68	30	in	in	ADP
ejpam-4931	68	31	vertical	vertical	ADJ
ejpam-4931	68	32	density	density	NOUN
ejpam-4931	68	33	has	have	VERB
ejpam-4931	68	34	a	a	DET
ejpam-4931	68	35	negligible	negligible	ADJ
ejpam-4931	68	36	effect	effect	NOUN
ejpam-4931	68	37	on	on	ADP
ejpam-4931	68	38	fluid	fluid	ADJ
ejpam-4931	68	39	velocity	velocity	NOUN
ejpam-4931	68	40	.	.	PUNCT
ejpam-4931	69	1	for	for	ADP
ejpam-4931	69	2	example	example	NOUN
ejpam-4931	69	3	,	,	PUNCT
ejpam-4931	69	4	in	in	ADP
ejpam-4931	69	5	a	a	DET
ejpam-4931	69	6	situation	situation	NOUN
ejpam-4931	69	7	where	where	SCONJ
ejpam-4931	69	8	atmospheric	atmospheric	ADJ
ejpam-4931	69	9	pressure	pressure	NOUN
ejpam-4931	69	10	gradients	gradient	NOUN
ejpam-4931	69	11	are	be	AUX
ejpam-4931	69	12	very	very	ADV
ejpam-4931	69	13	steep	steep	ADJ
ejpam-4931	69	14	,	,	PUNCT
ejpam-4931	69	15	pressure	pressure	NOUN
ejpam-4931	69	16	differences	difference	NOUN
ejpam-4931	69	17	may	may	AUX
ejpam-4931	69	18	be	be	AUX
ejpam-4931	69	19	the	the	DET
ejpam-4931	69	20	main	main	ADJ
ejpam-4931	69	21	driver	driver	NOUN
ejpam-4931	69	22	of	of	ADP
ejpam-4931	69	23	atmospheric	atmospheric	ADJ
ejpam-4931	69	24	motions	motion	NOUN
ejpam-4931	69	25	,	,	PUNCT
ejpam-4931	69	26	and	and	CCONJ
ejpam-4931	69	27	the	the	DET
ejpam-4931	69	28	vertical	vertical	ADJ
ejpam-4931	69	29	density	density	NOUN
ejpam-4931	69	30	variation	variation	NOUN
ejpam-4931	69	31	may	may	AUX
ejpam-4931	69	32	have	have	VERB
ejpam-4931	69	33	a	a	DET
ejpam-4931	69	34	relatively	relatively	ADV
ejpam-4931	69	35	small	small	ADJ
ejpam-4931	69	36	effect	effect	NOUN
ejpam-4931	69	37	on	on	ADP
ejpam-4931	69	38	fluid	fluid	ADJ
ejpam-4931	69	39	velocity	velocity	NOUN
ejpam-4931	69	40	.	.	PUNCT
ejpam-4931	70	1	in	in	ADP
ejpam-4931	70	2	such	such	DET
ejpam-4931	70	3	a	a	DET
ejpam-4931	70	4	case	case	NOUN
ejpam-4931	70	5	,	,	PUNCT
ejpam-4931	70	6	the	the	DET
ejpam-4931	70	7	factor	factor	NOUN
ejpam-4931	70	8	1	1	NUM
ejpam-4931	70	9	+	+	CCONJ
ejpam-4931	70	10	ϕ	ϕ	X
ejpam-4931	70	11	ξ	ξ	X
ejpam-4931	70	12	may	may	AUX
ejpam-4931	70	13	be	be	AUX
ejpam-4931	70	14	close	close	ADJ
ejpam-4931	70	15	to	to	ADP
ejpam-4931	70	16	1	1	NUM
ejpam-4931	70	17	.	.	PUNCT
ejpam-4931	71	1	formally	formally	ADV
ejpam-4931	71	2	,	,	PUNCT
ejpam-4931	71	3	multiplying	multiply	VERB
ejpam-4931	71	4	the	the	DET
ejpam-4931	71	5	momentum	momentum	NOUN
ejpam-4931	71	6	equation	equation	NOUN
ejpam-4931	71	7	(	(	PUNCT
ejpam-4931	71	8	5)2	5)2	NUM
ejpam-4931	71	9	by	by	ADP
ejpam-4931	71	10	horizontal	horizontal	ADJ
ejpam-4931	71	11	velocity	velocity	NOUN
ejpam-4931	71	12	u	u	PROPN
ejpam-4931	71	13	,	,	PUNCT
ejpam-4931	71	14	then	then	ADV
ejpam-4931	71	15	integrating	integrate	VERB
ejpam-4931	71	16	by	by	ADP
ejpam-4931	71	17	parts	part	NOUN
ejpam-4931	71	18	on	on	ADP
ejpam-4931	71	19	ω	ω	NUM
ejpam-4931	71	20	,	,	PUNCT
ejpam-4931	71	21	we	we	PRON
ejpam-4931	71	22	obtain	obtain	VERB
ejpam-4931	71	23	the	the	DET
ejpam-4931	71	24	energy	energy	NOUN
ejpam-4931	71	25	equality	equality	NOUN
ejpam-4931	72	1	d	d	X
ejpam-4931	72	2	dt	dt	NOUN
ejpam-4931	72	3	∫	∫	PROPN
ejpam-4931	72	4	ω	ω	PROPN
ejpam-4931	72	5	(	(	PUNCT
ejpam-4931	72	6	1	1	NUM
ejpam-4931	72	7	2	2	NUM
ejpam-4931	72	8	ξ|u|2	ξ|u|2	NOUN
ejpam-4931	72	9	+	+	CCONJ
ejpam-4931	72	10	ξ2	ξ2	NOUN
ejpam-4931	72	11	)	)	PUNCT
ejpam-4931	72	12	dxdy	dxdy	NOUN
ejpam-4931	72	13	+	+	CCONJ
ejpam-4931	72	14	r	r	NOUN
ejpam-4931	72	15	∫	∫	PROPN
ejpam-4931	72	16	ω	ω	PROPN
ejpam-4931	72	17	ξ|u|3	ξ|u|3	PROPN
ejpam-4931	72	18	dxdy	dxdy	PROPN
ejpam-4931	72	19	+	+	CCONJ
ejpam-4931	73	1	∫	∫	PROPN
ejpam-4931	73	2	ω	ω	X
ejpam-4931	73	3	ξ	ξ	PROPN
ejpam-4931	73	4	(	(	PUNCT
ejpam-4931	73	5	2|dx(u)|2	2|dx(u)|2	NUM
ejpam-4931	73	6	+	+	CCONJ
ejpam-4931	73	7	|∂yu|2	|∂yu|2	PROPN
ejpam-4931	73	8	)	)	PUNCT
ejpam-4931	73	9	dxdy	dxdy	NOUN
ejpam-4931	73	10	=	=	PUNCT
ejpam-4931	73	11	0	0	X
ejpam-4931	73	12	.	.	PUNCT
ejpam-4931	74	1	in	in	ADP
ejpam-4931	74	2	this	this	DET
ejpam-4931	74	3	paper	paper	NOUN
ejpam-4931	74	4	,	,	PUNCT
ejpam-4931	74	5	motivated	motivate	VERB
ejpam-4931	74	6	by	by	ADP
ejpam-4931	74	7	[	[	X
ejpam-4931	74	8	17	17	NUM
ejpam-4931	74	9	]	]	PUNCT
ejpam-4931	74	10	and	and	CCONJ
ejpam-4931	74	11	especially	especially	ADV
ejpam-4931	74	12	[	[	X
ejpam-4931	74	13	19	19	NUM
ejpam-4931	74	14	]	]	PUNCT
ejpam-4931	74	15	,	,	PUNCT
ejpam-4931	74	16	we	we	PRON
ejpam-4931	74	17	will	will	AUX
ejpam-4931	74	18	investigate	investigate	VERB
ejpam-4931	74	19	the	the	DET
ejpam-4931	74	20	global	global	ADJ
ejpam-4931	74	21	existence	existence	NOUN
ejpam-4931	74	22	of	of	ADP
ejpam-4931	74	23	weak	weak	ADJ
ejpam-4931	74	24	solutions	solution	NOUN
ejpam-4931	74	25	to	to	ADP
ejpam-4931	74	26	cpe	cpe	PROPN
ejpam-4931	74	27	(	(	PUNCT
ejpam-4931	74	28	1	1	NUM
ejpam-4931	74	29	)	)	PUNCT
ejpam-4931	74	30	in	in	ADP
ejpam-4931	74	31	which	which	PRON
ejpam-4931	74	32	the	the	DET
ejpam-4931	74	33	pressure	pressure	NOUN
ejpam-4931	74	34	is	be	AUX
ejpam-4931	74	35	assumed	assume	VERB
ejpam-4931	74	36	to	to	PART
ejpam-4931	74	37	be	be	AUX
ejpam-4931	74	38	p	p	X
ejpam-4931	74	39	(	(	PUNCT
ejpam-4931	74	40	ρ	ρ	NOUN
ejpam-4931	74	41	)	)	PUNCT
ejpam-4931	74	42	=	=	PUNCT
ejpam-4931	74	43	aργ	aργ	NOUN
ejpam-4931	74	44	with	with	ADP
ejpam-4931	74	45	γ	γ	PROPN
ejpam-4931	74	46	>	>	X
ejpam-4931	74	47	1	1	NUM
ejpam-4931	74	48	and	and	CCONJ
ejpam-4931	74	49	a	a	DET
ejpam-4931	74	50	>	>	X
ejpam-4931	74	51	0	0	PUNCT
ejpam-4931	74	52	a	a	DET
ejpam-4931	74	53	constant	constant	ADJ
ejpam-4931	74	54	(	(	PUNCT
ejpam-4931	74	55	a	a	DET
ejpam-4931	74	56	=	=	SYM
ejpam-4931	74	57	1	1	NUM
ejpam-4931	74	58	,	,	PUNCT
ejpam-4931	74	59	γ	γ	NOUN
ejpam-4931	74	60	=	=	SYM
ejpam-4931	74	61	2	2	NUM
ejpam-4931	74	62	for	for	ADP
ejpam-4931	74	63	simplicity	simplicity	NOUN
ejpam-4931	74	64	)	)	PUNCT
ejpam-4931	74	65	.	.	PUNCT
ejpam-4931	75	1	the	the	DET
ejpam-4931	75	2	key	key	ADJ
ejpam-4931	75	3	issue	issue	NOUN
ejpam-4931	75	4	in	in	ADP
ejpam-4931	75	5	our	our	PRON
ejpam-4931	75	6	proof	proof	NOUN
ejpam-4931	75	7	is	be	AUX
ejpam-4931	75	8	to	to	PART
ejpam-4931	75	9	construct	construct	VERB
ejpam-4931	75	10	the	the	DET
ejpam-4931	75	11	approximate	approximate	ADJ
ejpam-4931	75	12	solutions	solution	NOUN
ejpam-4931	75	13	satisfying	satisfy	VERB
ejpam-4931	75	14	lower	lower	ADV
ejpam-4931	75	15	bound	bind	VERB
ejpam-4931	75	16	of	of	ADP
ejpam-4931	75	17	the	the	DET
ejpam-4931	75	18	density	density	NOUN
ejpam-4931	75	19	and	and	CCONJ
ejpam-4931	75	20	breschdesjardins	breschdesjardin	NOUN
ejpam-4931	75	21	entropy	entropy	VERB
ejpam-4931	75	22	.	.	PUNCT
ejpam-4931	76	1	we	we	PRON
ejpam-4931	76	2	will	will	AUX
ejpam-4931	76	3	first	first	ADV
ejpam-4931	76	4	face	face	VERB
ejpam-4931	76	5	a	a	DET
ejpam-4931	76	6	new	new	ADJ
ejpam-4931	76	7	difficulty	difficulty	NOUN
ejpam-4931	76	8	on	on	ADP
ejpam-4931	76	9	how	how	SCONJ
ejpam-4931	76	10	to	to	PART
ejpam-4931	76	11	estimate	estimate	VERB
ejpam-4931	76	12	the	the	DET
ejpam-4931	76	13	vertical	vertical	ADJ
ejpam-4931	76	14	velocity	velocity	NOUN
ejpam-4931	76	15	v	v	NOUN
ejpam-4931	76	16	since	since	SCONJ
ejpam-4931	76	17	there	there	PRON
ejpam-4931	76	18	is	be	VERB
ejpam-4931	76	19	no	no	DET
ejpam-4931	76	20	equation	equation	NOUN
ejpam-4931	76	21	on	on	ADP
ejpam-4931	76	22	it	it	PRON
ejpam-4931	76	23	.	.	PUNCT
ejpam-4931	77	1	in	in	ADP
ejpam-4931	77	2	order	order	NOUN
ejpam-4931	77	3	to	to	PART
ejpam-4931	77	4	overcome	overcome	VERB
ejpam-4931	77	5	this	this	DET
ejpam-4931	77	6	difficulty	difficulty	NOUN
ejpam-4931	77	7	,	,	PUNCT
ejpam-4931	77	8	we	we	PRON
ejpam-4931	77	9	represent	represent	VERB
ejpam-4931	77	10	the	the	DET
ejpam-4931	77	11	vertical	vertical	ADJ
ejpam-4931	77	12	velocity	velocity	NOUN
ejpam-4931	77	13	v	v	NOUN
ejpam-4931	77	14	as	as	ADP
ejpam-4931	77	15	a	a	DET
ejpam-4931	77	16	function	function	NOUN
ejpam-4931	77	17	of	of	ADP
ejpam-4931	77	18	the	the	DET
ejpam-4931	77	19	density	density	NOUN
ejpam-4931	77	20	ξ	ξ	PROPN
ejpam-4931	77	21	and	and	CCONJ
ejpam-4931	77	22	the	the	DET
ejpam-4931	77	23	horizontal	horizontal	ADJ
ejpam-4931	77	24	velocity	velocity	NOUN
ejpam-4931	77	25	u	u	NOUN
ejpam-4931	77	26	and	and	CCONJ
ejpam-4931	77	27	use	use	VERB
ejpam-4931	77	28	the	the	DET
ejpam-4931	77	29	faedo	faedo	NOUN
ejpam-4931	77	30	-	-	PUNCT
ejpam-4931	77	31	galerkin	galerkin	ADJ
ejpam-4931	77	32	method	method	NOUN
ejpam-4931	77	33	to	to	PART
ejpam-4931	77	34	prove	prove	VERB
ejpam-4931	77	35	the	the	DET
ejpam-4931	77	36	existence	existence	NOUN
ejpam-4931	77	37	of	of	ADP
ejpam-4931	77	38	the	the	DET
ejpam-4931	77	39	approximate	approximate	ADJ
ejpam-4931	77	40	solutions	solution	NOUN
ejpam-4931	77	41	.	.	PUNCT
ejpam-4931	78	1	what	what	PRON
ejpam-4931	78	2	’s	’	VERB
ejpam-4931	78	3	more	more	ADJ
ejpam-4931	78	4	,	,	PUNCT
ejpam-4931	78	5	similar	similar	ADJ
ejpam-4931	78	6	to	to	ADP
ejpam-4931	78	7	[	[	X
ejpam-4931	78	8	10	10	NUM
ejpam-4931	78	9	,	,	PUNCT
ejpam-4931	78	10	17–19	17–19	NUM
ejpam-4931	78	11	]	]	PUNCT
ejpam-4931	78	12	,	,	PUNCT
ejpam-4931	78	13	we	we	PRON
ejpam-4931	78	14	construct	construct	VERB
ejpam-4931	78	15	the	the	DET
ejpam-4931	78	16	approximate	approximate	ADJ
ejpam-4931	78	17	solutions	solution	NOUN
ejpam-4931	78	18	by	by	ADP
ejpam-4931	78	19	adding	add	VERB
ejpam-4931	78	20	viscosity	viscosity	NOUN
ejpam-4931	78	21	term	term	NOUN
ejpam-4931	78	22	in	in	ADP
ejpam-4931	78	23	the	the	DET
ejpam-4931	78	24	continuity	continuity	NOUN
ejpam-4931	78	25	equation	equation	NOUN
ejpam-4931	78	26	,	,	PUNCT
ejpam-4931	78	27	adding	add	VERB
ejpam-4931	78	28	drag	drag	ADJ
ejpam-4931	78	29	,	,	PUNCT
ejpam-4931	78	30	cold	cold	ADJ
ejpam-4931	78	31	pressure	pressure	NOUN
ejpam-4931	78	32	,	,	PUNCT
ejpam-4931	78	33	quantum	quantum	NOUN
ejpam-4931	78	34	and	and	CCONJ
ejpam-4931	78	35	higher	high	ADJ
ejpam-4931	78	36	derivative	derivative	ADJ
ejpam-4931	78	37	terms	term	NOUN
ejpam-4931	78	38	in	in	ADP
ejpam-4931	78	39	the	the	DET
ejpam-4931	78	40	momentum	momentum	NOUN
ejpam-4931	78	41	equation	equation	NOUN
ejpam-4931	78	42	(	(	PUNCT
ejpam-4931	78	43	see	see	VERB
ejpam-4931	78	44	(	(	PUNCT
ejpam-4931	78	45	17	17	NUM
ejpam-4931	78	46	)	)	PUNCT
ejpam-4931	78	47	for	for	ADP
ejpam-4931	78	48	details	detail	NOUN
ejpam-4931	78	49	)	)	PUNCT
ejpam-4931	78	50	.	.	PUNCT
ejpam-4931	79	1	using	use	VERB
ejpam-4931	79	2	compactness	compactness	NOUN
ejpam-4931	79	3	arguments	argument	NOUN
ejpam-4931	79	4	,	,	PUNCT
ejpam-4931	79	5	we	we	PRON
ejpam-4931	79	6	prove	prove	VERB
ejpam-4931	79	7	the	the	DET
ejpam-4931	79	8	global	global	ADJ
ejpam-4931	79	9	existence	existence	NOUN
ejpam-4931	79	10	of	of	ADP
ejpam-4931	79	11	weak	weak	ADJ
ejpam-4931	79	12	solutions	solution	NOUN
ejpam-4931	79	13	of	of	ADP
ejpam-4931	79	14	cpe	cpe	NOUN
ejpam-4931	79	15	by	by	ADP
ejpam-4931	79	16	vanishing	vanish	VERB
ejpam-4931	79	17	the	the	DET
ejpam-4931	79	18	parameters	parameter	NOUN
ejpam-4931	79	19	in	in	ADP
ejpam-4931	79	20	our	our	PRON
ejpam-4931	79	21	approximate	approximate	ADJ
ejpam-4931	79	22	system	system	NOUN
ejpam-4931	79	23	step	step	NOUN
ejpam-4931	79	24	by	by	ADP
ejpam-4931	79	25	step	step	NOUN
ejpam-4931	79	26	.	.	PUNCT
ejpam-4931	80	1	the	the	DET
ejpam-4931	80	2	rest	rest	NOUN
ejpam-4931	80	3	of	of	ADP
ejpam-4931	80	4	the	the	DET
ejpam-4931	80	5	paper	paper	NOUN
ejpam-4931	80	6	is	be	AUX
ejpam-4931	80	7	organized	organize	VERB
ejpam-4931	80	8	as	as	SCONJ
ejpam-4931	80	9	follows	follow	VERB
ejpam-4931	80	10	.	.	PUNCT
ejpam-4931	81	1	in	in	ADP
ejpam-4931	81	2	the	the	DET
ejpam-4931	81	3	next	next	ADJ
ejpam-4931	81	4	section	section	NOUN
ejpam-4931	81	5	,	,	PUNCT
ejpam-4931	81	6	we	we	PRON
ejpam-4931	81	7	present	present	VERB
ejpam-4931	81	8	some	some	DET
ejpam-4931	81	9	elementary	elementary	ADJ
ejpam-4931	81	10	inequality	inequality	NOUN
ejpam-4931	81	11	and	and	CCONJ
ejpam-4931	81	12	compactness	compactness	NOUN
ejpam-4931	81	13	theorems	theorem	NOUN
ejpam-4931	81	14	which	which	PRON
ejpam-4931	81	15	will	will	AUX
ejpam-4931	81	16	be	be	AUX
ejpam-4931	81	17	used	use	VERB
ejpam-4931	81	18	frequently	frequently	ADV
ejpam-4931	81	19	in	in	ADP
ejpam-4931	81	20	the	the	DET
ejpam-4931	81	21	whole	whole	ADJ
ejpam-4931	81	22	proof	proof	NOUN
ejpam-4931	81	23	.	.	PUNCT
ejpam-4931	82	1	in	in	ADP
ejpam-4931	82	2	section	section	NOUN
ejpam-4931	82	3	3	3	NUM
ejpam-4931	82	4	,	,	PUNCT
ejpam-4931	82	5	we	we	PRON
ejpam-4931	82	6	show	show	VERB
ejpam-4931	82	7	the	the	DET
ejpam-4931	82	8	existence	existence	NOUN
ejpam-4931	82	9	of	of	ADP
ejpam-4931	82	10	global	global	ADJ
ejpam-4931	82	11	solutions	solution	NOUN
ejpam-4931	82	12	to	to	ADP
ejpam-4931	82	13	the	the	DET
ejpam-4931	82	14	approximate	approximate	ADJ
ejpam-4931	82	15	system	system	NOUN
ejpam-4931	82	16	by	by	ADP
ejpam-4931	82	17	using	use	VERB
ejpam-4931	82	18	the	the	DET
ejpam-4931	82	19	faedo	faedo	ADJ
ejpam-4931	82	20	-	-	PUNCT
ejpam-4931	82	21	galerkin	galerkin	ADJ
ejpam-4931	82	22	method	method	NOUN
ejpam-4931	82	23	.	.	PUNCT
ejpam-4931	83	1	in	in	ADP
ejpam-4931	83	2	section	section	NOUN
ejpam-4931	83	3	4	4	NUM
ejpam-4931	83	4	,	,	PUNCT
ejpam-4931	83	5	we	we	PRON
ejpam-4931	83	6	deduce	deduce	VERB
ejpam-4931	83	7	the	the	DET
ejpam-4931	83	8	bresch	bresch	NOUN
ejpam-4931	83	9	-	-	PUNCT
ejpam-4931	83	10	desjardins	desjardins	PROPN
ejpam-4931	83	11	entropy	entropy	NOUN
ejpam-4931	83	12	estimates	estimate	NOUN
ejpam-4931	83	13	.	.	PUNCT
ejpam-4931	84	1	in	in	ADP
ejpam-4931	84	2	section	section	NOUN
ejpam-4931	84	3	5	5	NUM
ejpam-4931	84	4	,	,	PUNCT
ejpam-4931	84	5	using	use	VERB
ejpam-4931	84	6	the	the	DET
ejpam-4931	84	7	standard	standard	ADJ
ejpam-4931	84	8	compactness	compactness	NOUN
ejpam-4931	84	9	arguments	argument	NOUN
ejpam-4931	84	10	,	,	PUNCT
ejpam-4931	84	11	we	we	PRON
ejpam-4931	84	12	pass	pass	VERB
ejpam-4931	84	13	to	to	ADP
ejpam-4931	84	14	the	the	DET
ejpam-4931	84	15	limits	limit	NOUN
ejpam-4931	84	16	as	as	SCONJ
ejpam-4931	84	17	the	the	DET
ejpam-4931	84	18	parameters	parameter	NOUN
ejpam-4931	84	19	tend	tend	VERB
ejpam-4931	84	20	to	to	ADP
ejpam-4931	84	21	zero	zero	NUM
ejpam-4931	84	22	,	,	PUNCT
ejpam-4931	84	23	step	step	NOUN
ejpam-4931	84	24	by	by	ADP
ejpam-4931	84	25	step	step	NOUN
ejpam-4931	84	26	.	.	PUNCT
ejpam-4931	85	1	j.	j.	PROPN
ejpam-4931	85	2	ouya	ouya	PROPN
ejpam-4931	85	3	,	,	PUNCT
ejpam-4931	85	4	a.	a.	NOUN
ejpam-4931	85	5	ouédraogo	ouédraogo	PROPN
ejpam-4931	85	6	/	/	SYM
ejpam-4931	85	7	eur	eur	PROPN
ejpam-4931	85	8	.	.	PUNCT
ejpam-4931	86	1	j.	j.	PROPN
ejpam-4931	86	2	pure	pure	PROPN
ejpam-4931	86	3	appl	appl	PROPN
ejpam-4931	86	4	.	.	PROPN
ejpam-4931	86	5	math	math	PROPN
ejpam-4931	86	6	,	,	PUNCT
ejpam-4931	86	7	16	16	NUM
ejpam-4931	86	8	(	(	PUNCT
ejpam-4931	86	9	4	4	NUM
ejpam-4931	86	10	)	)	PUNCT
ejpam-4931	86	11	(	(	PUNCT
ejpam-4931	86	12	2023	2023	NUM
ejpam-4931	86	13	)	)	PUNCT
ejpam-4931	86	14	,	,	PUNCT
ejpam-4931	86	15	2247	2247	NUM
ejpam-4931	86	16	-	-	SYM
ejpam-4931	86	17	2285	2285	NUM
ejpam-4931	86	18	2251	2251	NUM
ejpam-4931	86	19	2	2	NUM
ejpam-4931	86	20	.	.	PUNCT
ejpam-4931	86	21	preliminary	preliminary	ADJ
ejpam-4931	86	22	and	and	CCONJ
ejpam-4931	86	23	main	main	ADJ
ejpam-4931	86	24	results	result	NOUN
ejpam-4931	86	25	we	we	PRON
ejpam-4931	86	26	give	give	VERB
ejpam-4931	86	27	here	here	ADV
ejpam-4931	86	28	the	the	DET
ejpam-4931	86	29	basic	basic	ADJ
ejpam-4931	86	30	inequalities	inequality	NOUN
ejpam-4931	86	31	which	which	PRON
ejpam-4931	86	32	are	be	AUX
ejpam-4931	86	33	useful	useful	ADJ
ejpam-4931	86	34	for	for	ADP
ejpam-4931	86	35	the	the	DET
ejpam-4931	86	36	next	next	ADJ
ejpam-4931	86	37	,	,	PUNCT
ejpam-4931	86	38	the	the	DET
ejpam-4931	86	39	definition	definition	NOUN
ejpam-4931	86	40	of	of	ADP
ejpam-4931	86	41	solution	solution	NOUN
ejpam-4931	86	42	in	in	ADP
ejpam-4931	86	43	our	our	PRON
ejpam-4931	86	44	context	context	NOUN
ejpam-4931	86	45	and	and	CCONJ
ejpam-4931	86	46	state	state	VERB
ejpam-4931	86	47	the	the	DET
ejpam-4931	86	48	main	main	ADJ
ejpam-4931	86	49	theorems	theorem	NOUN
ejpam-4931	86	50	.	.	PUNCT
ejpam-4931	87	1	lemma	lemma	PROPN
ejpam-4931	87	2	1	1	NUM
ejpam-4931	87	3	.	.	PUNCT
ejpam-4931	88	1	(	(	PUNCT
ejpam-4931	88	2	aubin	aubin	NOUN
ejpam-4931	88	3	-	-	PUNCT
ejpam-4931	88	4	lions	lion	NOUN
ejpam-4931	88	5	,	,	PUNCT
ejpam-4931	88	6	see	see	VERB
ejpam-4931	88	7	[	[	X
ejpam-4931	88	8	16	16	NUM
ejpam-4931	88	9	]	]	PUNCT
ejpam-4931	88	10	)	)	PUNCT
ejpam-4931	88	11	.	.	PUNCT
ejpam-4931	89	1	let	let	VERB
ejpam-4931	89	2	x0	x0	PROPN
ejpam-4931	89	3	,	,	PUNCT
ejpam-4931	89	4	x	x	SYM
ejpam-4931	89	5	and	and	CCONJ
ejpam-4931	89	6	x1	x1	PROPN
ejpam-4931	89	7	be	be	VERB
ejpam-4931	89	8	three	three	NUM
ejpam-4931	89	9	banach	banach	NOUN
ejpam-4931	89	10	spaces	space	NOUN
ejpam-4931	89	11	with	with	ADP
ejpam-4931	89	12	x0	x0	PROPN
ejpam-4931	89	13	⊆	⊆	NUM
ejpam-4931	89	14	x	x	SYM
ejpam-4931	89	15	⊆	⊆	NUM
ejpam-4931	89	16	x1	x1	PROPN
ejpam-4931	89	17	.	.	PUNCT
ejpam-4931	90	1	suppose	suppose	VERB
ejpam-4931	90	2	that	that	SCONJ
ejpam-4931	90	3	x0	x0	PROPN
ejpam-4931	90	4	is	be	AUX
ejpam-4931	90	5	compactly	compactly	ADV
ejpam-4931	90	6	embedded	embed	VERB
ejpam-4931	90	7	in	in	ADP
ejpam-4931	90	8	x	x	PUNCT
ejpam-4931	90	9	and	and	CCONJ
ejpam-4931	90	10	x	x	X
ejpam-4931	90	11	is	be	AUX
ejpam-4931	90	12	continuously	continuously	ADV
ejpam-4931	90	13	embedded	embed	VERB
ejpam-4931	90	14	in	in	ADP
ejpam-4931	90	15	x1	x1	PROPN
ejpam-4931	90	16	.	.	PUNCT
ejpam-4931	91	1	for	for	ADP
ejpam-4931	91	2	1	1	NUM
ejpam-4931	91	3	≤	≤	NOUN
ejpam-4931	91	4	p	p	NOUN
ejpam-4931	91	5	,	,	PUNCT
ejpam-4931	91	6	q	q	PROPN
ejpam-4931	91	7	≤	≤	NOUN
ejpam-4931	91	8	+	+	CCONJ
ejpam-4931	91	9	∞	∞	PROPN
ejpam-4931	91	10	,	,	PUNCT
ejpam-4931	91	11	let	let	VERB
ejpam-4931	91	12	w	w	NOUN
ejpam-4931	91	13	=	=	PRON
ejpam-4931	91	14	{	{	PUNCT
ejpam-4931	91	15	u	u	NOUN
ejpam-4931	91	16	∈	∈	PROPN
ejpam-4931	91	17	lp	lp	NOUN
ejpam-4931	91	18	(	(	PUNCT
ejpam-4931	91	19	[	[	X
ejpam-4931	91	20	0	0	NUM
ejpam-4931	91	21	,	,	PUNCT
ejpam-4931	91	22	t	t	X
ejpam-4931	91	23	]	]	PUNCT
ejpam-4931	91	24	;	;	PUNCT
ejpam-4931	91	25	x0	x0	PROPN
ejpam-4931	91	26	)	)	PUNCT
ejpam-4931	91	27	:	:	PUNCT
ejpam-4931	91	28	∂tu	∂tu	ADV
ejpam-4931	91	29	∈	∈	ADJ
ejpam-4931	91	30	lq	lq	X
ejpam-4931	91	31	(	(	PUNCT
ejpam-4931	91	32	[	[	X
ejpam-4931	91	33	0	0	NUM
ejpam-4931	91	34	,	,	PUNCT
ejpam-4931	91	35	t	t	X
ejpam-4931	91	36	]	]	PUNCT
ejpam-4931	91	37	;	;	PUNCT
ejpam-4931	91	38	x1	x1	NUM
ejpam-4931	91	39	)	)	PUNCT
ejpam-4931	91	40	}	}	PUNCT
ejpam-4931	91	41	.	.	PUNCT
ejpam-4931	92	1	(	(	PUNCT
ejpam-4931	92	2	i	i	NOUN
ejpam-4931	92	3	)	)	PUNCT
ejpam-4931	92	4	if	if	SCONJ
ejpam-4931	92	5	p	p	X
ejpam-4931	92	6	<	<	X
ejpam-4931	92	7	+	+	NOUN
ejpam-4931	92	8	∞	∞	PROPN
ejpam-4931	92	9	,	,	PUNCT
ejpam-4931	92	10	then	then	ADV
ejpam-4931	92	11	the	the	DET
ejpam-4931	92	12	embedding	embedding	NOUN
ejpam-4931	92	13	of	of	ADP
ejpam-4931	92	14	w	w	NOUN
ejpam-4931	92	15	into	into	ADP
ejpam-4931	92	16	lp	lp	PROPN
ejpam-4931	92	17	(	(	PUNCT
ejpam-4931	92	18	[	[	X
ejpam-4931	92	19	0	0	NUM
ejpam-4931	92	20	,	,	PUNCT
ejpam-4931	92	21	t	t	X
ejpam-4931	92	22	]	]	PUNCT
ejpam-4931	92	23	;	;	PUNCT
ejpam-4931	92	24	x	x	X
ejpam-4931	92	25	)	)	PUNCT
ejpam-4931	92	26	is	be	AUX
ejpam-4931	92	27	compact	compact	ADJ
ejpam-4931	92	28	;	;	PUNCT
ejpam-4931	92	29	(	(	PUNCT
ejpam-4931	92	30	ii	ii	NOUN
ejpam-4931	92	31	)	)	PUNCT
ejpam-4931	92	32	if	if	SCONJ
ejpam-4931	92	33	p	p	X
ejpam-4931	92	34	=	=	PUNCT
ejpam-4931	92	35	+	+	NOUN
ejpam-4931	92	36	∞	∞	NUM
ejpam-4931	92	37	and	and	CCONJ
ejpam-4931	92	38	q	q	ADJ
ejpam-4931	93	1	>	>	X
ejpam-4931	93	2	1	1	NUM
ejpam-4931	93	3	,	,	PUNCT
ejpam-4931	93	4	then	then	ADV
ejpam-4931	93	5	the	the	DET
ejpam-4931	93	6	embedding	embedding	NOUN
ejpam-4931	93	7	of	of	ADP
ejpam-4931	93	8	w	w	NOUN
ejpam-4931	93	9	into	into	ADP
ejpam-4931	93	10	c	c	PROPN
ejpam-4931	93	11	(	(	PUNCT
ejpam-4931	93	12	[	[	X
ejpam-4931	93	13	0	0	NUM
ejpam-4931	93	14	,	,	PUNCT
ejpam-4931	93	15	t	t	X
ejpam-4931	93	16	]	]	PUNCT
ejpam-4931	93	17	;	;	PUNCT
ejpam-4931	93	18	x	x	X
ejpam-4931	93	19	)	)	PUNCT
ejpam-4931	93	20	is	be	AUX
ejpam-4931	93	21	compact	compact	ADJ
ejpam-4931	93	22	.	.	PUNCT
ejpam-4931	94	1	lemma	lemma	PROPN
ejpam-4931	94	2	2	2	NUM
ejpam-4931	94	3	.	.	PUNCT
ejpam-4931	95	1	(	(	PUNCT
ejpam-4931	95	2	see	see	VERB
ejpam-4931	95	3	[	[	X
ejpam-4931	95	4	19	19	NUM
ejpam-4931	95	5	]	]	X
ejpam-4931	95	6	lemma	lemma	PROPN
ejpam-4931	95	7	2.3	2.3	NUM
ejpam-4931	95	8	)	)	PUNCT
ejpam-4931	95	9	.	.	PUNCT
ejpam-4931	96	1	let	let	VERB
ejpam-4931	96	2	ω	ω	PROPN
ejpam-4931	96	3	⊂	⊂	PROPN
ejpam-4931	96	4	rn	rn	AUX
ejpam-4931	96	5	be	be	AUX
ejpam-4931	96	6	a	a	DET
ejpam-4931	96	7	bounded	bounded	ADJ
ejpam-4931	96	8	measurable	measurable	ADJ
ejpam-4931	96	9	set	set	NOUN
ejpam-4931	96	10	.	.	PUNCT
ejpam-4931	97	1	suppose	suppose	VERB
ejpam-4931	97	2	that	that	SCONJ
ejpam-4931	97	3	(	(	PUNCT
ejpam-4931	97	4	fn)n∈n	fn)n∈n	NUM
ejpam-4931	97	5	⊂	⊂	X
ejpam-4931	97	6	lp(ω	lp(ω	NOUN
ejpam-4931	97	7	)	)	PUNCT
ejpam-4931	97	8	,	,	PUNCT
ejpam-4931	97	9	∥fn∥lp(ω)≤	∥fn∥lp(ω)≤	PROPN
ejpam-4931	97	10	c	c	NOUN
ejpam-4931	97	11	with	with	ADP
ejpam-4931	97	12	c	c	PROPN
ejpam-4931	97	13	a	a	DET
ejpam-4931	97	14	positive	positive	ADJ
ejpam-4931	97	15	constant	constant	NOUN
ejpam-4931	97	16	and	and	CCONJ
ejpam-4931	97	17	fn	fn	NOUN
ejpam-4931	97	18	−→	−→	NOUN
ejpam-4931	97	19	f	f	PROPN
ejpam-4931	97	20	a.e	a.e	PROPN
ejpam-4931	97	21	in	in	ADP
ejpam-4931	97	22	ω	ω	PROPN
ejpam-4931	97	23	.	.	PUNCT
ejpam-4931	98	1	then	then	ADV
ejpam-4931	98	2	(	(	PUNCT
ejpam-4931	98	3	i	i	NOUN
ejpam-4931	98	4	)	)	PUNCT
ejpam-4931	98	5	f	f	PROPN
ejpam-4931	98	6	∈	∈	PROPN
ejpam-4931	98	7	lp(ω	lp(ω	X
ejpam-4931	98	8	)	)	PUNCT
ejpam-4931	98	9	and	and	CCONJ
ejpam-4931	98	10	∥f∥lp(ω)≤	∥f∥lp(ω)≤	NOUN
ejpam-4931	98	11	c	c	NOUN
ejpam-4931	98	12	;	;	PUNCT
ejpam-4931	98	13	(	(	PUNCT
ejpam-4931	98	14	ii	ii	NOUN
ejpam-4931	98	15	)	)	PUNCT
ejpam-4931	98	16	fn	fn	VERB
ejpam-4931	99	1	−→	−→	NOUN
ejpam-4931	99	2	f	f	X
ejpam-4931	99	3	strongly	strongly	ADV
ejpam-4931	99	4	in	in	ADP
ejpam-4931	99	5	lp̄(ω	lp̄(ω	NOUN
ejpam-4931	99	6	)	)	PUNCT
ejpam-4931	99	7	,	,	PUNCT
ejpam-4931	99	8	for	for	ADP
ejpam-4931	99	9	any	any	DET
ejpam-4931	99	10	p̄	p̄	NOUN
ejpam-4931	99	11	∈	∈	PROPN
ejpam-4931	100	1	[	[	X
ejpam-4931	100	2	1	1	NUM
ejpam-4931	100	3	,	,	PUNCT
ejpam-4931	100	4	p	p	NOUN
ejpam-4931	100	5	)	)	PUNCT
ejpam-4931	100	6	.	.	PUNCT
ejpam-4931	101	1	lemma	lemma	PROPN
ejpam-4931	101	2	3	3	X
ejpam-4931	101	3	.	.	PUNCT
ejpam-4931	102	1	(	(	PUNCT
ejpam-4931	102	2	see	see	VERB
ejpam-4931	102	3	[	[	X
ejpam-4931	102	4	14	14	NUM
ejpam-4931	102	5	]	]	PUNCT
ejpam-4931	102	6	,	,	PUNCT
ejpam-4931	102	7	theorem	theorem	VERB
ejpam-4931	102	8	9.3)(gagliardo	9.3)(gagliardo	PROPN
ejpam-4931	102	9	-	-	PUNCT
ejpam-4931	102	10	nirenberg	nirenberg	PROPN
ejpam-4931	102	11	interpolation	interpolation	NOUN
ejpam-4931	102	12	inequality	inequality	NOUN
ejpam-4931	102	13	)	)	PUNCT
ejpam-4931	102	14	for	for	ADP
ejpam-4931	102	15	a	a	DET
ejpam-4931	102	16	function	function	NOUN
ejpam-4931	102	17	u	u	NOUN
ejpam-4931	102	18	:	:	PUNCT
ejpam-4931	102	19	ω	ω	NUM
ejpam-4931	102	20	−→	−→	NOUN
ejpam-4931	102	21	r	r	NOUN
ejpam-4931	102	22	defined	define	VERB
ejpam-4931	102	23	on	on	ADP
ejpam-4931	102	24	a	a	DET
ejpam-4931	102	25	bounded	bounded	ADJ
ejpam-4931	102	26	lipschitz	lipschitz	NOUN
ejpam-4931	102	27	domain	domain	NOUN
ejpam-4931	102	28	ω	ω	PROPN
ejpam-4931	102	29	⊂	⊂	PROPN
ejpam-4931	102	30	rn	rn	PROPN
ejpam-4931	102	31	and	and	CCONJ
ejpam-4931	102	32	for	for	ADP
ejpam-4931	102	33	all	all	DET
ejpam-4931	102	34	1	1	NUM
ejpam-4931	102	35	≤	≤	NUM
ejpam-4931	102	36	q	q	NOUN
ejpam-4931	102	37	,	,	PUNCT
ejpam-4931	102	38	r	r	NOUN
ejpam-4931	102	39	≤	≤	NOUN
ejpam-4931	102	40	∞	∞	ADP
ejpam-4931	102	41	and	and	CCONJ
ejpam-4931	102	42	an	an	DET
ejpam-4931	102	43	integer	integer	NOUN
ejpam-4931	102	44	m	m	NOUN
ejpam-4931	102	45	,	,	PUNCT
ejpam-4931	102	46	suppose	suppose	VERB
ejpam-4931	102	47	that	that	SCONJ
ejpam-4931	102	48	a	a	DET
ejpam-4931	102	49	real	real	ADJ
ejpam-4931	102	50	number	number	NOUN
ejpam-4931	102	51	θ	θ	PROPN
ejpam-4931	102	52	and	and	CCONJ
ejpam-4931	102	53	a	a	DET
ejpam-4931	102	54	natural	natural	ADJ
ejpam-4931	102	55	number	number	NOUN
ejpam-4931	102	56	j	j	PROPN
ejpam-4931	102	57	are	be	AUX
ejpam-4931	102	58	such	such	ADJ
ejpam-4931	102	59	that	that	SCONJ
ejpam-4931	102	60	1	1	NUM
ejpam-4931	102	61	p	p	NOUN
ejpam-4931	102	62	=	=	PUNCT
ejpam-4931	102	63	j	j	PROPN
ejpam-4931	102	64	n	n	PROPN
ejpam-4931	102	65	+	+	CCONJ
ejpam-4931	102	66	(	(	PUNCT
ejpam-4931	102	67	1	1	NUM
ejpam-4931	102	68	r	r	NOUN
ejpam-4931	102	69	−	−	NOUN
ejpam-4931	102	70	m	m	NOUN
ejpam-4931	102	71	n	n	NOUN
ejpam-4931	102	72	)	)	PUNCT
ejpam-4931	102	73	θ	θ	PROPN
ejpam-4931	103	1	+	+	PUNCT
ejpam-4931	103	2	1−	1−	NUM
ejpam-4931	103	3	θ	θ	NOUN
ejpam-4931	103	4	q	q	NOUN
ejpam-4931	103	5	and	and	CCONJ
ejpam-4931	103	6	j	j	PROPN
ejpam-4931	103	7	m	m	VERB
ejpam-4931	103	8	≤	≤	NUM
ejpam-4931	103	9	θ	θ	PROPN
ejpam-4931	103	10	≤	≤	NUM
ejpam-4931	103	11	1	1	NUM
ejpam-4931	103	12	.	.	PUNCT
ejpam-4931	104	1	then	then	ADV
ejpam-4931	104	2	we	we	PRON
ejpam-4931	104	3	have	have	AUX
ejpam-4931	104	4	∥dju∥p≤	∥dju∥p≤	AUX
ejpam-4931	104	5	c1∥dmu∥θr∥u∥1−θ	c1∥dmu∥θr∥u∥1−θ	VERB
ejpam-4931	104	6	q	q	PROPN
ejpam-4931	104	7	+	+	PROPN
ejpam-4931	104	8	c2∥u∥s	c2∥u∥	NOUN
ejpam-4931	104	9	,	,	PUNCT
ejpam-4931	104	10	(	(	PUNCT
ejpam-4931	104	11	11	11	NUM
ejpam-4931	104	12	)	)	PUNCT
ejpam-4931	104	13	where	where	SCONJ
ejpam-4931	104	14	s	s	VERB
ejpam-4931	104	15	>	>	X
ejpam-4931	104	16	0	0	NUM
ejpam-4931	104	17	is	be	AUX
ejpam-4931	104	18	an	an	DET
ejpam-4931	104	19	arbitrary	arbitrary	ADJ
ejpam-4931	104	20	constant	constant	ADJ
ejpam-4931	104	21	.	.	PUNCT
ejpam-4931	105	1	the	the	DET
ejpam-4931	105	2	constants	constant	NOUN
ejpam-4931	105	3	c1	c1	PROPN
ejpam-4931	105	4	and	and	CCONJ
ejpam-4931	105	5	c2	c2	PROPN
ejpam-4931	105	6	depend	depend	VERB
ejpam-4931	105	7	upon	upon	SCONJ
ejpam-4931	105	8	the	the	DET
ejpam-4931	105	9	domain	domain	NOUN
ejpam-4931	105	10	ω	ω	NOUN
ejpam-4931	105	11	as	as	ADV
ejpam-4931	105	12	well	well	ADV
ejpam-4931	105	13	as	as	ADP
ejpam-4931	105	14	m	m	PROPN
ejpam-4931	105	15	,	,	PUNCT
ejpam-4931	105	16	n	n	CCONJ
ejpam-4931	105	17	,	,	PUNCT
ejpam-4931	105	18	j	j	PROPN
ejpam-4931	105	19	,	,	PUNCT
ejpam-4931	105	20	r	r	NOUN
ejpam-4931	105	21	,	,	PUNCT
ejpam-4931	105	22	q	q	NOUN
ejpam-4931	105	23	et	et	NOUN
ejpam-4931	105	24	θ	θ	PROPN
ejpam-4931	105	25	.	.	PUNCT
ejpam-4931	105	26	to	to	PART
ejpam-4931	105	27	construct	construct	VERB
ejpam-4931	105	28	the	the	DET
ejpam-4931	105	29	regular	regular	ADJ
ejpam-4931	105	30	solutions	solution	NOUN
ejpam-4931	105	31	of	of	ADP
ejpam-4931	105	32	the	the	DET
ejpam-4931	105	33	approximation	approximation	NOUN
ejpam-4931	105	34	scheme	scheme	NOUN
ejpam-4931	105	35	,	,	PUNCT
ejpam-4931	105	36	we	we	PRON
ejpam-4931	105	37	represent	represent	VERB
ejpam-4931	105	38	the	the	DET
ejpam-4931	105	39	unknown	unknown	ADJ
ejpam-4931	105	40	vertical	vertical	ADJ
ejpam-4931	105	41	velocity	velocity	NOUN
ejpam-4931	105	42	v	v	NOUN
ejpam-4931	105	43	as	as	ADP
ejpam-4931	105	44	a	a	DET
ejpam-4931	105	45	function	function	NOUN
ejpam-4931	105	46	of	of	ADP
ejpam-4931	105	47	the	the	DET
ejpam-4931	105	48	density	density	NOUN
ejpam-4931	105	49	ξ	ξ	PROPN
ejpam-4931	105	50	and	and	CCONJ
ejpam-4931	105	51	the	the	DET
ejpam-4931	105	52	horizontal	horizontal	ADJ
ejpam-4931	105	53	velocity	velocity	NOUN
ejpam-4931	105	54	u.	u.	VERB
ejpam-4931	105	55	to	to	ADP
ejpam-4931	105	56	this	this	DET
ejpam-4931	105	57	end	end	NOUN
ejpam-4931	105	58	,	,	PUNCT
ejpam-4931	105	59	by	by	ADP
ejpam-4931	105	60	differentiating	differentiate	VERB
ejpam-4931	105	61	(	(	PUNCT
ejpam-4931	105	62	5)1	5)1	ADJ
ejpam-4931	105	63	with	with	ADP
ejpam-4931	105	64	respect	respect	NOUN
ejpam-4931	105	65	to	to	ADP
ejpam-4931	105	66	y	y	PROPN
ejpam-4931	105	67	,	,	PUNCT
ejpam-4931	105	68	we	we	PRON
ejpam-4931	105	69	obtain	obtain	VERB
ejpam-4931	105	70	−ξ∂2yv	−ξ∂2yv	NOUN
ejpam-4931	105	71	=	=	SYM
ejpam-4931	105	72	∂ydivx(ξu	∂ydivx(ξu	PROPN
ejpam-4931	105	73	)	)	PUNCT
ejpam-4931	105	74	.	.	PUNCT
ejpam-4931	106	1	(	(	PUNCT
ejpam-4931	106	2	12	12	X
ejpam-4931	106	3	)	)	PUNCT
ejpam-4931	106	4	solving	solving	NOUN
ejpam-4931	106	5	(	(	PUNCT
ejpam-4931	106	6	12	12	NUM
ejpam-4931	106	7	)	)	PUNCT
ejpam-4931	106	8	yields	yield	NOUN
ejpam-4931	106	9	v(y	v(y	NUM
ejpam-4931	106	10	)	)	PUNCT
ejpam-4931	106	11	=	=	PUNCT
ejpam-4931	107	1	−divx(ξũ(y	−divx(ξũ(y	PROPN
ejpam-4931	107	2	)	)	PUNCT
ejpam-4931	107	3	)	)	PUNCT
ejpam-4931	108	1	ξ	ξ	X
ejpam-4931	109	1	+	+	NUM
ejpam-4931	109	2	y	y	PROPN
ejpam-4931	109	3	divx(ξū	divx(ξū	PROPN
ejpam-4931	109	4	)	)	PUNCT
ejpam-4931	109	5	ξ	ξ	X
ejpam-4931	109	6	.	.	PUNCT
ejpam-4931	110	1	(	(	PUNCT
ejpam-4931	110	2	13	13	NUM
ejpam-4931	110	3	)	)	PUNCT
ejpam-4931	110	4	then	then	ADV
ejpam-4931	110	5	∂yv(y	∂yv(y	VERB
ejpam-4931	110	6	)	)	PUNCT
ejpam-4931	110	7	=	=	SYM
ejpam-4931	110	8	−divx(ξu	−divx(ξu	X
ejpam-4931	110	9	)	)	PUNCT
ejpam-4931	111	1	ξ	ξ	X
ejpam-4931	111	2	+	+	PUNCT
ejpam-4931	111	3	divx(ξū	divx(ξū	NOUN
ejpam-4931	111	4	)	)	PUNCT
ejpam-4931	111	5	ξ	ξ	PROPN
ejpam-4931	111	6	,	,	PUNCT
ejpam-4931	111	7	(	(	PUNCT
ejpam-4931	111	8	14	14	NUM
ejpam-4931	111	9	)	)	PUNCT
ejpam-4931	111	10	where	where	SCONJ
ejpam-4931	111	11	ũ(y	ũ(y	PROPN
ejpam-4931	111	12	)	)	PUNCT
ejpam-4931	111	13	=	=	PUNCT
ejpam-4931	112	1	∫	∫	PROPN
ejpam-4931	112	2	y	y	PROPN
ejpam-4931	112	3	0	0	NUM
ejpam-4931	112	4	u(τ)dτ	u(τ)dτ	PROPN
ejpam-4931	112	5	and	and	CCONJ
ejpam-4931	112	6	ū	ū	NOUN
ejpam-4931	112	7	=	=	SYM
ejpam-4931	112	8	∫	∫	PROPN
ejpam-4931	112	9	1	1	NUM
ejpam-4931	112	10	0	0	NUM
ejpam-4931	112	11	u(τ)dτ	u(τ)dτ	PROPN
ejpam-4931	112	12	.	.	PUNCT
ejpam-4931	113	1	we	we	PRON
ejpam-4931	113	2	now	now	ADV
ejpam-4931	113	3	give	give	VERB
ejpam-4931	113	4	the	the	DET
ejpam-4931	113	5	definition	definition	NOUN
ejpam-4931	113	6	of	of	ADP
ejpam-4931	113	7	weak	weak	ADJ
ejpam-4931	113	8	solutions	solution	NOUN
ejpam-4931	113	9	in	in	ADP
ejpam-4931	113	10	our	our	PRON
ejpam-4931	113	11	context	context	NOUN
ejpam-4931	113	12	.	.	PUNCT
ejpam-4931	114	1	j.	j.	PROPN
ejpam-4931	114	2	ouya	ouya	PROPN
ejpam-4931	114	3	,	,	PUNCT
ejpam-4931	114	4	a.	a.	NOUN
ejpam-4931	114	5	ouédraogo	ouédraogo	PROPN
ejpam-4931	114	6	/	/	SYM
ejpam-4931	114	7	eur	eur	PROPN
ejpam-4931	114	8	.	.	PUNCT
ejpam-4931	115	1	j.	j.	PROPN
ejpam-4931	115	2	pure	pure	PROPN
ejpam-4931	115	3	appl	appl	PROPN
ejpam-4931	115	4	.	.	PROPN
ejpam-4931	115	5	math	math	PROPN
ejpam-4931	115	6	,	,	PUNCT
ejpam-4931	115	7	16	16	NUM
ejpam-4931	115	8	(	(	PUNCT
ejpam-4931	115	9	4	4	NUM
ejpam-4931	115	10	)	)	PUNCT
ejpam-4931	115	11	(	(	PUNCT
ejpam-4931	115	12	2023	2023	NUM
ejpam-4931	115	13	)	)	PUNCT
ejpam-4931	115	14	,	,	PUNCT
ejpam-4931	115	15	2247	2247	NUM
ejpam-4931	115	16	-	-	SYM
ejpam-4931	115	17	2285	2285	NUM
ejpam-4931	115	18	2252	2252	NUM
ejpam-4931	115	19	definition	definition	NOUN
ejpam-4931	115	20	2.1	2.1	NUM
ejpam-4931	115	21	.	.	PUNCT
ejpam-4931	116	1	a	a	DET
ejpam-4931	116	2	weak	weak	ADJ
ejpam-4931	116	3	solution	solution	NOUN
ejpam-4931	116	4	of	of	ADP
ejpam-4931	116	5	the	the	DET
ejpam-4931	116	6	problem	problem	NOUN
ejpam-4931	116	7	(	(	PUNCT
ejpam-4931	116	8	5)-(7	5)-(7	NUM
ejpam-4931	116	9	)	)	PUNCT
ejpam-4931	116	10	is	be	AUX
ejpam-4931	116	11	a	a	DET
ejpam-4931	116	12	triplet	triplet	NOUN
ejpam-4931	116	13	(	(	PUNCT
ejpam-4931	116	14	ξ	ξ	PROPN
ejpam-4931	116	15	,	,	PUNCT
ejpam-4931	116	16	u	u	NOUN
ejpam-4931	116	17	,	,	PUNCT
ejpam-4931	116	18	v	v	NOUN
ejpam-4931	116	19	)	)	PUNCT
ejpam-4931	116	20	satisfying	satisfying	NOUN
ejpam-4931	116	21	:	:	PUNCT
ejpam-4931	116	22	(	(	PUNCT
ejpam-4931	116	23	1	1	X
ejpam-4931	116	24	)	)	PUNCT
ejpam-4931	116	25	(	(	PUNCT
ejpam-4931	116	26	7	7	X
ejpam-4931	116	27	)	)	PUNCT
ejpam-4931	116	28	holds	hold	VERB
ejpam-4931	116	29	in	in	ADP
ejpam-4931	116	30	d′(ω	d′(ω	PROPN
ejpam-4931	116	31	)	)	PUNCT
ejpam-4931	116	32	;	;	PUNCT
ejpam-4931	116	33	(	(	PUNCT
ejpam-4931	116	34	2	2	X
ejpam-4931	116	35	)	)	PUNCT
ejpam-4931	116	36	ξ	ξ	PROPN
ejpam-4931	116	37	,	,	PUNCT
ejpam-4931	116	38	u	u	NOUN
ejpam-4931	116	39	and	and	CCONJ
ejpam-4931	116	40	v	v	NOUN
ejpam-4931	116	41	belong	belong	VERB
ejpam-4931	116	42	to	to	ADP
ejpam-4931	116	43	the	the	DET
ejpam-4931	116	44	classes	classes	PROPN
ejpam-4931	116	45	ξ	ξ	PROPN
ejpam-4931	116	46	∈	∈	PROPN
ejpam-4931	116	47	l∞	l∞	NOUN
ejpam-4931	116	48	(	(	PUNCT
ejpam-4931	116	49	[	[	X
ejpam-4931	116	50	0	0	NUM
ejpam-4931	116	51	,	,	PUNCT
ejpam-4931	116	52	t	t	X
ejpam-4931	116	53	]	]	PUNCT
ejpam-4931	116	54	;	;	PUNCT
ejpam-4931	116	55	l1(ω	l1(ω	X
ejpam-4931	116	56	)	)	PUNCT
ejpam-4931	116	57	∩	∩	NOUN
ejpam-4931	116	58	l2(ω	l2(ω	NOUN
ejpam-4931	116	59	)	)	PUNCT
ejpam-4931	116	60	)	)	PUNCT
ejpam-4931	116	61	,	,	PUNCT
ejpam-4931	116	62	√	√	NUM
ejpam-4931	116	63	ξu	ξu	ADP
ejpam-4931	116	64	∈	∈	PROPN
ejpam-4931	116	65	l∞	l∞	PROPN
ejpam-4931	116	66	(	(	PUNCT
ejpam-4931	116	67	[	[	X
ejpam-4931	116	68	0	0	NUM
ejpam-4931	116	69	,	,	PUNCT
ejpam-4931	116	70	t	t	X
ejpam-4931	116	71	]	]	PUNCT
ejpam-4931	116	72	;	;	PUNCT
ejpam-4931	116	73	l2(ω	l2(ω	NUM
ejpam-4931	116	74	)	)	PUNCT
ejpam-4931	116	75	)	)	PUNCT
ejpam-4931	116	76	,	,	PUNCT
ejpam-4931	116	77	√	√	NUM
ejpam-4931	116	78	ξ	ξ	PROPN
ejpam-4931	116	79	∈	∈	PROPN
ejpam-4931	116	80	l∞	l∞	NOUN
ejpam-4931	116	81	(	(	PUNCT
ejpam-4931	116	82	[	[	X
ejpam-4931	116	83	0	0	NUM
ejpam-4931	116	84	,	,	PUNCT
ejpam-4931	116	85	t	t	X
ejpam-4931	116	86	]	]	PUNCT
ejpam-4931	116	87	;	;	PUNCT
ejpam-4931	116	88	h1(ω	h1(ω	PROPN
ejpam-4931	116	89	)	)	PUNCT
ejpam-4931	116	90	)	)	PUNCT
ejpam-4931	116	91	,	,	PUNCT
ejpam-4931	116	92	ξ	ξ	X
ejpam-4931	116	93	1	1	NUM
ejpam-4931	116	94	3u	3u	NUM
ejpam-4931	116	95	∈	∈	PROPN
ejpam-4931	116	96	l3	l3	NOUN
ejpam-4931	116	97	(	(	PUNCT
ejpam-4931	116	98	[	[	X
ejpam-4931	116	99	0	0	NUM
ejpam-4931	116	100	,	,	PUNCT
ejpam-4931	116	101	t	t	X
ejpam-4931	116	102	]	]	PUNCT
ejpam-4931	116	103	;	;	PUNCT
ejpam-4931	116	104	l3(ω	l3(ω	X
ejpam-4931	116	105	)	)	PUNCT
ejpam-4931	116	106	)	)	PUNCT
ejpam-4931	116	107	,	,	PUNCT
ejpam-4931	116	108	ξ∇xu	ξ∇xu	PROPN
ejpam-4931	116	109	∈	∈	NOUN
ejpam-4931	116	110	l2	l2	NOUN
ejpam-4931	116	111	(	(	PUNCT
ejpam-4931	116	112	[	[	X
ejpam-4931	116	113	0	0	NUM
ejpam-4931	116	114	,	,	PUNCT
ejpam-4931	116	115	t	t	X
ejpam-4931	116	116	]	]	PUNCT
ejpam-4931	116	117	;	;	PUNCT
ejpam-4931	116	118	l2(ω	l2(ω	NUM
ejpam-4931	116	119	)	)	PUNCT
ejpam-4931	116	120	)	)	PUNCT
ejpam-4931	116	121	,	,	PUNCT
ejpam-4931	116	122	ξ(∇xu	ξ(∇xu	NUM
ejpam-4931	116	123	)	)	PUNCT
ejpam-4931	116	124	t	t	PROPN
ejpam-4931	116	125	∈	∈	NOUN
ejpam-4931	116	126	l2	l2	NOUN
ejpam-4931	116	127	(	(	PUNCT
ejpam-4931	116	128	[	[	X
ejpam-4931	116	129	0	0	NUM
ejpam-4931	116	130	,	,	PUNCT
ejpam-4931	116	131	t	t	X
ejpam-4931	116	132	]	]	PUNCT
ejpam-4931	116	133	;	;	PUNCT
ejpam-4931	116	134	l2(ω	l2(ω	NUM
ejpam-4931	116	135	)	)	PUNCT
ejpam-4931	116	136	)	)	PUNCT
ejpam-4931	116	137	,	,	PUNCT
ejpam-4931	116	138	√	√	VERB
ejpam-4931	116	139	ξv	ξv	DET
ejpam-4931	116	140	∈	∈	NOUN
ejpam-4931	116	141	l2	l2	NOUN
ejpam-4931	116	142	(	(	PUNCT
ejpam-4931	116	143	[	[	X
ejpam-4931	116	144	0	0	NUM
ejpam-4931	116	145	,	,	PUNCT
ejpam-4931	116	146	t	t	X
ejpam-4931	116	147	]	]	PUNCT
ejpam-4931	116	148	;	;	PUNCT
ejpam-4931	116	149	l2(ω	l2(ω	NUM
ejpam-4931	116	150	)	)	PUNCT
ejpam-4931	116	151	)	)	PUNCT
ejpam-4931	116	152	,	,	PUNCT
ejpam-4931	116	153	√	√	NUM
ejpam-4931	116	154	ξ∂yv	ξ∂yv	PROPN
ejpam-4931	116	155	∈	∈	NOUN
ejpam-4931	116	156	l2	l2	NOUN
ejpam-4931	116	157	(	(	PUNCT
ejpam-4931	116	158	[	[	X
ejpam-4931	116	159	0	0	NUM
ejpam-4931	116	160	,	,	PUNCT
ejpam-4931	116	161	t	t	X
ejpam-4931	116	162	]	]	PUNCT
ejpam-4931	116	163	;	;	PUNCT
ejpam-4931	116	164	l2(ω	l2(ω	NUM
ejpam-4931	116	165	)	)	PUNCT
ejpam-4931	116	166	)	)	PUNCT
ejpam-4931	116	167	,	,	PUNCT
ejpam-4931	116	168	√	√	CCONJ
ejpam-4931	116	169	ξ∂yu	ξ∂yu	NOUN
ejpam-4931	116	170	∈	∈	NOUN
ejpam-4931	116	171	l2	l2	NOUN
ejpam-4931	116	172	(	(	PUNCT
ejpam-4931	116	173	[	[	X
ejpam-4931	116	174	0	0	NUM
ejpam-4931	116	175	,	,	PUNCT
ejpam-4931	116	176	t	t	X
ejpam-4931	116	177	]	]	PUNCT
ejpam-4931	116	178	;	;	PUNCT
ejpam-4931	116	179	l2(ω	l2(ω	NUM
ejpam-4931	116	180	)	)	PUNCT
ejpam-4931	116	181	)	)	PUNCT
ejpam-4931	116	182	,	,	PUNCT
ejpam-4931	116	183	∇xξ	∇xξ	PROPN
ejpam-4931	116	184	∈	∈	PROPN
ejpam-4931	116	185	l2	l2	NOUN
ejpam-4931	116	186	(	(	PUNCT
ejpam-4931	116	187	[	[	X
ejpam-4931	116	188	0	0	NUM
ejpam-4931	116	189	,	,	PUNCT
ejpam-4931	116	190	t	t	X
ejpam-4931	116	191	]	]	PUNCT
ejpam-4931	116	192	;	;	PUNCT
ejpam-4931	116	193	l2(ω	l2(ω	NUM
ejpam-4931	116	194	)	)	PUNCT
ejpam-4931	116	195	)	)	PUNCT
ejpam-4931	116	196	,	,	PUNCT
ejpam-4931	116	197	∇x	∇x	NOUN
ejpam-4931	116	198	√	√	ADP
ejpam-4931	116	199	ξ	ξ	PROPN
ejpam-4931	116	200	∈	∈	PROPN
ejpam-4931	116	201	l∞	l∞	NOUN
ejpam-4931	116	202	(	(	PUNCT
ejpam-4931	116	203	[	[	X
ejpam-4931	116	204	0	0	NUM
ejpam-4931	116	205	,	,	PUNCT
ejpam-4931	116	206	t	t	X
ejpam-4931	116	207	]	]	PUNCT
ejpam-4931	116	208	;	;	PUNCT
ejpam-4931	116	209	l2(ω	l2(ω	NUM
ejpam-4931	116	210	)	)	PUNCT
ejpam-4931	116	211	)	)	PUNCT
ejpam-4931	116	212	.	.	PUNCT
ejpam-4931	117	1	(	(	PUNCT
ejpam-4931	117	2	15	15	NUM
ejpam-4931	117	3	)	)	PUNCT
ejpam-4931	117	4	(	(	PUNCT
ejpam-4931	117	5	3	3	X
ejpam-4931	117	6	)	)	PUNCT
ejpam-4931	117	7	the	the	DET
ejpam-4931	117	8	mass	mass	ADJ
ejpam-4931	117	9	equation	equation	NOUN
ejpam-4931	117	10	is	be	AUX
ejpam-4931	117	11	valid	valid	ADJ
ejpam-4931	117	12	in	in	ADP
ejpam-4931	117	13	the	the	DET
ejpam-4931	117	14	sense	sense	NOUN
ejpam-4931	117	15	of	of	ADP
ejpam-4931	117	16	the	the	DET
ejpam-4931	117	17	distributions	distribution	NOUN
ejpam-4931	117	18	and	and	CCONJ
ejpam-4931	117	19	the	the	DET
ejpam-4931	117	20	following	follow	VERB
ejpam-4931	117	21	equality	equality	NOUN
ejpam-4931	117	22	holds:∫	holds:∫	PROPN
ejpam-4931	117	23	ω	ω	PROPN
ejpam-4931	117	24	m0φ(0	m0φ(0	PROPN
ejpam-4931	117	25	,	,	PUNCT
ejpam-4931	117	26	x	x	PRON
ejpam-4931	117	27	,	,	PUNCT
ejpam-4931	117	28	y)dxdy	y)dxdy	PROPN
ejpam-4931	118	1	−	−	PROPN
ejpam-4931	119	1	∫	∫	PROPN
ejpam-4931	119	2	ω	ω	PROPN
ejpam-4931	119	3	ξuφ(t	ξuφ(t	PROPN
ejpam-4931	119	4	,	,	PUNCT
ejpam-4931	119	5	x	x	X
ejpam-4931	119	6	,	,	PUNCT
ejpam-4931	119	7	y)dxdy	y)dxdy	PROPN
ejpam-4931	120	1	+	+	CCONJ
ejpam-4931	120	2	∫	∫	PROPN
ejpam-4931	120	3	t	t	PROPN
ejpam-4931	120	4	0	0	NUM
ejpam-4931	120	5	∫	∫	PROPN
ejpam-4931	120	6	ω	ω	PROPN
ejpam-4931	120	7	(	(	PUNCT
ejpam-4931	120	8	ξu∂tφ+	ξu∂tφ+	PROPN
ejpam-4931	120	9	ξu⊗	ξu⊗	PROPN
ejpam-4931	120	10	u	u	PROPN
ejpam-4931	120	11	:	:	PUNCT
ejpam-4931	120	12	∇xφ	∇xφ	NOUN
ejpam-4931	120	13	)	)	PUNCT
ejpam-4931	120	14	dxdydt	dxdydt	NOUN
ejpam-4931	120	15	+	+	CCONJ
ejpam-4931	121	1	∫	∫	PROPN
ejpam-4931	121	2	t	t	PROPN
ejpam-4931	121	3	0	0	NUM
ejpam-4931	122	1	∫	∫	PROPN
ejpam-4931	122	2	ω	ω	PROPN
ejpam-4931	122	3	(	(	PUNCT
ejpam-4931	122	4	ξuv∂yφ+	ξuv∂yφ+	PRON
ejpam-4931	122	5	ξ2divxφ	ξ2divxφ	VERB
ejpam-4931	122	6	)	)	PUNCT
ejpam-4931	122	7	dxdydt−	dxdydt−	VERB
ejpam-4931	122	8	∫	∫	PROPN
ejpam-4931	122	9	t	t	PROPN
ejpam-4931	122	10	0	0	NUM
ejpam-4931	122	11	∫	∫	PROPN
ejpam-4931	122	12	ω	ω	NUM
ejpam-4931	122	13	rξ|u|uφdxdydt	rξ|u|uφdxdydt	NOUN
ejpam-4931	122	14	−	−	PROPN
ejpam-4931	123	1	∫	∫	PROPN
ejpam-4931	124	1	t	t	PROPN
ejpam-4931	124	2	0	0	NUM
ejpam-4931	124	3	∫	∫	PROPN
ejpam-4931	124	4	ω	ω	PROPN
ejpam-4931	124	5	(	(	PUNCT
ejpam-4931	124	6	2ξdxu	2ξdxu	NUM
ejpam-4931	124	7	:	:	PUNCT
ejpam-4931	124	8	∇xφ+	∇xφ+	PROPN
ejpam-4931	124	9	ξ∂yu∂yφ	ξ∂yu∂yφ	PROPN
ejpam-4931	124	10	)	)	PUNCT
ejpam-4931	124	11	dxdydt	dxdydt	NOUN
ejpam-4931	124	12	=	=	SYM
ejpam-4931	124	13	0	0	NUM
ejpam-4931	124	14	,	,	PUNCT
ejpam-4931	124	15	(	(	PUNCT
ejpam-4931	124	16	16	16	NUM
ejpam-4931	124	17	)	)	PUNCT
ejpam-4931	124	18	for	for	ADP
ejpam-4931	124	19	any	any	DET
ejpam-4931	124	20	regular	regular	ADJ
ejpam-4931	124	21	test	test	NOUN
ejpam-4931	124	22	function	function	NOUN
ejpam-4931	124	23	φ(t	φ(t	PROPN
ejpam-4931	124	24	,	,	PUNCT
ejpam-4931	124	25	x	x	NOUN
ejpam-4931	124	26	,	,	PUNCT
ejpam-4931	124	27	y	y	NOUN
ejpam-4931	124	28	)	)	PUNCT
ejpam-4931	124	29	∈	∈	PROPN
ejpam-4931	124	30	c∞	c∞	PROPN
ejpam-4931	124	31	c	c	NOUN
ejpam-4931	124	32	(	(	PUNCT
ejpam-4931	124	33	[	[	X
ejpam-4931	124	34	0	0	NUM
ejpam-4931	124	35	,	,	PUNCT
ejpam-4931	124	36	t	t	X
ejpam-4931	124	37	]	]	X
ejpam-4931	124	38	×	×	PROPN
ejpam-4931	124	39	ω	ω	NUM
ejpam-4931	124	40	)	)	PUNCT
ejpam-4931	124	41	.	.	PUNCT
ejpam-4931	125	1	we	we	PRON
ejpam-4931	125	2	now	now	ADV
ejpam-4931	125	3	state	state	VERB
ejpam-4931	125	4	our	our	PRON
ejpam-4931	125	5	main	main	ADJ
ejpam-4931	125	6	results	result	NOUN
ejpam-4931	125	7	.	.	PUNCT
ejpam-4931	126	1	theorem	theorem	NOUN
ejpam-4931	126	2	1	1	NUM
ejpam-4931	126	3	.	.	PUNCT
ejpam-4931	126	4	suppose	suppose	VERB
ejpam-4931	126	5	that	that	SCONJ
ejpam-4931	126	6	the	the	DET
ejpam-4931	126	7	initial	initial	ADJ
ejpam-4931	126	8	data	data	NOUN
ejpam-4931	126	9	satisfies	satisfie	NOUN
ejpam-4931	126	10	(	(	PUNCT
ejpam-4931	126	11	10	10	NUM
ejpam-4931	126	12	)	)	PUNCT
ejpam-4931	126	13	.	.	PUNCT
ejpam-4931	127	1	then	then	ADV
ejpam-4931	127	2	,	,	PUNCT
ejpam-4931	127	3	∀	∀	X
ejpam-4931	127	4	t	t	X
ejpam-4931	127	5	>	>	X
ejpam-4931	127	6	0	0	NUM
ejpam-4931	127	7	,	,	PUNCT
ejpam-4931	127	8	(	(	PUNCT
ejpam-4931	127	9	5)-(7	5)-(7	NOUN
ejpam-4931	127	10	)	)	PUNCT
ejpam-4931	127	11	has	have	VERB
ejpam-4931	127	12	a	a	DET
ejpam-4931	127	13	weak	weak	ADJ
ejpam-4931	127	14	solution	solution	NOUN
ejpam-4931	127	15	(	(	PUNCT
ejpam-4931	127	16	ξ	ξ	X
ejpam-4931	127	17	,	,	PUNCT
ejpam-4931	127	18	u	u	NOUN
ejpam-4931	127	19	,	,	PUNCT
ejpam-4931	127	20	v	v	NOUN
ejpam-4931	127	21	)	)	PUNCT
ejpam-4931	127	22	in	in	ADP
ejpam-4931	127	23	the	the	DET
ejpam-4931	127	24	sense	sense	NOUN
ejpam-4931	127	25	of	of	ADP
ejpam-4931	127	26	definition	definition	NOUN
ejpam-4931	127	27	2.1	2.1	NUM
ejpam-4931	127	28	.	.	PUNCT
ejpam-4931	128	1	theorem	theorem	NOUN
ejpam-4931	128	2	2	2	NUM
ejpam-4931	128	3	.	.	PUNCT
ejpam-4931	129	1	under	under	ADP
ejpam-4931	129	2	an	an	DET
ejpam-4931	129	3	assumption	assumption	NOUN
ejpam-4931	129	4	similar	similar	ADJ
ejpam-4931	129	5	to	to	ADP
ejpam-4931	129	6	the	the	DET
ejpam-4931	129	7	theorem	theorem	NOUN
ejpam-4931	129	8	1	1	NUM
ejpam-4931	129	9	,	,	PUNCT
ejpam-4931	129	10	(	(	PUNCT
ejpam-4931	129	11	1)-(3	1)-(3	NOUN
ejpam-4931	129	12	)	)	PUNCT
ejpam-4931	129	13	and	and	CCONJ
ejpam-4931	129	14	(	(	PUNCT
ejpam-4931	129	15	6	6	NUM
ejpam-4931	129	16	)	)	PUNCT
ejpam-4931	129	17	−	−	PROPN
ejpam-4931	129	18	(	(	PUNCT
ejpam-4931	129	19	7	7	X
ejpam-4931	129	20	)	)	PUNCT
ejpam-4931	129	21	has	have	VERB
ejpam-4931	129	22	a	a	DET
ejpam-4931	129	23	weak	weak	ADJ
ejpam-4931	129	24	solution	solution	NOUN
ejpam-4931	129	25	(	(	PUNCT
ejpam-4931	129	26	ρ	ρ	NOUN
ejpam-4931	129	27	,	,	PUNCT
ejpam-4931	129	28	u	u	NOUN
ejpam-4931	129	29	,	,	PUNCT
ejpam-4931	129	30	v	v	NOUN
ejpam-4931	129	31	)	)	PUNCT
ejpam-4931	129	32	in	in	ADP
ejpam-4931	129	33	the	the	DET
ejpam-4931	129	34	sense	sense	NOUN
ejpam-4931	129	35	of	of	ADP
ejpam-4931	129	36	definition	definition	NOUN
ejpam-4931	129	37	2.1	2.1	NUM
ejpam-4931	129	38	,	,	PUNCT
ejpam-4931	129	39	if	if	SCONJ
ejpam-4931	129	40	we	we	PRON
ejpam-4931	129	41	replace	replace	VERB
ejpam-4931	129	42	(	(	PUNCT
ejpam-4931	129	43	ξ	ξ	PROPN
ejpam-4931	129	44	,	,	PUNCT
ejpam-4931	129	45	u	u	NOUN
ejpam-4931	129	46	,	,	PUNCT
ejpam-4931	129	47	v	v	NOUN
ejpam-4931	129	48	)	)	PUNCT
ejpam-4931	129	49	by	by	ADP
ejpam-4931	129	50	(	(	PUNCT
ejpam-4931	129	51	ρ	ρ	PROPN
ejpam-4931	129	52	,	,	PUNCT
ejpam-4931	129	53	u	u	NOUN
ejpam-4931	129	54	,	,	PUNCT
ejpam-4931	129	55	v	v	NOUN
ejpam-4931	129	56	)	)	PUNCT
ejpam-4931	129	57	accordingly	accordingly	ADV
ejpam-4931	129	58	.	.	PUNCT
ejpam-4931	130	1	3	3	X
ejpam-4931	130	2	.	.	X
ejpam-4931	130	3	approximation	approximation	NOUN
ejpam-4931	130	4	problem	problem	NOUN
ejpam-4931	130	5	in	in	ADP
ejpam-4931	130	6	this	this	DET
ejpam-4931	130	7	section	section	NOUN
ejpam-4931	130	8	,	,	PUNCT
ejpam-4931	130	9	we	we	PRON
ejpam-4931	130	10	construct	construct	VERB
ejpam-4931	130	11	in	in	ADP
ejpam-4931	130	12	a	a	DET
ejpam-4931	130	13	similar	similar	ADJ
ejpam-4931	130	14	way	way	NOUN
ejpam-4931	130	15	to	to	ADP
ejpam-4931	130	16	[	[	X
ejpam-4931	130	17	9	9	NUM
ejpam-4931	130	18	,	,	PUNCT
ejpam-4931	130	19	18	18	NUM
ejpam-4931	130	20	,	,	PUNCT
ejpam-4931	130	21	19	19	NUM
ejpam-4931	130	22	]	]	PUNCT
ejpam-4931	130	23	and	and	CCONJ
ejpam-4931	130	24	chapter	chapter	NOUN
ejpam-4931	130	25	7	7	NUM
ejpam-4931	130	26	of	of	ADP
ejpam-4931	130	27	[	[	X
ejpam-4931	130	28	4	4	X
ejpam-4931	130	29	]	]	PUNCT
ejpam-4931	130	30	the	the	DET
ejpam-4931	130	31	faedogalerkin	faedogalerkin	NOUN
ejpam-4931	130	32	scheme	scheme	NOUN
ejpam-4931	130	33	of	of	ADP
ejpam-4931	130	34	the	the	DET
ejpam-4931	130	35	approximate	approximate	ADJ
ejpam-4931	130	36	system	system	NOUN
ejpam-4931	130	37	(	(	PUNCT
ejpam-4931	130	38	17	17	NUM
ejpam-4931	130	39	)	)	PUNCT
ejpam-4931	130	40	below	below	ADV
ejpam-4931	130	41	,	,	PUNCT
ejpam-4931	130	42	and	and	CCONJ
ejpam-4931	130	43	prove	prove	VERB
ejpam-4931	130	44	the	the	DET
ejpam-4931	130	45	global	global	ADJ
ejpam-4931	130	46	existence	existence	NOUN
ejpam-4931	130	47	of	of	ADP
ejpam-4931	130	48	solutions	solution	NOUN
ejpam-4931	130	49	to	to	ADP
ejpam-4931	130	50	this	this	DET
ejpam-4931	130	51	system	system	NOUN
ejpam-4931	130	52	.	.	PUNCT
ejpam-4931	131	1	then	then	ADV
ejpam-4931	131	2	,	,	PUNCT
ejpam-4931	131	3	we	we	PRON
ejpam-4931	131	4	will	will	AUX
ejpam-4931	131	5	show	show	VERB
ejpam-4931	131	6	the	the	DET
ejpam-4931	131	7	global	global	ADJ
ejpam-4931	131	8	existence	existence	NOUN
ejpam-4931	131	9	of	of	ADP
ejpam-4931	131	10	weak	weak	ADJ
ejpam-4931	131	11	solutions	solution	NOUN
ejpam-4931	131	12	to	to	ADP
ejpam-4931	131	13	the	the	DET
ejpam-4931	131	14	problem	problem	NOUN
ejpam-4931	131	15	(	(	PUNCT
ejpam-4931	131	16	1)-(3	1)-(3	NUM
ejpam-4931	131	17	)	)	PUNCT
ejpam-4931	131	18	(	(	PUNCT
ejpam-4931	131	19	6)−	6)−	NUM
ejpam-4931	131	20	(	(	PUNCT
ejpam-4931	131	21	7	7	NUM
ejpam-4931	131	22	)	)	PUNCT
ejpam-4931	131	23	by	by	ADP
ejpam-4931	131	24	making	make	VERB
ejpam-4931	131	25	the	the	DET
ejpam-4931	131	26	parameters	parameter	NOUN
ejpam-4931	131	27	of	of	ADP
ejpam-4931	131	28	our	our	PRON
ejpam-4931	131	29	approximate	approximate	ADJ
ejpam-4931	131	30	system	system	NOUN
ejpam-4931	131	31	tend	tend	VERB
ejpam-4931	131	32	to	to	PART
ejpam-4931	131	33	0	0	NUM
ejpam-4931	131	34	step	step	NOUN
ejpam-4931	131	35	by	by	ADP
ejpam-4931	131	36	step	step	NOUN
ejpam-4931	131	37	.	.	PUNCT
ejpam-4931	132	1	j.	j.	PROPN
ejpam-4931	132	2	ouya	ouya	PROPN
ejpam-4931	132	3	,	,	PUNCT
ejpam-4931	132	4	a.	a.	NOUN
ejpam-4931	132	5	ouédraogo	ouédraogo	PROPN
ejpam-4931	132	6	/	/	SYM
ejpam-4931	132	7	eur	eur	PROPN
ejpam-4931	132	8	.	.	PUNCT
ejpam-4931	133	1	j.	j.	PROPN
ejpam-4931	133	2	pure	pure	PROPN
ejpam-4931	133	3	appl	appl	PROPN
ejpam-4931	133	4	.	.	PROPN
ejpam-4931	133	5	math	math	PROPN
ejpam-4931	133	6	,	,	PUNCT
ejpam-4931	133	7	16	16	NUM
ejpam-4931	133	8	(	(	PUNCT
ejpam-4931	133	9	4	4	NUM
ejpam-4931	133	10	)	)	PUNCT
ejpam-4931	133	11	(	(	PUNCT
ejpam-4931	133	12	2023	2023	NUM
ejpam-4931	133	13	)	)	PUNCT
ejpam-4931	133	14	,	,	PUNCT
ejpam-4931	133	15	2247	2247	NUM
ejpam-4931	133	16	-	-	SYM
ejpam-4931	133	17	2285	2285	NUM
ejpam-4931	133	18	2253	2253	NUM
ejpam-4931	133	19	3.1	3.1	NUM
ejpam-4931	133	20	.	.	PUNCT
ejpam-4931	134	1	faedo	faedo	PROPN
ejpam-4931	134	2	-	-	PUNCT
ejpam-4931	134	3	galerkin	galerkin	PROPN
ejpam-4931	134	4	scheme	scheme	NOUN
ejpam-4931	134	5	in	in	ADP
ejpam-4931	134	6	order	order	NOUN
ejpam-4931	134	7	to	to	PART
ejpam-4931	134	8	prove	prove	VERB
ejpam-4931	134	9	the	the	DET
ejpam-4931	134	10	global	global	ADJ
ejpam-4931	134	11	existence	existence	NOUN
ejpam-4931	134	12	of	of	ADP
ejpam-4931	134	13	weak	weak	ADJ
ejpam-4931	134	14	solutions	solution	NOUN
ejpam-4931	134	15	for	for	ADP
ejpam-4931	134	16	the	the	DET
ejpam-4931	134	17	compressible	compressible	ADJ
ejpam-4931	134	18	primitive	primitive	ADJ
ejpam-4931	134	19	equations	equation	NOUN
ejpam-4931	134	20	,	,	PUNCT
ejpam-4931	134	21	we	we	PRON
ejpam-4931	134	22	consider	consider	VERB
ejpam-4931	134	23	the	the	DET
ejpam-4931	134	24	following	follow	VERB
ejpam-4931	134	25	approximate	approximate	ADJ
ejpam-4931	134	26	system	system	NOUN
ejpam-4931	134	27	:	:	PUNCT
ejpam-4931	134	28			X
ejpam-4931	134	29	∂tξ	∂tξ	VERB
ejpam-4931	134	30	+	+	CCONJ
ejpam-4931	134	31	divx(ξu	divx(ξu	NOUN
ejpam-4931	134	32	)	)	PUNCT
ejpam-4931	135	1	+	+	CCONJ
ejpam-4931	135	2	∂y	∂y	SYM
ejpam-4931	135	3	(	(	PUNCT
ejpam-4931	135	4	ξv	ξv	NOUN
ejpam-4931	135	5	)	)	PUNCT
ejpam-4931	135	6	=	=	SYM
ejpam-4931	135	7	ϵ∆xξ	ϵ∆xξ	NOUN
ejpam-4931	135	8	,	,	PUNCT
ejpam-4931	135	9	∂t(ξu	∂t(ξu	X
ejpam-4931	135	10	)	)	PUNCT
ejpam-4931	135	11	+	+	CCONJ
ejpam-4931	135	12	divx(ξu⊗	divx(ξu⊗	NOUN
ejpam-4931	135	13	u	u	NOUN
ejpam-4931	135	14	)	)	PUNCT
ejpam-4931	135	15	+	+	CCONJ
ejpam-4931	135	16	∂y(ξuv	∂y(ξuv	X
ejpam-4931	135	17	)	)	PUNCT
ejpam-4931	136	1	+	+	X
ejpam-4931	136	2	∇xξ	∇xξ	PROPN
ejpam-4931	136	3	2	2	NUM
ejpam-4931	136	4	+	+	CCONJ
ejpam-4931	136	5	rξ|u|u+	rξ|u|u+	ADJ
ejpam-4931	136	6	r1u	r1u	NOUN
ejpam-4931	136	7	+	+	PROPN
ejpam-4931	136	8	α∆2	α∆2	INTJ
ejpam-4931	136	9	xu	xu	PROPN
ejpam-4931	136	10	=	=	SYM
ejpam-4931	136	11	divx	divx	PROPN
ejpam-4931	136	12	(	(	PUNCT
ejpam-4931	136	13	2ξd(u	2ξd(u	NUM
ejpam-4931	136	14	)	)	PUNCT
ejpam-4931	136	15	)	)	PUNCT
ejpam-4931	137	1	+	+	CCONJ
ejpam-4931	137	2	∂y	∂y	SYM
ejpam-4931	137	3	(	(	PUNCT
ejpam-4931	137	4	ξ∂yu	ξ∂yu	PROPN
ejpam-4931	137	5	)	)	PUNCT
ejpam-4931	137	6	+	+	CCONJ
ejpam-4931	137	7	ϵ∇xξ	ϵ∇xξ	PROPN
ejpam-4931	137	8	·	·	PUNCT
ejpam-4931	137	9	∇xu	∇xu	PROPN
ejpam-4931	138	1	+	+	ADJ
ejpam-4931	138	2	r2∇xξ	r2∇xξ	NOUN
ejpam-4931	138	3	−β	−β	NOUN
ejpam-4931	138	4	+	+	CCONJ
ejpam-4931	138	5	k1ξ∇x	k1ξ∇x	PROPN
ejpam-4931	138	6	(	(	PUNCT
ejpam-4931	138	7	∆x	∆x	PROPN
ejpam-4931	138	8	√	√	PROPN
ejpam-4931	138	9	ξ√	ξ√	PROPN
ejpam-4931	138	10	ξ	ξ	PROPN
ejpam-4931	138	11	)	)	PUNCT
ejpam-4931	139	1	+	+	CCONJ
ejpam-4931	139	2	δξ∇x∆	δξ∇x∆	PROPN
ejpam-4931	139	3	5	5	NUM
ejpam-4931	139	4	xξ	xξ	NOUN
ejpam-4931	139	5	,	,	PUNCT
ejpam-4931	139	6	∂yξ	∂yξ	PROPN
ejpam-4931	139	7	=	=	SYM
ejpam-4931	139	8	0	0	NUM
ejpam-4931	139	9	,	,	PUNCT
ejpam-4931	139	10	(	(	PUNCT
ejpam-4931	139	11	17	17	NUM
ejpam-4931	139	12	)	)	PUNCT
ejpam-4931	139	13	where	where	SCONJ
ejpam-4931	139	14	(	(	PUNCT
ejpam-4931	139	15	x	x	NOUN
ejpam-4931	139	16	,	,	PUNCT
ejpam-4931	139	17	y	y	NOUN
ejpam-4931	139	18	)	)	PUNCT
ejpam-4931	139	19	∈	∈	PROPN
ejpam-4931	139	20	ω	ω	PROPN
ejpam-4931	139	21	,	,	PUNCT
ejpam-4931	139	22	t	t	PROPN
ejpam-4931	139	23	≥	≥	PROPN
ejpam-4931	139	24	0	0	NUM
ejpam-4931	139	25	,	,	PUNCT
ejpam-4931	139	26	β	β	X
ejpam-4931	139	27	≥	≥	NUM
ejpam-4931	139	28	10	10	NUM
ejpam-4931	139	29	and	and	CCONJ
ejpam-4931	139	30	the	the	DET
ejpam-4931	139	31	vertical	vertical	ADJ
ejpam-4931	139	32	velocity	velocity	NOUN
ejpam-4931	139	33	v	v	NOUN
ejpam-4931	139	34	can	can	AUX
ejpam-4931	139	35	be	be	AUX
ejpam-4931	139	36	expressed	express	VERB
ejpam-4931	139	37	as	as	ADP
ejpam-4931	139	38	v(y	v(y	NUM
ejpam-4931	139	39	)	)	PUNCT
ejpam-4931	139	40	=	=	PUNCT
ejpam-4931	139	41	−divx(ξũ(y	−divx(ξũ(y	PROPN
ejpam-4931	139	42	)	)	PUNCT
ejpam-4931	139	43	)	)	PUNCT
ejpam-4931	140	1	ξ	ξ	X
ejpam-4931	141	1	+	+	NUM
ejpam-4931	141	2	y	y	PROPN
ejpam-4931	141	3	divx(ξū	divx(ξū	PROPN
ejpam-4931	141	4	)	)	PUNCT
ejpam-4931	141	5	ξ	ξ	X
ejpam-4931	141	6	.	.	PUNCT
ejpam-4931	142	1	in	in	ADP
ejpam-4931	142	2	order	order	NOUN
ejpam-4931	142	3	to	to	PART
ejpam-4931	142	4	keep	keep	VERB
ejpam-4931	142	5	the	the	DET
ejpam-4931	142	6	density	density	NOUN
ejpam-4931	142	7	bounded	bound	VERB
ejpam-4931	142	8	,	,	PUNCT
ejpam-4931	142	9	we	we	PRON
ejpam-4931	142	10	add	add	VERB
ejpam-4931	142	11	the	the	DET
ejpam-4931	142	12	extra	extra	ADJ
ejpam-4931	142	13	terms	term	NOUN
ejpam-4931	142	14	ϵ∇xξ	ϵ∇xξ	ADP
ejpam-4931	142	15	−β	−β	PROPN
ejpam-4931	142	16	and	and	CCONJ
ejpam-4931	142	17	δξ∇x∆	δξ∇x∆	PRON
ejpam-4931	142	18	5	5	NUM
ejpam-4931	142	19	xξ	xξ	NOUN
ejpam-4931	142	20	.	.	PUNCT
ejpam-4931	143	1	this	this	PRON
ejpam-4931	143	2	allows	allow	VERB
ejpam-4931	143	3	us	we	PRON
ejpam-4931	143	4	to	to	PART
ejpam-4931	143	5	take	take	VERB
ejpam-4931	143	6	∇	∇	X
ejpam-4931	143	7	(	(	PUNCT
ejpam-4931	143	8	ln	ln	NOUN
ejpam-4931	143	9	ξ	ξ	NOUN
ejpam-4931	143	10	)	)	PUNCT
ejpam-4931	143	11	as	as	ADP
ejpam-4931	143	12	a	a	DET
ejpam-4931	143	13	test	test	NOUN
ejpam-4931	143	14	function	function	NOUN
ejpam-4931	143	15	to	to	PART
ejpam-4931	143	16	derive	derive	VERB
ejpam-4931	143	17	the	the	DET
ejpam-4931	143	18	bresch	bresch	NOUN
ejpam-4931	143	19	-	-	PUNCT
ejpam-4931	143	20	desjardins	desjardin	NOUN
ejpam-4931	143	21	entropy	entropy	NOUN
ejpam-4931	143	22	.	.	PUNCT
ejpam-4931	144	1	moreover	moreover	ADV
ejpam-4931	144	2	,	,	PUNCT
ejpam-4931	144	3	the	the	DET
ejpam-4931	144	4	term	term	NOUN
ejpam-4931	144	5	r1u	r1u	NOUN
ejpam-4931	144	6	is	be	AUX
ejpam-4931	144	7	used	use	VERB
ejpam-4931	144	8	to	to	PART
ejpam-4931	144	9	control	control	VERB
ejpam-4931	144	10	the	the	DET
ejpam-4931	144	11	density	density	NOUN
ejpam-4931	144	12	near	near	ADP
ejpam-4931	144	13	the	the	DET
ejpam-4931	144	14	vacuum	vacuum	NOUN
ejpam-4931	144	15	,	,	PUNCT
ejpam-4931	144	16	and	and	CCONJ
ejpam-4931	144	17	rξ|u|u	rξ|u|u	NOUN
ejpam-4931	144	18	is	be	AUX
ejpam-4931	144	19	used	use	VERB
ejpam-4931	144	20	to	to	PART
ejpam-4931	144	21	make	make	VERB
ejpam-4931	144	22	sure	sure	ADJ
ejpam-4931	144	23	that	that	SCONJ
ejpam-4931	144	24	√	√	ADJ
ejpam-4931	144	25	ξu	ξu	PROPN
ejpam-4931	144	26	is	be	AUX
ejpam-4931	144	27	strong	strong	ADJ
ejpam-4931	144	28	convergence	convergence	NOUN
ejpam-4931	144	29	in	in	ADP
ejpam-4931	144	30	l2	l2	NOUN
ejpam-4931	144	31	(	(	PUNCT
ejpam-4931	144	32	[	[	X
ejpam-4931	144	33	0	0	NUM
ejpam-4931	144	34	,	,	PUNCT
ejpam-4931	144	35	t	t	X
ejpam-4931	144	36	]	]	PUNCT
ejpam-4931	144	37	;	;	PUNCT
ejpam-4931	144	38	l2(ω	l2(ω	NUM
ejpam-4931	144	39	)	)	PUNCT
ejpam-4931	144	40	)	)	PUNCT
ejpam-4931	144	41	.	.	PUNCT
ejpam-4931	145	1	the	the	DET
ejpam-4931	145	2	term	term	NOUN
ejpam-4931	145	3	∆x	∆x	PROPN
ejpam-4931	145	4	√	√	NOUN
ejpam-4931	145	5	ξ√	ξ√	PROPN
ejpam-4931	145	6	ξ	ξ	PROPN
ejpam-4931	145	7	is	be	AUX
ejpam-4931	145	8	called	call	VERB
ejpam-4931	145	9	bohm	bohm	PROPN
ejpam-4931	145	10	potential	potential	NOUN
ejpam-4931	145	11	which	which	PRON
ejpam-4931	145	12	can	can	AUX
ejpam-4931	145	13	be	be	AUX
ejpam-4931	145	14	interpreted	interpret	VERB
ejpam-4931	145	15	as	as	ADP
ejpam-4931	145	16	a	a	DET
ejpam-4931	145	17	quantum	quantum	NOUN
ejpam-4931	145	18	potential	potential	NOUN
ejpam-4931	145	19	.	.	PUNCT
ejpam-4931	146	1	for	for	ADP
ejpam-4931	146	2	t	t	PROPN
ejpam-4931	146	3	>	>	X
ejpam-4931	146	4	0	0	PROPN
ejpam-4931	146	5	,	,	PUNCT
ejpam-4931	146	6	we	we	PRON
ejpam-4931	146	7	introduce	introduce	VERB
ejpam-4931	146	8	a	a	DET
ejpam-4931	146	9	finite	finite	ADJ
ejpam-4931	146	10	dimensional	dimensional	ADJ
ejpam-4931	146	11	space	space	NOUN
ejpam-4931	146	12	xn	xn	PROPN
ejpam-4931	147	1	=	=	SYM
ejpam-4931	147	2	span{ψ1	span{ψ1	PROPN
ejpam-4931	147	3	,	,	PUNCT
ejpam-4931	147	4	.	.	PUNCT
ejpam-4931	147	5	.	.	PUNCT
ejpam-4931	148	1	.	.	PUNCT
ejpam-4931	149	1	,	,	PUNCT
ejpam-4931	149	2	ψn	ψn	ADP
ejpam-4931	149	3	}	}	PUNCT
ejpam-4931	149	4	,	,	PUNCT
ejpam-4931	149	5	n	n	PROPN
ejpam-4931	149	6	∈	∈	PROPN
ejpam-4931	149	7	n	n	CCONJ
ejpam-4931	149	8	,	,	PUNCT
ejpam-4931	149	9	where	where	SCONJ
ejpam-4931	149	10	ψi	ψi	NOUN
ejpam-4931	149	11	is	be	AUX
ejpam-4931	149	12	the	the	DET
ejpam-4931	149	13	eigenfunction	eigenfunction	NOUN
ejpam-4931	149	14	of	of	ADP
ejpam-4931	149	15	the	the	DET
ejpam-4931	149	16	laplacian	laplacian	NOUN
ejpam-4931	149	17	:	:	PUNCT
ejpam-4931	149	18	−∆ψi	−∆ψi	NOUN
ejpam-4931	149	19	=	=	PUNCT
ejpam-4931	149	20	λiψi	λiψi	NOUN
ejpam-4931	149	21	in	in	ADP
ejpam-4931	149	22	ω	ω	PROPN
ejpam-4931	149	23	with	with	ADP
ejpam-4931	149	24	λi	λi	ADP
ejpam-4931	149	25	the	the	DET
ejpam-4931	149	26	eigenvalue	eigenvalue	NOUN
ejpam-4931	149	27	for	for	ADP
ejpam-4931	149	28	ψi	ψi	NOUN
ejpam-4931	149	29	.	.	PUNCT
ejpam-4931	150	1	we	we	PRON
ejpam-4931	150	2	have	have	VERB
ejpam-4931	150	3	the	the	DET
ejpam-4931	150	4	periodic	periodic	ADJ
ejpam-4931	150	5	conditions	condition	NOUN
ejpam-4931	150	6	on	on	ADP
ejpam-4931	150	7	∂ωx	∂ωx	PROPN
ejpam-4931	150	8	:	:	PUNCT
ejpam-4931	150	9	∂yψi	∂yψi	NUM
ejpam-4931	150	10	/	/	SYM
ejpam-4931	150	11	y=0	y=0	X
ejpam-4931	150	12	=	=	SYM
ejpam-4931	150	13	∂yψi	∂yψi	NUM
ejpam-4931	150	14	/	/	SYM
ejpam-4931	150	15	y=1	y=1	SYM
ejpam-4931	151	1	=	=	SYM
ejpam-4931	151	2	0	0	X
ejpam-4931	151	3	.	.	PUNCT
ejpam-4931	151	4	{	{	PUNCT
ejpam-4931	151	5	ψi	ψi	NOUN
ejpam-4931	151	6	}	}	PUNCT
ejpam-4931	151	7	is	be	AUX
ejpam-4931	151	8	an	an	DET
ejpam-4931	151	9	orthonormal	orthonormal	ADJ
ejpam-4931	151	10	basis	basis	NOUN
ejpam-4931	151	11	of	of	ADP
ejpam-4931	151	12	l2(ω	l2(ω	NOUN
ejpam-4931	151	13	)	)	PUNCT
ejpam-4931	151	14	which	which	PRON
ejpam-4931	151	15	is	be	AUX
ejpam-4931	151	16	also	also	ADV
ejpam-4931	151	17	an	an	DET
ejpam-4931	151	18	orthogonal	orthogonal	ADJ
ejpam-4931	151	19	basis	basis	NOUN
ejpam-4931	151	20	of	of	ADP
ejpam-4931	151	21	h2(ω	h2(ω	NOUN
ejpam-4931	151	22	)	)	PUNCT
ejpam-4931	151	23	.	.	PUNCT
ejpam-4931	152	1	let	let	VERB
ejpam-4931	152	2	(	(	PUNCT
ejpam-4931	152	3	ξ0	ξ0	ADJ
ejpam-4931	152	4	,	,	PUNCT
ejpam-4931	152	5	u0	u0	ADJ
ejpam-4931	152	6	)	)	PUNCT
ejpam-4931	152	7	∈	∈	PROPN
ejpam-4931	152	8	c∞(ω	c∞(ω	NOUN
ejpam-4931	152	9	)	)	PUNCT
ejpam-4931	152	10	be	be	VERB
ejpam-4931	152	11	some	some	DET
ejpam-4931	152	12	initial	initial	ADJ
ejpam-4931	152	13	data	datum	NOUN
ejpam-4931	152	14	satisfying	satisfy	VERB
ejpam-4931	152	15	ξ0	ξ0	PROPN
ejpam-4931	152	16	≥	≥	NOUN
ejpam-4931	152	17	λ	λ	NOUN
ejpam-4931	152	18	for	for	ADP
ejpam-4931	152	19	some	some	DET
ejpam-4931	152	20	λ	λ	PROPN
ejpam-4931	152	21	>	>	X
ejpam-4931	152	22	0	0	NUM
ejpam-4931	152	23	.	.	PUNCT
ejpam-4931	153	1	we	we	PRON
ejpam-4931	153	2	notice	notice	VERB
ejpam-4931	153	3	that	that	SCONJ
ejpam-4931	153	4	the	the	DET
ejpam-4931	153	5	velocity	velocity	NOUN
ejpam-4931	153	6	u	u	NOUN
ejpam-4931	153	7	∈	∈	NOUN
ejpam-4931	153	8	c	c	X
ejpam-4931	153	9	(	(	PUNCT
ejpam-4931	153	10	[	[	X
ejpam-4931	153	11	0	0	NUM
ejpam-4931	153	12	,	,	PUNCT
ejpam-4931	153	13	t	t	X
ejpam-4931	153	14	]	]	PUNCT
ejpam-4931	153	15	;	;	PUNCT
ejpam-4931	153	16	xn	xn	PROPN
ejpam-4931	153	17	)	)	PUNCT
ejpam-4931	153	18	is	be	AUX
ejpam-4931	153	19	given	give	VERB
ejpam-4931	153	20	by	by	ADP
ejpam-4931	153	21	u(x	u(x	NOUN
ejpam-4931	153	22	,	,	PUNCT
ejpam-4931	153	23	y	y	PROPN
ejpam-4931	153	24	,	,	PUNCT
ejpam-4931	153	25	t	t	PROPN
ejpam-4931	153	26	)	)	PUNCT
ejpam-4931	154	1	=	=	SYM
ejpam-4931	155	1	n∑	n∑	NOUN
ejpam-4931	155	2	i=1	i=1	PROPN
ejpam-4931	156	1	λi(t)ψi(x	λi(t)ψi(x	PROPN
ejpam-4931	156	2	,	,	PUNCT
ejpam-4931	156	3	y	y	PROPN
ejpam-4931	156	4	)	)	PUNCT
ejpam-4931	156	5	,	,	PUNCT
ejpam-4931	156	6	(	(	PUNCT
ejpam-4931	156	7	t	t	PROPN
ejpam-4931	156	8	,	,	PUNCT
ejpam-4931	156	9	x	x	NOUN
ejpam-4931	156	10	,	,	PUNCT
ejpam-4931	156	11	y	y	NOUN
ejpam-4931	156	12	)	)	PUNCT
ejpam-4931	156	13	∈	∈	PROPN
ejpam-4931	157	1	[	[	X
ejpam-4931	157	2	0	0	NUM
ejpam-4931	157	3	,	,	PUNCT
ejpam-4931	157	4	t	t	X
ejpam-4931	157	5	]	]	X
ejpam-4931	157	6	×	×	PROPN
ejpam-4931	157	7	ω	ω	NOUN
ejpam-4931	157	8	for	for	ADP
ejpam-4931	157	9	some	some	DET
ejpam-4931	157	10	functions	function	NOUN
ejpam-4931	157	11	λi(t	λi(t	NOUN
ejpam-4931	157	12	)	)	PUNCT
ejpam-4931	157	13	,	,	PUNCT
ejpam-4931	157	14	and	and	CCONJ
ejpam-4931	157	15	the	the	DET
ejpam-4931	157	16	norm	norm	NOUN
ejpam-4931	157	17	of	of	ADP
ejpam-4931	157	18	u	u	NOUN
ejpam-4931	157	19	in	in	ADP
ejpam-4931	157	20	c	c	PROPN
ejpam-4931	157	21	(	(	PUNCT
ejpam-4931	157	22	[	[	X
ejpam-4931	157	23	0	0	NUM
ejpam-4931	157	24	,	,	PUNCT
ejpam-4931	157	25	t	t	X
ejpam-4931	157	26	]	]	PUNCT
ejpam-4931	157	27	;	;	PUNCT
ejpam-4931	157	28	xn	xn	X
ejpam-4931	157	29	)	)	PUNCT
ejpam-4931	157	30	can	can	AUX
ejpam-4931	157	31	be	be	AUX
ejpam-4931	157	32	written	write	VERB
ejpam-4931	157	33	as	as	ADP
ejpam-4931	157	34	∥u∥c([0,t	∥u∥c([0,t	PROPN
ejpam-4931	157	35	]	]	PUNCT
ejpam-4931	157	36	;	;	PUNCT
ejpam-4931	157	37	xn(ω))=	xn(ω))=	PROPN
ejpam-4931	157	38	sup	sup	PROPN
ejpam-4931	157	39	t∈[0,t	t∈[0,t	PROPN
ejpam-4931	157	40	]	]	PUNCT
ejpam-4931	157	41	n∑	n∑	PROPN
ejpam-4931	157	42	i=1	i=1	PROPN
ejpam-4931	157	43	|λi(t)|	|λi(t)|	PROPN
ejpam-4931	157	44	.	.	PUNCT
ejpam-4931	158	1	since	since	SCONJ
ejpam-4931	158	2	xn	xn	PROPN
ejpam-4931	158	3	is	be	AUX
ejpam-4931	158	4	a	a	DET
ejpam-4931	158	5	finite	finite	ADJ
ejpam-4931	158	6	-	-	ADJ
ejpam-4931	158	7	dimensional	dimensional	ADJ
ejpam-4931	158	8	space	space	NOUN
ejpam-4931	158	9	,	,	PUNCT
ejpam-4931	158	10	all	all	DET
ejpam-4931	158	11	the	the	DET
ejpam-4931	158	12	norms	norm	NOUN
ejpam-4931	158	13	are	be	AUX
ejpam-4931	158	14	equivalent	equivalent	ADJ
ejpam-4931	158	15	on	on	ADP
ejpam-4931	158	16	xn	xn	PROPN
ejpam-4931	158	17	.	.	PUNCT
ejpam-4931	159	1	hence	hence	ADV
ejpam-4931	159	2	,	,	PUNCT
ejpam-4931	159	3	u	u	PRON
ejpam-4931	159	4	can	can	AUX
ejpam-4931	159	5	be	be	AUX
ejpam-4931	159	6	bounded	bound	VERB
ejpam-4931	159	7	in	in	ADP
ejpam-4931	159	8	c	c	PROPN
ejpam-4931	159	9	(	(	PUNCT
ejpam-4931	159	10	[	[	X
ejpam-4931	159	11	0	0	NUM
ejpam-4931	159	12	,	,	PUNCT
ejpam-4931	159	13	t	t	X
ejpam-4931	159	14	]	]	PUNCT
ejpam-4931	159	15	;	;	PUNCT
ejpam-4931	159	16	ck(ω	ck(ω	NUM
ejpam-4931	159	17	)	)	PUNCT
ejpam-4931	159	18	)	)	PUNCT
ejpam-4931	159	19	for	for	ADP
ejpam-4931	159	20	all	all	DET
ejpam-4931	159	21	k	k	PROPN
ejpam-4931	159	22	∈	∈	PROPN
ejpam-4931	159	23	n	n	CCONJ
ejpam-4931	159	24	,	,	PUNCT
ejpam-4931	159	25	then	then	ADV
ejpam-4931	159	26	there	there	PRON
ejpam-4931	159	27	exists	exist	VERB
ejpam-4931	159	28	a	a	DET
ejpam-4931	159	29	constant	constant	ADJ
ejpam-4931	159	30	c	c	NOUN
ejpam-4931	159	31	>	>	X
ejpam-4931	159	32	0	0	PUNCT
ejpam-4931	160	1	dependent	dependent	ADJ
ejpam-4931	160	2	on	on	ADP
ejpam-4931	160	3	k	k	PROPN
ejpam-4931	160	4	such	such	ADJ
ejpam-4931	160	5	that	that	SCONJ
ejpam-4931	160	6	∥u∥c([0,t	∥u∥c([0,t	PROPN
ejpam-4931	160	7	]	]	X
ejpam-4931	160	8	;	;	PUNCT
ejpam-4931	160	9	ck(ω))≤	ck(ω))≤	PROPN
ejpam-4931	160	10	c∥u∥c([0,t	c∥u∥c([0,t	NOUN
ejpam-4931	160	11	]	]	X
ejpam-4931	160	12	;	;	PUNCT
ejpam-4931	160	13	l2(ω	l2(ω	NUM
ejpam-4931	160	14	)	)	PUNCT
ejpam-4931	160	15	)	)	PUNCT
ejpam-4931	160	16	.	.	PUNCT
ejpam-4931	161	1	(	(	PUNCT
ejpam-4931	161	2	18	18	NUM
ejpam-4931	161	3	)	)	PUNCT
ejpam-4931	161	4	now	now	ADV
ejpam-4931	161	5	,	,	PUNCT
ejpam-4931	161	6	we	we	PRON
ejpam-4931	161	7	approach	approach	VERB
ejpam-4931	161	8	the	the	DET
ejpam-4931	161	9	continuity	continuity	NOUN
ejpam-4931	161	10	equation	equation	NOUN
ejpam-4931	161	11	by	by	ADP
ejpam-4931	161	12	adding	add	VERB
ejpam-4931	161	13	a	a	DET
ejpam-4931	161	14	viscosity	viscosity	NOUN
ejpam-4931	161	15	term	term	NOUN
ejpam-4931	161	16	,	,	PUNCT
ejpam-4931	161	17	ϵ∆xξ	ϵ∆xξ	NOUN
ejpam-4931	161	18	:	:	PUNCT
ejpam-4931	161	19	∂tξ	∂tξ	NOUN
ejpam-4931	161	20	+	+	CCONJ
ejpam-4931	161	21	divx(ξu	divx(ξu	NOUN
ejpam-4931	161	22	)	)	PUNCT
ejpam-4931	161	23	+	+	SYM
ejpam-4931	161	24	∂y(ξv	∂y(ξv	NOUN
ejpam-4931	161	25	)	)	PUNCT
ejpam-4931	161	26	=	=	SYM
ejpam-4931	161	27	∂tξ	∂tξ	PROPN
ejpam-4931	161	28	+	+	CCONJ
ejpam-4931	161	29	divx(ξū	divx(ξū	NOUN
ejpam-4931	161	30	)	)	PUNCT
ejpam-4931	161	31	=	=	SYM
ejpam-4931	162	1	ϵ∆xξ	ϵ∆xξ	NOUN
ejpam-4931	162	2	,	,	PUNCT
ejpam-4931	162	3	ξ0	ξ0	PROPN
ejpam-4931	162	4	∈	∈	PROPN
ejpam-4931	162	5	c∞(ω	c∞(ω	NOUN
ejpam-4931	162	6	)	)	PUNCT
ejpam-4931	162	7	,	,	PUNCT
ejpam-4931	162	8	ξ0	ξ0	PROPN
ejpam-4931	162	9	≥	≥	X
ejpam-4931	162	10	λ	λ	X
ejpam-4931	162	11	>	>	X
ejpam-4931	162	12	0	0	NUM
ejpam-4931	162	13	,	,	PUNCT
ejpam-4931	162	14	(	(	PUNCT
ejpam-4931	162	15	19	19	NUM
ejpam-4931	162	16	)	)	PUNCT
ejpam-4931	162	17	j.	j.	PROPN
ejpam-4931	162	18	ouya	ouya	PROPN
ejpam-4931	162	19	,	,	PUNCT
ejpam-4931	162	20	a.	a.	NOUN
ejpam-4931	162	21	ouédraogo	ouédraogo	PROPN
ejpam-4931	162	22	/	/	SYM
ejpam-4931	162	23	eur	eur	PROPN
ejpam-4931	162	24	.	.	PUNCT
ejpam-4931	163	1	j.	j.	PROPN
ejpam-4931	163	2	pure	pure	PROPN
ejpam-4931	163	3	appl	appl	PROPN
ejpam-4931	163	4	.	.	PROPN
ejpam-4931	163	5	math	math	PROPN
ejpam-4931	163	6	,	,	PUNCT
ejpam-4931	163	7	16	16	NUM
ejpam-4931	163	8	(	(	PUNCT
ejpam-4931	163	9	4	4	NUM
ejpam-4931	163	10	)	)	PUNCT
ejpam-4931	163	11	(	(	PUNCT
ejpam-4931	163	12	2023	2023	NUM
ejpam-4931	163	13	)	)	PUNCT
ejpam-4931	163	14	,	,	PUNCT
ejpam-4931	163	15	2247	2247	NUM
ejpam-4931	163	16	-	-	SYM
ejpam-4931	163	17	2285	2285	NUM
ejpam-4931	163	18	2254	2254	NUM
ejpam-4931	163	19	where	where	SCONJ
ejpam-4931	163	20	(	(	PUNCT
ejpam-4931	163	21	t	t	PROPN
ejpam-4931	163	22	,	,	PUNCT
ejpam-4931	163	23	x	x	NOUN
ejpam-4931	163	24	,	,	PUNCT
ejpam-4931	163	25	y	y	NOUN
ejpam-4931	163	26	)	)	PUNCT
ejpam-4931	163	27	∈	∈	PROPN
ejpam-4931	164	1	[	[	X
ejpam-4931	164	2	0	0	NUM
ejpam-4931	164	3	,	,	PUNCT
ejpam-4931	164	4	t	t	X
ejpam-4931	164	5	]	]	X
ejpam-4931	164	6	×	×	PROPN
ejpam-4931	164	7	ω	ω	PROPN
ejpam-4931	164	8	with	with	ADP
ejpam-4931	164	9	t	t	PROPN
ejpam-4931	164	10	>	>	X
ejpam-4931	164	11	0	0	X
ejpam-4931	164	12	.	.	PUNCT
ejpam-4931	165	1	for	for	ADP
ejpam-4931	165	2	any	any	DET
ejpam-4931	165	3	given	give	VERB
ejpam-4931	165	4	u	u	NOUN
ejpam-4931	165	5	=	=	SYM
ejpam-4931	165	6	(	(	PUNCT
ejpam-4931	165	7	u	u	NOUN
ejpam-4931	165	8	,	,	PUNCT
ejpam-4931	165	9	v	v	NOUN
ejpam-4931	165	10	)	)	PUNCT
ejpam-4931	165	11	in	in	ADP
ejpam-4931	165	12	c	c	PROPN
ejpam-4931	165	13	(	(	PUNCT
ejpam-4931	165	14	[	[	X
ejpam-4931	165	15	0	0	NUM
ejpam-4931	165	16	,	,	PUNCT
ejpam-4931	165	17	t	t	X
ejpam-4931	165	18	]	]	PUNCT
ejpam-4931	165	19	;	;	PUNCT
ejpam-4931	165	20	xn	xn	X
ejpam-4931	165	21	)	)	PUNCT
ejpam-4931	165	22	,	,	PUNCT
ejpam-4931	165	23	by	by	ADP
ejpam-4931	165	24	the	the	DET
ejpam-4931	165	25	classical	classical	ADJ
ejpam-4931	165	26	theory	theory	NOUN
ejpam-4931	165	27	of	of	ADP
ejpam-4931	165	28	parabolic	parabolic	ADJ
ejpam-4931	165	29	equations	equation	NOUN
ejpam-4931	165	30	,	,	PUNCT
ejpam-4931	165	31	there	there	PRON
ejpam-4931	165	32	exists	exist	VERB
ejpam-4931	165	33	a	a	DET
ejpam-4931	165	34	classical	classical	ADJ
ejpam-4931	165	35	solution	solution	NOUN
ejpam-4931	165	36	ξ(t	ξ(t	NOUN
ejpam-4931	165	37	,	,	PUNCT
ejpam-4931	165	38	x	x	X
ejpam-4931	165	39	)	)	PUNCT
ejpam-4931	165	40	∈	∈	PROPN
ejpam-4931	165	41	c1	c1	NOUN
ejpam-4931	165	42	(	(	PUNCT
ejpam-4931	165	43	[	[	X
ejpam-4931	165	44	0	0	NUM
ejpam-4931	165	45	,	,	PUNCT
ejpam-4931	165	46	t	t	X
ejpam-4931	165	47	]	]	PUNCT
ejpam-4931	165	48	;	;	PUNCT
ejpam-4931	165	49	c3(ω	c3(ω	X
ejpam-4931	165	50	)	)	PUNCT
ejpam-4931	165	51	)	)	PUNCT
ejpam-4931	165	52	to	to	ADP
ejpam-4931	165	53	the	the	DET
ejpam-4931	165	54	approximated	approximate	VERB
ejpam-4931	165	55	system	system	NOUN
ejpam-4931	165	56	(	(	PUNCT
ejpam-4931	165	57	19	19	NUM
ejpam-4931	165	58	)	)	PUNCT
ejpam-4931	165	59	.	.	PUNCT
ejpam-4931	166	1	(	(	PUNCT
ejpam-4931	166	2	see	see	VERB
ejpam-4931	166	3	[	[	X
ejpam-4931	166	4	12	12	NUM
ejpam-4931	166	5	]	]	PUNCT
ejpam-4931	166	6	,	,	PUNCT
ejpam-4931	167	1	[	[	X
ejpam-4931	167	2	lemma	lemma	PROPN
ejpam-4931	167	3	3.1	3.1	NUM
ejpam-4931	167	4	,	,	PUNCT
ejpam-4931	167	5	[	[	X
ejpam-4931	167	6	19	19	NUM
ejpam-4931	167	7	]	]	NOUN
ejpam-4931	167	8	]	]	PUNCT
ejpam-4931	167	9	)	)	PUNCT
ejpam-4931	167	10	for	for	ADP
ejpam-4931	167	11	details	detail	NOUN
ejpam-4931	167	12	and	and	CCONJ
ejpam-4931	167	13	proofs	proof	NOUN
ejpam-4931	167	14	.	.	PUNCT
ejpam-4931	168	1	we	we	PRON
ejpam-4931	168	2	show	show	VERB
ejpam-4931	168	3	that	that	SCONJ
ejpam-4931	168	4	this	this	DET
ejpam-4931	168	5	solution	solution	NOUN
ejpam-4931	168	6	is	be	AUX
ejpam-4931	168	7	continuously	continuously	ADV
ejpam-4931	168	8	dependent	dependent	ADJ
ejpam-4931	168	9	on	on	ADP
ejpam-4931	168	10	u	u	NOUN
ejpam-4931	168	11	and	and	CCONJ
ejpam-4931	168	12	by	by	ADP
ejpam-4931	168	13	the	the	DET
ejpam-4931	168	14	comparison	comparison	NOUN
ejpam-4931	168	15	principle	principle	NOUN
ejpam-4931	168	16	,	,	PUNCT
ejpam-4931	168	17	we	we	PRON
ejpam-4931	168	18	also	also	ADV
ejpam-4931	168	19	show	show	VERB
ejpam-4931	168	20	that	that	SCONJ
ejpam-4931	168	21	it	it	PRON
ejpam-4931	168	22	satisfies	satisfy	VERB
ejpam-4931	168	23	the	the	DET
ejpam-4931	168	24	following	follow	VERB
ejpam-4931	168	25	inequality	inequality	NOUN
ejpam-4931	168	26	0	0	PUNCT
ejpam-4931	168	27	<	<	X
ejpam-4931	168	28	ξ(x)e−	ξ(x)e−	PROPN
ejpam-4931	168	29	∫	∫	PROPN
ejpam-4931	168	30	t	t	PROPN
ejpam-4931	168	31	0	0	NUM
ejpam-4931	169	1	∥divxu∥l∞dt	∥divxu∥l∞dt	PROPN
ejpam-4931	169	2	≤	≤	PUNCT
ejpam-4931	169	3	ξ(t	ξ(t	NOUN
ejpam-4931	169	4	,	,	PUNCT
ejpam-4931	169	5	x	x	NOUN
ejpam-4931	169	6	)	)	PUNCT
ejpam-4931	169	7	≤	≤	NOUN
ejpam-4931	170	1	ξ(x)e	ξ(x)e	PROPN
ejpam-4931	170	2	∫	∫	PROPN
ejpam-4931	170	3	t	t	NOUN
ejpam-4931	170	4	0	0	NUM
ejpam-4931	171	1	∥divxu∥l∞dt	∥divxu∥l∞dt	PROPN
ejpam-4931	171	2	,	,	PUNCT
ejpam-4931	171	3	∀x	∀x	VERB
ejpam-4931	171	4	∈	∈	PROPN
ejpam-4931	171	5	ωx	ωx	NOUN
ejpam-4931	171	6	=	=	SYM
ejpam-4931	171	7	t2	t2	PROPN
ejpam-4931	171	8	,	,	PUNCT
ejpam-4931	171	9	t	t	PROPN
ejpam-4931	171	10	≥	≥	PROPN
ejpam-4931	171	11	0	0	NUM
ejpam-4931	171	12	,	,	PUNCT
ejpam-4931	171	13	(	(	PUNCT
ejpam-4931	171	14	20	20	NUM
ejpam-4931	171	15	)	)	PUNCT
ejpam-4931	171	16	where	where	SCONJ
ejpam-4931	171	17	ξ(x	ξ(x	NOUN
ejpam-4931	171	18	)	)	PUNCT
ejpam-4931	171	19	=	=	SYM
ejpam-4931	171	20	inf	inf	NOUN
ejpam-4931	171	21	x∈t2	x∈t2	PROPN
ejpam-4931	171	22	ξ0(x	ξ0(x	PROPN
ejpam-4931	171	23	)	)	PUNCT
ejpam-4931	171	24	,	,	PUNCT
ejpam-4931	171	25	ξ(x	ξ(x	NOUN
ejpam-4931	171	26	)	)	PUNCT
ejpam-4931	171	27	=	=	SYM
ejpam-4931	171	28	sup	sup	NOUN
ejpam-4931	171	29	x∈t2	x∈t2	PROPN
ejpam-4931	171	30	ξ0(x	ξ0(x	PROPN
ejpam-4931	171	31	)	)	PUNCT
ejpam-4931	171	32	.	.	PUNCT
ejpam-4931	172	1	moreover	moreover	ADV
ejpam-4931	172	2	,	,	PUNCT
ejpam-4931	172	3	from	from	ADP
ejpam-4931	172	4	(	(	PUNCT
ejpam-4931	172	5	20	20	NUM
ejpam-4931	172	6	)	)	PUNCT
ejpam-4931	172	7	and	and	CCONJ
ejpam-4931	172	8	the	the	DET
ejpam-4931	172	9	initial	initial	ADJ
ejpam-4931	172	10	conditions	condition	NOUN
ejpam-4931	172	11	of	of	ADP
ejpam-4931	172	12	(	(	PUNCT
ejpam-4931	172	13	19	19	NUM
ejpam-4931	172	14	)	)	PUNCT
ejpam-4931	172	15	,	,	PUNCT
ejpam-4931	172	16	there	there	PRON
ejpam-4931	172	17	exists	exist	VERB
ejpam-4931	172	18	a	a	DET
ejpam-4931	172	19	positive	positive	ADJ
ejpam-4931	172	20	constant	constant	ADJ
ejpam-4931	172	21	η	η	NOUN
ejpam-4931	172	22	such	such	ADJ
ejpam-4931	172	23	that	that	SCONJ
ejpam-4931	172	24	0	0	NUM
ejpam-4931	172	25	<	<	X
ejpam-4931	172	26	η	η	PROPN
ejpam-4931	172	27	≤	≤	PROPN
ejpam-4931	172	28	ξ(t	ξ(t	PROPN
ejpam-4931	172	29	,	,	PUNCT
ejpam-4931	172	30	x	x	NOUN
ejpam-4931	172	31	)	)	PUNCT
ejpam-4931	172	32	≤	≤	PROPN
ejpam-4931	172	33	η−1	η−1	PROPN
ejpam-4931	172	34	,	,	PUNCT
ejpam-4931	172	35	for	for	ADP
ejpam-4931	172	36	(	(	PUNCT
ejpam-4931	172	37	t	t	PROPN
ejpam-4931	172	38	,	,	PUNCT
ejpam-4931	172	39	x	x	NOUN
ejpam-4931	172	40	)	)	PUNCT
ejpam-4931	172	41	∈	∈	PROPN
ejpam-4931	173	1	[	[	X
ejpam-4931	173	2	0	0	NUM
ejpam-4931	173	3	,	,	PUNCT
ejpam-4931	173	4	t	t	X
ejpam-4931	173	5	]	]	X
ejpam-4931	173	6	×	×	PROPN
ejpam-4931	173	7	ωx	ωx	PROPN
ejpam-4931	173	8	.	.	PUNCT
ejpam-4931	174	1	(	(	PUNCT
ejpam-4931	174	2	21	21	NUM
ejpam-4931	174	3	)	)	PUNCT
ejpam-4931	174	4	thus	thus	ADV
ejpam-4931	174	5	,	,	PUNCT
ejpam-4931	174	6	using	use	VERB
ejpam-4931	174	7	the	the	DET
ejpam-4931	174	8	mass	mass	NOUN
ejpam-4931	174	9	equation	equation	NOUN
ejpam-4931	174	10	,	,	PUNCT
ejpam-4931	174	11	we	we	PRON
ejpam-4931	174	12	construct	construct	VERB
ejpam-4931	174	13	the	the	DET
ejpam-4931	174	14	continuous	continuous	ADJ
ejpam-4931	174	15	linear	linear	NOUN
ejpam-4931	174	16	operator	operator	NOUN
ejpam-4931	174	17	s	s	PART
ejpam-4931	174	18	:	:	PUNCT
ejpam-4931	174	19	c0	c0	X
ejpam-4931	174	20	(	(	PUNCT
ejpam-4931	174	21	[	[	X
ejpam-4931	174	22	0	0	NUM
ejpam-4931	174	23	,	,	PUNCT
ejpam-4931	174	24	t	t	X
ejpam-4931	174	25	]	]	PUNCT
ejpam-4931	174	26	;	;	PUNCT
ejpam-4931	174	27	xn	xn	X
ejpam-4931	174	28	)	)	PUNCT
ejpam-4931	174	29	−→	−→	PROPN
ejpam-4931	174	30	c0	c0	NOUN
ejpam-4931	174	31	(	(	PUNCT
ejpam-4931	174	32	[	[	X
ejpam-4931	174	33	0	0	NUM
ejpam-4931	174	34	,	,	PUNCT
ejpam-4931	174	35	t	t	X
ejpam-4931	174	36	]	]	PUNCT
ejpam-4931	174	37	;	;	PUNCT
ejpam-4931	174	38	ck(ω	ck(ω	NUM
ejpam-4931	174	39	)	)	PUNCT
ejpam-4931	174	40	)	)	PUNCT
ejpam-4931	174	41	by	by	ADP
ejpam-4931	174	42	s(u	s(u	PROPN
ejpam-4931	174	43	)	)	PUNCT
ejpam-4931	174	44	=	=	SYM
ejpam-4931	174	45	ξ	ξ	PROPN
ejpam-4931	174	46	,	,	PUNCT
ejpam-4931	174	47	and	and	CCONJ
ejpam-4931	174	48	there	there	PRON
ejpam-4931	174	49	exists	exist	VERB
ejpam-4931	174	50	a	a	DET
ejpam-4931	174	51	constant	constant	ADJ
ejpam-4931	174	52	cn	cn	PROPN
ejpam-4931	174	53	,	,	PUNCT
ejpam-4931	174	54	k	k	PROPN
ejpam-4931	174	55	dependent	dependent	ADJ
ejpam-4931	174	56	on	on	ADP
ejpam-4931	174	57	k	k	PROPN
ejpam-4931	174	58	≥	≥	NUM
ejpam-4931	174	59	1	1	NUM
ejpam-4931	174	60	and	and	CCONJ
ejpam-4931	174	61	on	on	ADP
ejpam-4931	174	62	n	n	CCONJ
ejpam-4931	174	63	such	such	ADJ
ejpam-4931	174	64	that	that	DET
ejpam-4931	174	65	∥s(u1)−	∥s(u1)−	PROPN
ejpam-4931	174	66	s(u2)∥c([0,t	s(u2)∥c([0,t	PROPN
ejpam-4931	174	67	]	]	X
ejpam-4931	174	68	;	;	PUNCT
ejpam-4931	174	69	ck(ω))≤	ck(ω))≤	PROPN
ejpam-4931	174	70	cn	cn	PROPN
ejpam-4931	174	71	,	,	PUNCT
ejpam-4931	174	72	k∥u1	k∥u1	X
ejpam-4931	174	73	−	−	PROPN
ejpam-4931	175	1	u2∥c([0,t	u2∥c([0,t	ADJ
ejpam-4931	175	2	]	]	X
ejpam-4931	175	3	;	;	PUNCT
ejpam-4931	175	4	l2(ω	l2(ω	NUM
ejpam-4931	175	5	)	)	PUNCT
ejpam-4931	175	6	)	)	PUNCT
ejpam-4931	175	7	.	.	PUNCT
ejpam-4931	176	1	(	(	PUNCT
ejpam-4931	176	2	22	22	NUM
ejpam-4931	176	3	)	)	PUNCT
ejpam-4931	176	4	3.2	3.2	NUM
ejpam-4931	176	5	.	.	PUNCT
ejpam-4931	177	1	faedo	faedo	PROPN
ejpam-4931	177	2	-	-	PUNCT
ejpam-4931	177	3	galerkin	galerkin	PROPN
ejpam-4931	177	4	approximation	approximation	NOUN
ejpam-4931	177	5	for	for	ADP
ejpam-4931	177	6	the	the	DET
ejpam-4931	177	7	weak	weak	ADJ
ejpam-4931	177	8	formulation	formulation	NOUN
ejpam-4931	177	9	of	of	ADP
ejpam-4931	177	10	the	the	DET
ejpam-4931	177	11	momentum	momentum	NOUN
ejpam-4931	177	12	we	we	PRON
ejpam-4931	177	13	now	now	ADV
ejpam-4931	177	14	want	want	VERB
ejpam-4931	177	15	to	to	PART
ejpam-4931	177	16	solve	solve	VERB
ejpam-4931	177	17	the	the	DET
ejpam-4931	177	18	momentum	momentum	NOUN
ejpam-4931	177	19	equation	equation	NOUN
ejpam-4931	177	20	(	(	PUNCT
ejpam-4931	177	21	17)2	17)2	NUM
ejpam-4931	177	22	on	on	ADP
ejpam-4931	177	23	the	the	DET
ejpam-4931	177	24	space	space	NOUN
ejpam-4931	177	25	xn	xn	PROPN
ejpam-4931	177	26	.	.	PUNCT
ejpam-4931	178	1	for	for	ADP
ejpam-4931	178	2	any	any	DET
ejpam-4931	178	3	test	test	NOUN
ejpam-4931	178	4	function	function	NOUN
ejpam-4931	178	5	φ	φ	PROPN
ejpam-4931	178	6	∈	∈	PROPN
ejpam-4931	178	7	xn	xn	PROPN
ejpam-4931	178	8	,	,	PUNCT
ejpam-4931	178	9	the	the	DET
ejpam-4931	178	10	approximate	approximate	ADJ
ejpam-4931	178	11	solution	solution	NOUN
ejpam-4931	178	12	un	un	PROPN
ejpam-4931	178	13	∈	∈	PROPN
ejpam-4931	178	14	c0	c0	PROPN
ejpam-4931	178	15	(	(	PUNCT
ejpam-4931	178	16	[	[	X
ejpam-4931	178	17	0	0	NUM
ejpam-4931	178	18	,	,	PUNCT
ejpam-4931	178	19	t	t	X
ejpam-4931	178	20	]	]	PUNCT
ejpam-4931	178	21	;	;	PUNCT
ejpam-4931	178	22	xn	xn	X
ejpam-4931	178	23	)	)	PUNCT
ejpam-4931	178	24	satisfies	satisfie	NOUN
ejpam-4931	178	25	:	:	PUNCT
ejpam-4931	178	26	∫	∫	PROPN
ejpam-4931	178	27	ω	ω	NUM
ejpam-4931	178	28	ξnun(t	ξnun(t	NOUN
ejpam-4931	178	29	)	)	PUNCT
ejpam-4931	178	30	φdx	φdx	NOUN
ejpam-4931	178	31	−	−	PROPN
ejpam-4931	179	1	∫	∫	PROPN
ejpam-4931	180	1	ω	ω	PROPN
ejpam-4931	181	1	m0φdx	m0φdx	PROPN
ejpam-4931	182	1	−	−	PROPN
ejpam-4931	183	1	∫	∫	PROPN
ejpam-4931	184	1	t	t	PROPN
ejpam-4931	184	2	0	0	NUM
ejpam-4931	184	3	∫	∫	PROPN
ejpam-4931	184	4	ω	ω	PROPN
ejpam-4931	184	5	(	(	PUNCT
ejpam-4931	184	6	ξnun	ξnun	PROPN
ejpam-4931	184	7	⊗	⊗	PROPN
ejpam-4931	184	8	un	un	PROPN
ejpam-4931	184	9	)	)	PUNCT
ejpam-4931	184	10	:	:	PUNCT
ejpam-4931	184	11	∇xφdxdt	∇xφdxdt	NOUN
ejpam-4931	184	12	−	−	PROPN
ejpam-4931	185	1	∫	∫	PROPN
ejpam-4931	185	2	t	t	PROPN
ejpam-4931	185	3	0	0	NUM
ejpam-4931	185	4	∫	∫	PROPN
ejpam-4931	185	5	ω	ω	NUM
ejpam-4931	185	6	ξnunvn∂yφdxdt+	ξnunvn∂yφdxdt+	PROPN
ejpam-4931	185	7	r	r	NOUN
ejpam-4931	185	8	∫	∫	PROPN
ejpam-4931	185	9	t	t	PROPN
ejpam-4931	185	10	0	0	NUM
ejpam-4931	185	11	∫	∫	PROPN
ejpam-4931	186	1	ω	ω	PROPN
ejpam-4931	187	1	ξn|un|unφdxdt+	ξn|un|unφdxdt+	PROPN
ejpam-4931	187	2	∫	∫	PROPN
ejpam-4931	187	3	t	t	PROPN
ejpam-4931	187	4	0	0	NUM
ejpam-4931	188	1	∫	∫	PROPN
ejpam-4931	188	2	ω	ω	PROPN
ejpam-4931	188	3	∇xξ	∇xξ	PROPN
ejpam-4931	188	4	2	2	NUM
ejpam-4931	188	5	n	n	NOUN
ejpam-4931	188	6	·	·	PUNCT
ejpam-4931	188	7	φdxdt	φdxdt	NOUN
ejpam-4931	188	8	+	+	CCONJ
ejpam-4931	189	1	r1	r1	PROPN
ejpam-4931	189	2	∫	∫	PROPN
ejpam-4931	189	3	t	t	PROPN
ejpam-4931	189	4	0	0	NUM
ejpam-4931	189	5	∫	∫	PROPN
ejpam-4931	189	6	ω	ω	PROPN
ejpam-4931	189	7	unφdxdt+	unφdxdt+	ADP
ejpam-4931	189	8	α	α	PROPN
ejpam-4931	189	9	∫	∫	PROPN
ejpam-4931	189	10	t	t	PROPN
ejpam-4931	189	11	0	0	NUM
ejpam-4931	189	12	∫	∫	PROPN
ejpam-4931	189	13	ω	ω	PROPN
ejpam-4931	189	14	∆xun	∆xun	X
ejpam-4931	189	15	·	·	PUNCT
ejpam-4931	189	16	∆xφdxdt+	∆xφdxdt+	NUM
ejpam-4931	190	1	∫	∫	PROPN
ejpam-4931	190	2	t	t	PROPN
ejpam-4931	190	3	0	0	NUM
ejpam-4931	190	4	∫	∫	PROPN
ejpam-4931	190	5	ω	ω	NUM
ejpam-4931	190	6	ξn∂yun∂yφdxdt	ξn∂yun∂yφdxdt	PROPN
ejpam-4931	190	7	(	(	PUNCT
ejpam-4931	190	8	23	23	NUM
ejpam-4931	190	9	)	)	PUNCT
ejpam-4931	190	10	=	=	SYM
ejpam-4931	191	1	−2	−2	PROPN
ejpam-4931	191	2	∫	∫	PROPN
ejpam-4931	191	3	t	t	PROPN
ejpam-4931	191	4	0	0	NUM
ejpam-4931	192	1	∫	∫	PROPN
ejpam-4931	193	1	ω	ω	PROPN
ejpam-4931	193	2	ξndx(un	ξndx(un	PROPN
ejpam-4931	193	3	)	)	PUNCT
ejpam-4931	193	4	:	:	PUNCT
ejpam-4931	194	1	∇xφdxdt+	∇xφdxdt+	X
ejpam-4931	195	1	ϵ	ϵ	X
ejpam-4931	195	2	∫	∫	PROPN
ejpam-4931	195	3	t	t	PROPN
ejpam-4931	195	4	0	0	NUM
ejpam-4931	196	1	∫	∫	PROPN
ejpam-4931	196	2	ω	ω	PROPN
ejpam-4931	196	3	(	(	PUNCT
ejpam-4931	196	4	∇xξn	∇xξn	PROPN
ejpam-4931	196	5	·	·	PUNCT
ejpam-4931	196	6	∇xun	∇xun	ADJ
ejpam-4931	196	7	)	)	PUNCT
ejpam-4931	196	8	φdxdt	φdxdt	NOUN
ejpam-4931	196	9	−	−	PROPN
ejpam-4931	196	10	r2	r2	PROPN
ejpam-4931	197	1	∫	∫	PROPN
ejpam-4931	198	1	t	t	PROPN
ejpam-4931	198	2	0	0	NUM
ejpam-4931	199	1	∫	∫	PROPN
ejpam-4931	200	1	ω	ω	PROPN
ejpam-4931	200	2	ξ−β	ξ−β	PROPN
ejpam-4931	200	3	n	n	PRON
ejpam-4931	200	4	divxφdxdt−	divxφdxdt−	VERB
ejpam-4931	200	5	2k1	2k1	NUM
ejpam-4931	201	1	∫	∫	PROPN
ejpam-4931	201	2	t	t	PROPN
ejpam-4931	201	3	0	0	NUM
ejpam-4931	201	4	∫	∫	PROPN
ejpam-4931	201	5	ω	ω	PROPN
ejpam-4931	201	6	φ∆x	φ∆x	VERB
ejpam-4931	201	7	√	√	PUNCT
ejpam-4931	201	8	ξn∇x	ξn∇x	VERB
ejpam-4931	201	9	√	√	ADP
ejpam-4931	202	1	ξndxdt	ξndxdt	NOUN
ejpam-4931	202	2	−	−	PROPN
ejpam-4931	202	3	k1	k1	PROPN
ejpam-4931	202	4	∫	∫	PROPN
ejpam-4931	202	5	t	t	PROPN
ejpam-4931	202	6	0	0	NUM
ejpam-4931	203	1	∫	∫	PROPN
ejpam-4931	203	2	ω	ω	PROPN
ejpam-4931	203	3	divxφ	divxφ	VERB
ejpam-4931	203	4	(	(	PUNCT
ejpam-4931	203	5	∆x	∆x	PROPN
ejpam-4931	203	6	√	√	PROPN
ejpam-4931	203	7	ξn	ξn	PROPN
ejpam-4931	203	8	)	)	PUNCT
ejpam-4931	203	9	√	√	PROPN
ejpam-4931	203	10	ξndxdt+	ξndxdt+	PRON
ejpam-4931	204	1	δ	δ	X
ejpam-4931	204	2	∫	∫	PROPN
ejpam-4931	204	3	t	t	PROPN
ejpam-4931	204	4	0	0	NUM
ejpam-4931	205	1	∫	∫	PROPN
ejpam-4931	205	2	ω	ω	NUM
ejpam-4931	205	3	φξn∇x∆	φξn∇x∆	PROPN
ejpam-4931	205	4	5	5	NUM
ejpam-4931	205	5	xξndxdt	xξndxdt	PROPN
ejpam-4931	205	6	,	,	PUNCT
ejpam-4931	205	7	j.	j.	PROPN
ejpam-4931	205	8	ouya	ouya	PROPN
ejpam-4931	205	9	,	,	PUNCT
ejpam-4931	205	10	a.	a.	NOUN
ejpam-4931	205	11	ouédraogo	ouédraogo	PROPN
ejpam-4931	205	12	/	/	SYM
ejpam-4931	205	13	eur	eur	PROPN
ejpam-4931	205	14	.	.	PUNCT
ejpam-4931	206	1	j.	j.	PROPN
ejpam-4931	206	2	pure	pure	PROPN
ejpam-4931	206	3	appl	appl	PROPN
ejpam-4931	206	4	.	.	PROPN
ejpam-4931	206	5	math	math	PROPN
ejpam-4931	206	6	,	,	PUNCT
ejpam-4931	206	7	16	16	NUM
ejpam-4931	206	8	(	(	PUNCT
ejpam-4931	206	9	4	4	NUM
ejpam-4931	206	10	)	)	PUNCT
ejpam-4931	206	11	(	(	PUNCT
ejpam-4931	206	12	2023	2023	NUM
ejpam-4931	206	13	)	)	PUNCT
ejpam-4931	206	14	,	,	PUNCT
ejpam-4931	206	15	2247	2247	NUM
ejpam-4931	206	16	-	-	SYM
ejpam-4931	206	17	2285	2285	NUM
ejpam-4931	206	18	2255	2255	NUM
ejpam-4931	206	19	where	where	SCONJ
ejpam-4931	206	20	m0	m0	PROPN
ejpam-4931	206	21	=	=	SYM
ejpam-4931	206	22	ξn(0	ξn(0	PROPN
ejpam-4931	206	23	,	,	PUNCT
ejpam-4931	206	24	x	x	NOUN
ejpam-4931	206	25	,	,	PUNCT
ejpam-4931	206	26	y)un(0	y)un(0	PROPN
ejpam-4931	206	27	,	,	PUNCT
ejpam-4931	206	28	x	x	NOUN
ejpam-4931	206	29	,	,	PUNCT
ejpam-4931	206	30	y	y	PROPN
ejpam-4931	206	31	)	)	PUNCT
ejpam-4931	206	32	and	and	CCONJ
ejpam-4931	206	33	dx	dx	PROPN
ejpam-4931	206	34	=	=	PUNCT
ejpam-4931	206	35	dxdy	dxdy	PROPN
ejpam-4931	206	36	.	.	PUNCT
ejpam-4931	207	1	as	as	ADP
ejpam-4931	207	2	in	in	ADP
ejpam-4931	207	3	[	[	X
ejpam-4931	207	4	4	4	NUM
ejpam-4931	207	5	,	,	PUNCT
ejpam-4931	207	6	5	5	NUM
ejpam-4931	207	7	,	,	PUNCT
ejpam-4931	207	8	9	9	NUM
ejpam-4931	207	9	,	,	PUNCT
ejpam-4931	207	10	19	19	NUM
ejpam-4931	207	11	]	]	PUNCT
ejpam-4931	207	12	,	,	PUNCT
ejpam-4931	207	13	to	to	PART
ejpam-4931	207	14	solve	solve	VERB
ejpam-4931	207	15	(	(	PUNCT
ejpam-4931	207	16	23	23	NUM
ejpam-4931	207	17	)	)	PUNCT
ejpam-4931	207	18	we	we	PRON
ejpam-4931	207	19	introduce	introduce	VERB
ejpam-4931	207	20	the	the	DET
ejpam-4931	207	21	linear	linear	ADJ
ejpam-4931	207	22	operator	operator	NOUN
ejpam-4931	207	23	m[ξ	m[ξ	NOUN
ejpam-4931	207	24	]	]	PUNCT
ejpam-4931	207	25	:	:	PUNCT
ejpam-4931	207	26	xn	xn	PUNCT
ejpam-4931	208	1	−→	−→	NOUN
ejpam-4931	208	2	x	x	SYM
ejpam-4931	208	3	′	′	NOUN
ejpam-4931	208	4	n	n	CCONJ
ejpam-4931	208	5	,	,	PUNCT
ejpam-4931	208	6	<	<	X
ejpam-4931	208	7	m[ξ]u	m[ξ]u	NOUN
ejpam-4931	208	8	,	,	PUNCT
ejpam-4931	208	9	v	v	X
ejpam-4931	208	10	>	>	X
ejpam-4931	208	11	=	=	SYM
ejpam-4931	209	1	∫	∫	PROPN
ejpam-4931	209	2	ω	ω	NUM
ejpam-4931	209	3	ξu.vdx	ξu.vdx	PROPN
ejpam-4931	209	4	,	,	PUNCT
ejpam-4931	209	5	u	u	NOUN
ejpam-4931	209	6	,	,	PUNCT
ejpam-4931	209	7	v	v	NOUN
ejpam-4931	209	8	∈	∈	PROPN
ejpam-4931	209	9	xn	xn	NOUN
ejpam-4931	209	10	.	.	PUNCT
ejpam-4931	210	1	using	use	VERB
ejpam-4931	210	2	the	the	DET
ejpam-4931	210	3	lax	lax	PROPN
ejpam-4931	210	4	-	-	PUNCT
ejpam-4931	210	5	milgram	milgram	NOUN
ejpam-4931	210	6	theorem	theorem	NOUN
ejpam-4931	210	7	,	,	PUNCT
ejpam-4931	210	8	we	we	PRON
ejpam-4931	210	9	show	show	VERB
ejpam-4931	210	10	that	that	SCONJ
ejpam-4931	210	11	this	this	DET
ejpam-4931	210	12	operator	operator	NOUN
ejpam-4931	210	13	is	be	AUX
ejpam-4931	210	14	invertible	invertible	ADJ
ejpam-4931	210	15	and	and	CCONJ
ejpam-4931	210	16	m−1	m−1	PROPN
ejpam-4931	210	17	is	be	AUX
ejpam-4931	210	18	lipschitz	lipschitz	ADV
ejpam-4931	210	19	continuous	continuous	ADJ
ejpam-4931	210	20	.	.	PUNCT
ejpam-4931	211	1	let	let	VERB
ejpam-4931	211	2	us	we	PRON
ejpam-4931	211	3	reformulate	reformulate	VERB
ejpam-4931	211	4	equation	equation	NOUN
ejpam-4931	211	5	(	(	PUNCT
ejpam-4931	211	6	23	23	NUM
ejpam-4931	211	7	)	)	PUNCT
ejpam-4931	211	8	as	as	SCONJ
ejpam-4931	211	9	follows	follow	VERB
ejpam-4931	211	10	:	:	PUNCT
ejpam-4931	211	11	un(t	un(t	NUM
ejpam-4931	211	12	)	)	PUNCT
ejpam-4931	211	13	=	=	SYM
ejpam-4931	211	14	m−1[s(un(t	m−1[s(un(t	NUM
ejpam-4931	211	15	)	)	PUNCT
ejpam-4931	211	16	)	)	PUNCT
ejpam-4931	211	17	]	]	PUNCT
ejpam-4931	212	1	(	(	PUNCT
ejpam-4931	212	2	m[ξ0](u0	m[ξ0](u0	NOUN
ejpam-4931	212	3	)	)	PUNCT
ejpam-4931	213	1	+	+	CCONJ
ejpam-4931	213	2	∫	∫	PROPN
ejpam-4931	213	3	t	t	PROPN
ejpam-4931	213	4	0	0	NUM
ejpam-4931	213	5	n	n	PROPN
ejpam-4931	213	6	(	(	PUNCT
ejpam-4931	213	7	s(un	s(un	PROPN
ejpam-4931	213	8	)	)	PUNCT
ejpam-4931	213	9	,	,	PUNCT
ejpam-4931	213	10	un	un	PROPN
ejpam-4931	213	11	)	)	PUNCT
ejpam-4931	213	12	(	(	PUNCT
ejpam-4931	213	13	s)ds	s)ds	PROPN
ejpam-4931	213	14	)	)	PUNCT
ejpam-4931	213	15	,	,	PUNCT
ejpam-4931	213	16	(	(	PUNCT
ejpam-4931	213	17	24	24	NUM
ejpam-4931	213	18	)	)	PUNCT
ejpam-4931	213	19	where	where	SCONJ
ejpam-4931	213	20	s(un	s(un	VERB
ejpam-4931	213	21	)	)	PUNCT
ejpam-4931	213	22	=	=	SYM
ejpam-4931	213	23	ξn	ξn	PROPN
ejpam-4931	213	24	,	,	PUNCT
ejpam-4931	213	25	n	n	PROPN
ejpam-4931	213	26	(	(	PUNCT
ejpam-4931	213	27	s(un	s(un	PROPN
ejpam-4931	213	28	)	)	PUNCT
ejpam-4931	213	29	,	,	PUNCT
ejpam-4931	213	30	un	un	PROPN
ejpam-4931	213	31	)	)	PUNCT
ejpam-4931	213	32	(	(	PUNCT
ejpam-4931	213	33	s	s	X
ejpam-4931	213	34	)	)	PUNCT
ejpam-4931	213	35	=	=	SYM
ejpam-4931	213	36	divx	divx	X
ejpam-4931	213	37	(	(	PUNCT
ejpam-4931	213	38	2ξndx(un	2ξndx(un	NUM
ejpam-4931	213	39	)	)	PUNCT
ejpam-4931	213	40	)	)	PUNCT
ejpam-4931	214	1	+	+	CCONJ
ejpam-4931	214	2	∂y	∂y	SYM
ejpam-4931	214	3	(	(	PUNCT
ejpam-4931	214	4	ξn∂yun)−	ξn∂yun)−	PROPN
ejpam-4931	214	5	divx(ξun	divx(ξun	PROPN
ejpam-4931	215	1	⊗	⊗	PROPN
ejpam-4931	215	2	un)−	un)−	PROPN
ejpam-4931	216	1	∂y(ξnunvn	∂y(ξnunvn	PROPN
ejpam-4931	216	2	)	)	PUNCT
ejpam-4931	217	1	−α∆2	−α∆2	ADP
ejpam-4931	217	2	xun	xun	PROPN
ejpam-4931	217	3	−	−	PROPN
ejpam-4931	218	1	ϵ∇xξn	ϵ∇xξn	X
ejpam-4931	219	1	·	·	PUNCT
ejpam-4931	219	2	∇xun	∇xun	ADJ
ejpam-4931	219	3	+	+	CCONJ
ejpam-4931	219	4	k1ξ∇x	k1ξ∇x	PROPN
ejpam-4931	219	5	(	(	PUNCT
ejpam-4931	219	6	∆x	∆x	PROPN
ejpam-4931	219	7	√	√	NUM
ejpam-4931	219	8	ξn√	ξn√	PROPN
ejpam-4931	219	9	ξn	ξn	PROPN
ejpam-4931	219	10	)	)	PUNCT
ejpam-4931	219	11	−∇xξ	−∇xξ	PROPN
ejpam-4931	219	12	2	2	NUM
ejpam-4931	219	13	n	n	PRON
ejpam-4931	219	14	+	+	PRON
ejpam-4931	219	15	r2∇xξ	r2∇xξ	NOUN
ejpam-4931	219	16	−β	−β	NOUN
ejpam-4931	219	17	n	n	PRON
ejpam-4931	219	18	−	−	PROPN
ejpam-4931	219	19	r1un	r1un	NOUN
ejpam-4931	219	20	−	−	PROPN
ejpam-4931	220	1	rξ|un|un	rξ|un|un	PROPN
ejpam-4931	220	2	+	+	NOUN
ejpam-4931	220	3	δξn∇x∆	δξn∇x∆	NOUN
ejpam-4931	220	4	5	5	NUM
ejpam-4931	220	5	xξn	xξn	PROPN
ejpam-4931	220	6	.	.	PUNCT
ejpam-4931	221	1	for	for	ADP
ejpam-4931	221	2	more	more	ADJ
ejpam-4931	221	3	details	detail	NOUN
ejpam-4931	221	4	,	,	PUNCT
ejpam-4931	221	5	we	we	PRON
ejpam-4931	221	6	refer	refer	VERB
ejpam-4931	221	7	the	the	DET
ejpam-4931	221	8	readers	reader	NOUN
ejpam-4931	221	9	to	to	ADP
ejpam-4931	221	10	[	[	X
ejpam-4931	221	11	4–9	4–9	NUM
ejpam-4931	221	12	,	,	PUNCT
ejpam-4931	221	13	13	13	NUM
ejpam-4931	221	14	,	,	PUNCT
ejpam-4931	221	15	15	15	NUM
ejpam-4931	221	16	,	,	PUNCT
ejpam-4931	221	17	19	19	NUM
ejpam-4931	221	18	]	]	PUNCT
ejpam-4931	221	19	.	.	PUNCT
ejpam-4931	222	1	in	in	ADP
ejpam-4931	222	2	view	view	NOUN
ejpam-4931	222	3	of	of	ADP
ejpam-4931	222	4	the	the	DET
ejpam-4931	222	5	lipschitz	lipschitz	ADJ
ejpam-4931	222	6	continuous	continuous	ADJ
ejpam-4931	222	7	estimates	estimate	NOUN
ejpam-4931	222	8	for	for	ADP
ejpam-4931	222	9	s	s	PRON
ejpam-4931	222	10	and	and	CCONJ
ejpam-4931	222	11	m−1	m−1	PROPN
ejpam-4931	222	12	,	,	PUNCT
ejpam-4931	222	13	the	the	DET
ejpam-4931	222	14	nonlinear	nonlinear	ADJ
ejpam-4931	222	15	equation	equation	NOUN
ejpam-4931	222	16	(	(	PUNCT
ejpam-4931	222	17	24	24	NUM
ejpam-4931	222	18	)	)	PUNCT
ejpam-4931	222	19	can	can	AUX
ejpam-4931	222	20	be	be	AUX
ejpam-4931	222	21	solved	solve	VERB
ejpam-4931	222	22	on	on	ADP
ejpam-4931	222	23	a	a	DET
ejpam-4931	222	24	short	short	ADJ
ejpam-4931	222	25	time	time	NOUN
ejpam-4931	222	26	interval	interval	NOUN
ejpam-4931	222	27	[	[	X
ejpam-4931	222	28	0	0	NUM
ejpam-4931	222	29	,	,	PUNCT
ejpam-4931	222	30	τ	τ	PROPN
ejpam-4931	222	31	]	]	X
ejpam-4931	222	32	,	,	PUNCT
ejpam-4931	222	33	where	where	SCONJ
ejpam-4931	222	34	τ	τ	PROPN
ejpam-4931	222	35	≤	≤	PROPN
ejpam-4931	222	36	t	t	NOUN
ejpam-4931	222	37	,	,	PUNCT
ejpam-4931	222	38	using	use	VERB
ejpam-4931	222	39	a	a	DET
ejpam-4931	222	40	fixed	fix	VERB
ejpam-4931	222	41	point	point	NOUN
ejpam-4931	222	42	theorem	theorem	VERB
ejpam-4931	222	43	on	on	ADP
ejpam-4931	222	44	the	the	DET
ejpam-4931	222	45	banach	banach	NOUN
ejpam-4931	222	46	space	space	NOUN
ejpam-4931	222	47	c	c	NOUN
ejpam-4931	222	48	(	(	PUNCT
ejpam-4931	222	49	[	[	X
ejpam-4931	222	50	0	0	NUM
ejpam-4931	222	51	,	,	PUNCT
ejpam-4931	222	52	t	t	X
ejpam-4931	222	53	]	]	PUNCT
ejpam-4931	222	54	;	;	PUNCT
ejpam-4931	222	55	xn	xn	NUM
ejpam-4931	222	56	)	)	PUNCT
ejpam-4931	222	57	.	.	PUNCT
ejpam-4931	223	1	we	we	PRON
ejpam-4931	223	2	thus	thus	ADV
ejpam-4931	223	3	obtain	obtain	VERB
ejpam-4931	223	4	a	a	DET
ejpam-4931	223	5	unique	unique	ADJ
ejpam-4931	223	6	local	local	ADJ
ejpam-4931	223	7	solution	solution	NOUN
ejpam-4931	223	8	in	in	ADP
ejpam-4931	223	9	time	time	NOUN
ejpam-4931	223	10	(	(	PUNCT
ejpam-4931	223	11	ξn	ξn	PROPN
ejpam-4931	223	12	,	,	PUNCT
ejpam-4931	223	13	un	un	PROPN
ejpam-4931	223	14	,	,	PUNCT
ejpam-4931	223	15	vn	vn	NOUN
ejpam-4931	223	16	)	)	PUNCT
ejpam-4931	223	17	to	to	ADP
ejpam-4931	223	18	problems	problem	NOUN
ejpam-4931	223	19	(	(	PUNCT
ejpam-4931	223	20	19	19	NUM
ejpam-4931	223	21	)	)	PUNCT
ejpam-4931	223	22	and	and	CCONJ
ejpam-4931	223	23	(	(	PUNCT
ejpam-4931	223	24	24	24	NUM
ejpam-4931	223	25	)	)	PUNCT
ejpam-4931	223	26	.	.	PUNCT
ejpam-4931	224	1	next	next	ADV
ejpam-4931	224	2	we	we	PRON
ejpam-4931	224	3	will	will	AUX
ejpam-4931	224	4	extend	extend	VERB
ejpam-4931	224	5	this	this	DET
ejpam-4931	224	6	obtained	obtain	VERB
ejpam-4931	224	7	local	local	ADJ
ejpam-4931	224	8	solution	solution	NOUN
ejpam-4931	224	9	to	to	PART
ejpam-4931	224	10	be	be	AUX
ejpam-4931	224	11	a	a	DET
ejpam-4931	224	12	global	global	ADJ
ejpam-4931	224	13	one	one	NUM
ejpam-4931	224	14	.	.	PUNCT
ejpam-4931	225	1	differentiating	differentiate	VERB
ejpam-4931	225	2	(	(	PUNCT
ejpam-4931	225	3	23	23	NUM
ejpam-4931	225	4	)	)	PUNCT
ejpam-4931	225	5	with	with	ADP
ejpam-4931	225	6	respect	respect	NOUN
ejpam-4931	225	7	to	to	ADP
ejpam-4931	225	8	time	time	NOUN
ejpam-4931	225	9	t	t	PROPN
ejpam-4931	225	10	,	,	PUNCT
ejpam-4931	225	11	taking	take	VERB
ejpam-4931	225	12	φ	φ	PROPN
ejpam-4931	225	13	=	=	SYM
ejpam-4931	225	14	un	un	PROPN
ejpam-4931	225	15	and	and	CCONJ
ejpam-4931	225	16	integrating	integrate	VERB
ejpam-4931	225	17	by	by	ADP
ejpam-4931	225	18	parts	part	NOUN
ejpam-4931	225	19	with	with	ADP
ejpam-4931	225	20	respect	respect	NOUN
ejpam-4931	225	21	to	to	ADP
ejpam-4931	225	22	x	x	PUNCT
ejpam-4931	225	23	over	over	ADP
ejpam-4931	225	24	ω	ω	PROPN
ejpam-4931	225	25	,	,	PUNCT
ejpam-4931	225	26	we	we	PRON
ejpam-4931	225	27	get	get	VERB
ejpam-4931	225	28	∫	∫	PROPN
ejpam-4931	226	1	ω	ω	PROPN
ejpam-4931	227	1	d	d	X
ejpam-4931	227	2	dt	dt	X
ejpam-4931	227	3	(	(	PUNCT
ejpam-4931	227	4	ξn	ξn	PROPN
ejpam-4931	227	5	u2n	u2n	PROPN
ejpam-4931	227	6	2	2	NUM
ejpam-4931	227	7	)	)	PUNCT
ejpam-4931	227	8	dx	dx	PROPN
ejpam-4931	228	1	+	+	CCONJ
ejpam-4931	228	2	∫	∫	PROPN
ejpam-4931	228	3	ω	ω	PROPN
ejpam-4931	228	4	un	un	PROPN
ejpam-4931	228	5	·	·	PUNCT
ejpam-4931	228	6	∇xξ	∇xξ	PROPN
ejpam-4931	228	7	2dx	2dx	PROPN
ejpam-4931	229	1	+	+	CCONJ
ejpam-4931	229	2	r	r	NOUN
ejpam-4931	229	3	∫	∫	PROPN
ejpam-4931	229	4	ω	ω	NUM
ejpam-4931	229	5	ξn|un|3dx	ξn|un|3dx	PROPN
ejpam-4931	230	1	+	+	CCONJ
ejpam-4931	230	2	∫	∫	PROPN
ejpam-4931	230	3	ω	ω	NUM
ejpam-4931	230	4	ξn|∂yun|2dx	ξn|∂yun|2dx	VERB
ejpam-4931	231	1	+	+	CCONJ
ejpam-4931	231	2	r1	r1	PROPN
ejpam-4931	231	3	∫	∫	PROPN
ejpam-4931	231	4	ω	ω	NUM
ejpam-4931	231	5	u2ndx	u2ndx	NUM
ejpam-4931	231	6	−	−	PROPN
ejpam-4931	232	1	r2	r2	PROPN
ejpam-4931	232	2	∫	∫	PROPN
ejpam-4931	232	3	ω	ω	PROPN
ejpam-4931	232	4	un	un	PROPN
ejpam-4931	232	5	·	·	PUNCT
ejpam-4931	232	6	∇xξ	∇xξ	VERB
ejpam-4931	232	7	−β	−β	PROPN
ejpam-4931	232	8	n	n	PROPN
ejpam-4931	232	9	dx	dx	PROPN
ejpam-4931	232	10	+	+	CCONJ
ejpam-4931	232	11	∫	∫	PROPN
ejpam-4931	232	12	ω	ω	NUM
ejpam-4931	232	13	2ξn|dx(un)|2dx	2ξn|dx(un)|2dx	PROPN
ejpam-4931	233	1	+	+	CCONJ
ejpam-4931	233	2	α	α	PROPN
ejpam-4931	233	3	∫	∫	PROPN
ejpam-4931	233	4	ω	ω	PROPN
ejpam-4931	233	5	|∆un|2dx	|∆un|2dx	ADJ
ejpam-4931	233	6	+	+	CCONJ
ejpam-4931	233	7	∫	∫	PROPN
ejpam-4931	233	8	ω	ω	NUM
ejpam-4931	233	9	ξn|∂yun|2dx	ξn|∂yun|2dx	VERB
ejpam-4931	233	10	+	+	CCONJ
ejpam-4931	233	11	k1	k1	PROPN
ejpam-4931	233	12	∫	∫	PROPN
ejpam-4931	233	13	ω	ω	PROPN
ejpam-4931	233	14	∆x	∆x	PROPN
ejpam-4931	233	15	√	√	NUM
ejpam-4931	233	16	ξn√	ξn√	PUNCT
ejpam-4931	234	1	ξn	ξn	PROPN
ejpam-4931	234	2	divx	divx	PROPN
ejpam-4931	234	3	(	(	PUNCT
ejpam-4931	234	4	ξnun	ξnun	PROPN
ejpam-4931	234	5	)	)	PUNCT
ejpam-4931	234	6	dx	dx	PROPN
ejpam-4931	235	1	+	+	CCONJ
ejpam-4931	235	2	δ	δ	PROPN
ejpam-4931	235	3	∫	∫	PROPN
ejpam-4931	235	4	ω	ω	PROPN
ejpam-4931	235	5	divx	divx	PROPN
ejpam-4931	235	6	(	(	PUNCT
ejpam-4931	235	7	ξnun)∆	ξnun)∆	NOUN
ejpam-4931	235	8	5	5	NUM
ejpam-4931	235	9	xξndx	xξndx	NOUN
ejpam-4931	235	10	=	=	SYM
ejpam-4931	235	11	0	0	X
ejpam-4931	235	12	.	.	PUNCT
ejpam-4931	235	13	(	(	PUNCT
ejpam-4931	235	14	25	25	NUM
ejpam-4931	235	15	)	)	PUNCT
ejpam-4931	235	16	furthermore	furthermore	ADV
ejpam-4931	235	17	,	,	PUNCT
ejpam-4931	235	18	we	we	PRON
ejpam-4931	235	19	estimate	estimate	VERB
ejpam-4931	235	20	the	the	DET
ejpam-4931	235	21	terms	term	NOUN
ejpam-4931	235	22	of	of	ADP
ejpam-4931	235	23	the	the	DET
ejpam-4931	235	24	left	left	ADJ
ejpam-4931	235	25	hand	hand	NOUN
ejpam-4931	235	26	side	side	NOUN
ejpam-4931	235	27	in	in	ADP
ejpam-4931	235	28	(	(	PUNCT
ejpam-4931	235	29	25	25	NUM
ejpam-4931	235	30	)	)	PUNCT
ejpam-4931	235	31	one	one	NUM
ejpam-4931	235	32	by	by	ADP
ejpam-4931	235	33	one	one	NUM
ejpam-4931	235	34	:	:	PUNCT
ejpam-4931	235	35	∫	∫	PROPN
ejpam-4931	235	36	ω	ω	PROPN
ejpam-4931	235	37	un	un	PROPN
ejpam-4931	235	38	·	·	PUNCT
ejpam-4931	235	39	∇xξ	∇xξ	PROPN
ejpam-4931	235	40	2	2	NUM
ejpam-4931	235	41	ndx	ndx	NOUN
ejpam-4931	235	42	=	=	SYM
ejpam-4931	235	43	−2	−2	PROPN
ejpam-4931	235	44	∫	∫	PROPN
ejpam-4931	235	45	ω	ω	INTJ
ejpam-4931	236	1	ξndivx(ξnun)dx	ξndivx(ξnun)dx	ADP
ejpam-4931	236	2	=	=	PUNCT
ejpam-4931	236	3	−2	−2	PROPN
ejpam-4931	236	4	∫	∫	PROPN
ejpam-4931	236	5	ω	ω	PROPN
ejpam-4931	236	6	ξn	ξn	PROPN
ejpam-4931	236	7	(	(	PUNCT
ejpam-4931	236	8	ϵ∆xξn	ϵ∆xξn	PROPN
ejpam-4931	236	9	−	−	PROPN
ejpam-4931	236	10	∂tξn	∂tξn	PUNCT
ejpam-4931	236	11	−	−	PROPN
ejpam-4931	236	12	∂y(ξnvn	∂y(ξnvn	NOUN
ejpam-4931	236	13	)	)	PUNCT
ejpam-4931	236	14	)	)	PUNCT
ejpam-4931	236	15	dx	dx	PROPN
ejpam-4931	236	16	j.	j.	PROPN
ejpam-4931	236	17	ouya	ouya	PROPN
ejpam-4931	236	18	,	,	PUNCT
ejpam-4931	236	19	a.	a.	NOUN
ejpam-4931	236	20	ouédraogo	ouédraogo	PROPN
ejpam-4931	236	21	/	/	SYM
ejpam-4931	236	22	eur	eur	PROPN
ejpam-4931	236	23	.	.	PUNCT
ejpam-4931	237	1	j.	j.	PROPN
ejpam-4931	237	2	pure	pure	PROPN
ejpam-4931	237	3	appl	appl	PROPN
ejpam-4931	237	4	.	.	PROPN
ejpam-4931	237	5	math	math	PROPN
ejpam-4931	237	6	,	,	PUNCT
ejpam-4931	237	7	16	16	NUM
ejpam-4931	237	8	(	(	PUNCT
ejpam-4931	237	9	4	4	NUM
ejpam-4931	237	10	)	)	PUNCT
ejpam-4931	237	11	(	(	PUNCT
ejpam-4931	237	12	2023	2023	NUM
ejpam-4931	237	13	)	)	PUNCT
ejpam-4931	237	14	,	,	PUNCT
ejpam-4931	237	15	2247	2247	NUM
ejpam-4931	237	16	-	-	SYM
ejpam-4931	237	17	2285	2285	NUM
ejpam-4931	237	18	2256	2256	NUM
ejpam-4931	238	1	=	=	PUNCT
ejpam-4931	239	1	d	d	X
ejpam-4931	239	2	dt	dt	X
ejpam-4931	239	3	∫	∫	PROPN
ejpam-4931	239	4	ω	ω	NUM
ejpam-4931	239	5	ξ2ndx	ξ2ndx	PROPN
ejpam-4931	240	1	+	+	PROPN
ejpam-4931	240	2	2ϵ	2ϵ	NUM
ejpam-4931	240	3	∫	∫	PROPN
ejpam-4931	240	4	ω	ω	NUM
ejpam-4931	240	5	|∇xξn|2	|∇xξn|2	PROPN
ejpam-4931	240	6	dx	dx	PROPN
ejpam-4931	240	7	,	,	PUNCT
ejpam-4931	240	8	(	(	PUNCT
ejpam-4931	240	9	26	26	NUM
ejpam-4931	240	10	)	)	PUNCT
ejpam-4931	240	11	where	where	SCONJ
ejpam-4931	240	12	we	we	PRON
ejpam-4931	240	13	used	use	VERB
ejpam-4931	240	14	the	the	DET
ejpam-4931	240	15	fact	fact	NOUN
ejpam-4931	240	16	that	that	SCONJ
ejpam-4931	240	17	∂yξn	∂yξn	AUX
ejpam-4931	240	18	=	=	SYM
ejpam-4931	240	19	0	0	NUM
ejpam-4931	240	20	and	and	CCONJ
ejpam-4931	240	21	integration	integration	NOUN
ejpam-4931	240	22	by	by	ADP
ejpam-4931	240	23	parts	part	NOUN
ejpam-4931	240	24	.	.	PUNCT
ejpam-4931	241	1	next	next	ADV
ejpam-4931	241	2	we	we	PRON
ejpam-4931	241	3	deal	deal	VERB
ejpam-4931	241	4	with	with	ADP
ejpam-4931	241	5	the	the	DET
ejpam-4931	241	6	cold	cold	ADJ
ejpam-4931	241	7	pressure	pressure	NOUN
ejpam-4931	241	8	and	and	CCONJ
ejpam-4931	241	9	high	high	ADJ
ejpam-4931	241	10	order	order	NOUN
ejpam-4931	241	11	derivative	derivative	NOUN
ejpam-4931	241	12	of	of	ADP
ejpam-4931	241	13	the	the	DET
ejpam-4931	241	14	density	density	NOUN
ejpam-4931	241	15	terms	term	NOUN
ejpam-4931	241	16	as	as	SCONJ
ejpam-4931	241	17	follows	follow	VERB
ejpam-4931	241	18	−r2	−r2	PROPN
ejpam-4931	241	19	∫	∫	PROPN
ejpam-4931	241	20	ω	ω	PROPN
ejpam-4931	241	21	un	un	PROPN
ejpam-4931	241	22	·	·	PUNCT
ejpam-4931	241	23	∇xξ	∇xξ	VERB
ejpam-4931	241	24	−β	−β	PROPN
ejpam-4931	241	25	n	n	X
ejpam-4931	241	26	dx	dx	PROPN
ejpam-4931	242	1	=	=	SYM
ejpam-4931	243	1	−r2	−r2	PROPN
ejpam-4931	243	2	β	β	X
ejpam-4931	243	3	β	β	NOUN
ejpam-4931	243	4	+	+	CCONJ
ejpam-4931	243	5	1	1	NUM
ejpam-4931	243	6	∫	∫	PROPN
ejpam-4931	243	7	ω	ω	PROPN
ejpam-4931	243	8	ξ−β−1	ξ−β−1	PUNCT
ejpam-4931	243	9	n	n	PROPN
ejpam-4931	243	10	(	(	PUNCT
ejpam-4931	243	11	ϵ∆xξn	ϵ∆xξn	PUNCT
ejpam-4931	243	12	−	−	PROPN
ejpam-4931	243	13	∂tξn	∂tξn	PUNCT
ejpam-4931	243	14	−	−	PROPN
ejpam-4931	243	15	∂y(ξnvn	∂y(ξnvn	NOUN
ejpam-4931	243	16	)	)	PUNCT
ejpam-4931	243	17	)	)	PUNCT
ejpam-4931	244	1	dx	dx	PROPN
ejpam-4931	245	1	=	=	PROPN
ejpam-4931	245	2	r2	r2	PROPN
ejpam-4931	245	3	β	β	X
ejpam-4931	245	4	+	+	NOUN
ejpam-4931	245	5	1	1	NUM
ejpam-4931	245	6	d	d	NOUN
ejpam-4931	245	7	dt	dt	X
ejpam-4931	245	8	∫	∫	PROPN
ejpam-4931	245	9	ω	ω	PROPN
ejpam-4931	245	10	ξ−β	ξ−β	PROPN
ejpam-4931	245	11	n	n	PRON
ejpam-4931	245	12	dx	dx	PROPN
ejpam-4931	246	1	+	+	CCONJ
ejpam-4931	246	2	4ϵr2	4ϵr2	X
ejpam-4931	246	3	β	β	PROPN
ejpam-4931	246	4	∫	∫	PROPN
ejpam-4931	246	5	ω	ω	PROPN
ejpam-4931	246	6	|∇xξ	|∇xξ	PROPN
ejpam-4931	246	7	−β	−β	ADJ
ejpam-4931	246	8	2	2	NUM
ejpam-4931	246	9	n	n	PRON
ejpam-4931	246	10	|2dx	|2dx	X
ejpam-4931	246	11	,	,	PUNCT
ejpam-4931	246	12	(	(	PUNCT
ejpam-4931	246	13	27	27	NUM
ejpam-4931	246	14	)	)	PUNCT
ejpam-4931	246	15	δ	δ	PROPN
ejpam-4931	247	1	∫	∫	PROPN
ejpam-4931	247	2	ω	ω	PROPN
ejpam-4931	247	3	divx(ξnun)∆	divx(ξnun)∆	PROPN
ejpam-4931	247	4	5	5	NUM
ejpam-4931	247	5	xξndx	xξndx	NOUN
ejpam-4931	247	6	=	=	SYM
ejpam-4931	247	7	δ	δ	PROPN
ejpam-4931	247	8	∫	∫	PROPN
ejpam-4931	247	9	ω	ω	PROPN
ejpam-4931	247	10	(	(	PUNCT
ejpam-4931	247	11	ϵ∆xξn	ϵ∆xξn	PRON
ejpam-4931	247	12	−	−	PROPN
ejpam-4931	247	13	∂tξn	∂tξn	NUM
ejpam-4931	247	14	−	−	PROPN
ejpam-4931	247	15	∂y(ξnvn))∆	∂y(ξnvn))∆	PROPN
ejpam-4931	247	16	5	5	NUM
ejpam-4931	247	17	xξndx	xξndx	NOUN
ejpam-4931	247	18	=	=	SYM
ejpam-4931	247	19	δ	δ	PROPN
ejpam-4931	247	20	2	2	NUM
ejpam-4931	247	21	d	d	NOUN
ejpam-4931	247	22	dt	dt	X
ejpam-4931	247	23	∫	∫	PROPN
ejpam-4931	247	24	ω	ω	PROPN
ejpam-4931	247	25	|∇x∆	|∇x∆	NOUN
ejpam-4931	247	26	2	2	NUM
ejpam-4931	247	27	xξn|2dx	xξn|2dx	PUNCT
ejpam-4931	248	1	+	+	CCONJ
ejpam-4931	248	2	δϵ	δϵ	PROPN
ejpam-4931	248	3	∫	∫	PROPN
ejpam-4931	248	4	ω	ω	PROPN
ejpam-4931	248	5	|∆3	|∆3	PROPN
ejpam-4931	248	6	xξn|2dx	xξn|2dx	PROPN
ejpam-4931	248	7	.	.	PUNCT
ejpam-4931	249	1	(	(	PUNCT
ejpam-4931	249	2	28	28	NUM
ejpam-4931	249	3	)	)	PUNCT
ejpam-4931	249	4	finally	finally	ADV
ejpam-4931	249	5	,	,	PUNCT
ejpam-4931	249	6	we	we	PRON
ejpam-4931	249	7	estimate	estimate	VERB
ejpam-4931	249	8	the	the	DET
ejpam-4931	249	9	quantum	quantum	ADJ
ejpam-4931	249	10	term	term	NOUN
ejpam-4931	249	11	k1	k1	PROPN
ejpam-4931	249	12	∫	∫	PROPN
ejpam-4931	249	13	ω	ω	PROPN
ejpam-4931	249	14	∆x	∆x	PROPN
ejpam-4931	249	15	√	√	NUM
ejpam-4931	249	16	ξn√	ξn√	PUNCT
ejpam-4931	250	1	ξn	ξn	PROPN
ejpam-4931	250	2	divx(ξnun)dx	divx(ξnun)dx	PROPN
ejpam-4931	250	3	=	=	SYM
ejpam-4931	250	4	k1	k1	PROPN
ejpam-4931	250	5	∫	∫	PROPN
ejpam-4931	250	6	ω	ω	PROPN
ejpam-4931	250	7	∆x	∆x	PROPN
ejpam-4931	250	8	√	√	NUM
ejpam-4931	250	9	ξn√	ξn√	PROPN
ejpam-4931	251	1	ξn	ξn	PROPN
ejpam-4931	251	2	(	(	PUNCT
ejpam-4931	251	3	ϵ∆xξn	ϵ∆xξn	PRON
ejpam-4931	251	4	−	−	PROPN
ejpam-4931	251	5	∂tξn	∂tξn	PUNCT
ejpam-4931	251	6	−	−	PROPN
ejpam-4931	251	7	∂y(ξnvn	∂y(ξnvn	NOUN
ejpam-4931	251	8	)	)	PUNCT
ejpam-4931	251	9	)	)	PUNCT
ejpam-4931	252	1	dx	dx	PROPN
ejpam-4931	253	1	=	=	SYM
ejpam-4931	253	2	k1	k1	PROPN
ejpam-4931	254	1	d	d	X
ejpam-4931	254	2	dt	dt	NOUN
ejpam-4931	254	3	∫	∫	PROPN
ejpam-4931	254	4	ω	ω	PROPN
ejpam-4931	254	5	|∇x	|∇x	VERB
ejpam-4931	254	6	√	√	NUM
ejpam-4931	255	1	ξn|2dx	ξn|2dx	PROPN
ejpam-4931	255	2	+	+	NUM
ejpam-4931	255	3	k1ϵ	k1ϵ	PROPN
ejpam-4931	255	4	2	2	NUM
ejpam-4931	255	5	∫	∫	PROPN
ejpam-4931	255	6	ω	ω	NUM
ejpam-4931	255	7	ξn|∇2	ξn|∇2	PROPN
ejpam-4931	255	8	x	x	PROPN
ejpam-4931	255	9	ln	ln	PROPN
ejpam-4931	255	10	ξn|2dx	ξn|2dx	PROPN
ejpam-4931	255	11	,	,	PUNCT
ejpam-4931	255	12	(	(	PUNCT
ejpam-4931	255	13	29	29	NUM
ejpam-4931	255	14	)	)	PUNCT
ejpam-4931	255	15	where	where	SCONJ
ejpam-4931	255	16	we	we	PRON
ejpam-4931	255	17	used	use	VERB
ejpam-4931	255	18	2ξn∇x	2ξn∇x	PROPN
ejpam-4931	255	19	(	(	PUNCT
ejpam-4931	255	20	∆x	∆x	PROPN
ejpam-4931	255	21	√	√	NUM
ejpam-4931	255	22	ξn√	ξn√	PROPN
ejpam-4931	256	1	ξn	ξn	NOUN
ejpam-4931	256	2	)	)	PUNCT
ejpam-4931	257	1	=	=	SYM
ejpam-4931	257	2	2ξn∇x	2ξn∇x	PROPN
ejpam-4931	257	3	(	(	PUNCT
ejpam-4931	257	4	divx	divx	PROPN
ejpam-4931	257	5	(	(	PUNCT
ejpam-4931	257	6	∇x	∇x	NOUN
ejpam-4931	257	7	√	√	NUM
ejpam-4931	257	8	ξn√	ξn√	PROPN
ejpam-4931	257	9	ξn	ξn	NOUN
ejpam-4931	257	10	)	)	PUNCT
ejpam-4931	257	11	−∇x	−∇x	VERB
ejpam-4931	257	12	√	√	PROPN
ejpam-4931	257	13	ξn	ξn	NOUN
ejpam-4931	257	14	·	·	PUNCT
ejpam-4931	257	15	∇x	∇x	PROPN
ejpam-4931	257	16	1√	1√	ADJ
ejpam-4931	257	17	ξn	ξn	NOUN
ejpam-4931	257	18	)	)	PUNCT
ejpam-4931	258	1	=	=	SYM
ejpam-4931	258	2	ξndivx	ξndivx	NOUN
ejpam-4931	258	3	(	(	PUNCT
ejpam-4931	258	4	∇2	∇2	PROPN
ejpam-4931	258	5	x	x	SYM
ejpam-4931	258	6	ln	ln	PROPN
ejpam-4931	258	7	ξn	ξn	PROPN
ejpam-4931	258	8	)	)	PUNCT
ejpam-4931	259	1	+	+	CCONJ
ejpam-4931	259	2	1	1	NUM
ejpam-4931	259	3	2	2	NUM
ejpam-4931	259	4	ξn∇x	ξn∇x	PROPN
ejpam-4931	259	5	(	(	PUNCT
ejpam-4931	259	6	∇x	∇x	PROPN
ejpam-4931	259	7	ln	ln	PROPN
ejpam-4931	259	8	ξn	ξn	NOUN
ejpam-4931	259	9	)	)	PUNCT
ejpam-4931	259	10	2	2	NUM
ejpam-4931	259	11	=	=	SYM
ejpam-4931	259	12	divx	divx	X
ejpam-4931	259	13	(	(	PUNCT
ejpam-4931	259	14	ξn∇2	ξn∇2	NOUN
ejpam-4931	259	15	x	x	SYM
ejpam-4931	259	16	ln	ln	NOUN
ejpam-4931	259	17	ξn	ξn	PROPN
ejpam-4931	259	18	)	)	PUNCT
ejpam-4931	259	19	.	.	PUNCT
ejpam-4931	260	1	substituting	substitute	VERB
ejpam-4931	260	2	(	(	PUNCT
ejpam-4931	260	3	26)-(29	26)-(29	NUM
ejpam-4931	260	4	)	)	PUNCT
ejpam-4931	260	5	in	in	ADP
ejpam-4931	260	6	(	(	PUNCT
ejpam-4931	260	7	25	25	NUM
ejpam-4931	260	8	)	)	PUNCT
ejpam-4931	260	9	,	,	PUNCT
ejpam-4931	260	10	we	we	PRON
ejpam-4931	260	11	obtain	obtain	VERB
ejpam-4931	260	12	the	the	DET
ejpam-4931	260	13	following	follow	VERB
ejpam-4931	260	14	energy	energy	NOUN
ejpam-4931	260	15	equality	equality	NOUN
ejpam-4931	260	16	:	:	PUNCT
ejpam-4931	260	17	d	d	X
ejpam-4931	260	18	dt	dt	PUNCT
ejpam-4931	260	19	e(ξn	e(ξn	PROPN
ejpam-4931	260	20	,	,	PUNCT
ejpam-4931	260	21	un	un	PROPN
ejpam-4931	260	22	)	)	PUNCT
ejpam-4931	261	1	+	+	NUM
ejpam-4931	261	2	2ϵ	2ϵ	NUM
ejpam-4931	261	3	∫	∫	PROPN
ejpam-4931	261	4	ω	ω	X
ejpam-4931	261	5	|∇xξn|2dx	|∇xξn|2dx	PROPN
ejpam-4931	261	6	+	+	PROPN
ejpam-4931	261	7	r1	r1	PROPN
ejpam-4931	261	8	∫	∫	PROPN
ejpam-4931	261	9	ω	ω	NUM
ejpam-4931	261	10	u2ndx	u2ndx	NOUN
ejpam-4931	262	1	+	+	CCONJ
ejpam-4931	262	2	r	r	NOUN
ejpam-4931	262	3	∫	∫	PROPN
ejpam-4931	262	4	ω	ω	NUM
ejpam-4931	262	5	ξn|un|3dx	ξn|un|3dx	PROPN
ejpam-4931	263	1	+	+	CCONJ
ejpam-4931	263	2	α	α	PROPN
ejpam-4931	263	3	∫	∫	PROPN
ejpam-4931	263	4	ω	ω	PROPN
ejpam-4931	263	5	|∆un|2dx	|∆un|2dx	ADJ
ejpam-4931	263	6	+	+	CCONJ
ejpam-4931	263	7	∫	∫	PROPN
ejpam-4931	263	8	ω	ω	NUM
ejpam-4931	263	9	2ξn|dx(un)|2dx	2ξn|dx(un)|2dx	NUM
ejpam-4931	263	10	+	+	CCONJ
ejpam-4931	263	11	4ϵr2	4ϵr2	NUM
ejpam-4931	263	12	β	β	PROPN
ejpam-4931	263	13	∫	∫	PROPN
ejpam-4931	263	14	ω	ω	PROPN
ejpam-4931	263	15	|∇xξ	|∇xξ	PROPN
ejpam-4931	263	16	−β	−β	ADJ
ejpam-4931	263	17	2	2	NUM
ejpam-4931	263	18	n	n	PRON
ejpam-4931	263	19	|2dx	|2dx	ADJ
ejpam-4931	263	20	+	+	CCONJ
ejpam-4931	263	21	∫	∫	PROPN
ejpam-4931	263	22	ω	ω	NUM
ejpam-4931	263	23	ξn|∂yun|2dx	ξn|∂yun|2dx	VERB
ejpam-4931	263	24	+	+	CCONJ
ejpam-4931	263	25	k1ϵ	k1ϵ	PROPN
ejpam-4931	263	26	2	2	NUM
ejpam-4931	263	27	∫	∫	PROPN
ejpam-4931	263	28	ω	ω	NUM
ejpam-4931	263	29	ξn|∇2	ξn|∇2	PROPN
ejpam-4931	264	1	x	x	X
ejpam-4931	264	2	ln	ln	PROPN
ejpam-4931	265	1	ξn|2dx	ξn|2dx	PROPN
ejpam-4931	265	2	+	+	CCONJ
ejpam-4931	265	3	δϵ	δϵ	ADP
ejpam-4931	265	4	∫	∫	PROPN
ejpam-4931	265	5	ω	ω	PROPN
ejpam-4931	265	6	|∆3	|∆3	PROPN
ejpam-4931	265	7	xξn|2dx	xξn|2dx	PROPN
ejpam-4931	266	1	=	=	SYM
ejpam-4931	266	2	0	0	PUNCT
ejpam-4931	266	3	(	(	PUNCT
ejpam-4931	266	4	30	30	NUM
ejpam-4931	266	5	)	)	PUNCT
ejpam-4931	266	6	on	on	ADP
ejpam-4931	266	7	[	[	X
ejpam-4931	266	8	0	0	NUM
ejpam-4931	266	9	,	,	PUNCT
ejpam-4931	266	10	τ	τ	X
ejpam-4931	266	11	]	]	PUNCT
ejpam-4931	266	12	where	where	SCONJ
ejpam-4931	266	13	,	,	PUNCT
ejpam-4931	266	14	e(ξn	e(ξn	PROPN
ejpam-4931	266	15	,	,	PUNCT
ejpam-4931	266	16	un	un	PROPN
ejpam-4931	266	17	)	)	PUNCT
ejpam-4931	266	18	=	=	SYM
ejpam-4931	266	19	∫	∫	PROPN
ejpam-4931	266	20	ω	ω	PROPN
ejpam-4931	266	21	(	(	PUNCT
ejpam-4931	266	22	1	1	NUM
ejpam-4931	266	23	2	2	NUM
ejpam-4931	266	24	ξnu	ξnu	NOUN
ejpam-4931	266	25	2	2	NUM
ejpam-4931	266	26	n	n	NOUN
ejpam-4931	266	27	+	+	CCONJ
ejpam-4931	266	28	ξ2n	ξ2n	PROPN
ejpam-4931	266	29	+	+	CCONJ
ejpam-4931	266	30	r2	r2	PROPN
ejpam-4931	266	31	β	β	X
ejpam-4931	266	32	+	+	CCONJ
ejpam-4931	266	33	1	1	NUM
ejpam-4931	266	34	ξ−β	ξ−β	VERB
ejpam-4931	266	35	n	n	NOUN
ejpam-4931	266	36	+	+	CCONJ
ejpam-4931	266	37	k1|∇x	k1|∇x	PROPN
ejpam-4931	266	38	√	√	X
ejpam-4931	267	1	ξn|2	ξn|2	PROPN
ejpam-4931	267	2	+	+	CCONJ
ejpam-4931	267	3	δ	δ	NOUN
ejpam-4931	267	4	2	2	NUM
ejpam-4931	267	5	|∇x∆	|∇x∆	NOUN
ejpam-4931	267	6	2	2	NUM
ejpam-4931	267	7	xξn|2	xξn|2	PUNCT
ejpam-4931	267	8	)	)	PUNCT
ejpam-4931	267	9	dx	dx	PROPN
ejpam-4931	267	10	,	,	PUNCT
ejpam-4931	267	11	j.	j.	PROPN
ejpam-4931	267	12	ouya	ouya	PROPN
ejpam-4931	267	13	,	,	PUNCT
ejpam-4931	267	14	a.	a.	NOUN
ejpam-4931	267	15	ouédraogo	ouédraogo	PROPN
ejpam-4931	267	16	/	/	SYM
ejpam-4931	267	17	eur	eur	PROPN
ejpam-4931	267	18	.	.	PUNCT
ejpam-4931	268	1	j.	j.	PROPN
ejpam-4931	268	2	pure	pure	PROPN
ejpam-4931	268	3	appl	appl	PROPN
ejpam-4931	268	4	.	.	PROPN
ejpam-4931	268	5	math	math	PROPN
ejpam-4931	268	6	,	,	PUNCT
ejpam-4931	268	7	16	16	NUM
ejpam-4931	268	8	(	(	PUNCT
ejpam-4931	268	9	4	4	NUM
ejpam-4931	268	10	)	)	PUNCT
ejpam-4931	268	11	(	(	PUNCT
ejpam-4931	268	12	2023	2023	NUM
ejpam-4931	268	13	)	)	PUNCT
ejpam-4931	268	14	,	,	PUNCT
ejpam-4931	268	15	2247	2247	NUM
ejpam-4931	268	16	-	-	SYM
ejpam-4931	268	17	2285	2285	NUM
ejpam-4931	268	18	2257	2257	NUM
ejpam-4931	268	19	and	and	CCONJ
ejpam-4931	268	20	e0(ξn	e0(ξn	PROPN
ejpam-4931	268	21	,	,	PUNCT
ejpam-4931	268	22	un	un	PROPN
ejpam-4931	268	23	)	)	PUNCT
ejpam-4931	268	24	=	=	SYM
ejpam-4931	269	1	∫	∫	PROPN
ejpam-4931	269	2	ω	ω	PROPN
ejpam-4931	269	3	(	(	PUNCT
ejpam-4931	269	4	1	1	NUM
ejpam-4931	269	5	2	2	NUM
ejpam-4931	269	6	ξ0u	ξ0u	NOUN
ejpam-4931	269	7	2	2	NUM
ejpam-4931	269	8	0	0	NUM
ejpam-4931	269	9	+	+	CCONJ
ejpam-4931	269	10	ξ20	ξ20	X
ejpam-4931	269	11	+	+	X
ejpam-4931	269	12	r2	r2	PROPN
ejpam-4931	269	13	β	β	X
ejpam-4931	269	14	+	+	CCONJ
ejpam-4931	269	15	1	1	NUM
ejpam-4931	269	16	ξ−β	ξ−β	NOUN
ejpam-4931	269	17	0	0	PUNCT
ejpam-4931	270	1	+	+	CCONJ
ejpam-4931	270	2	k1|∇x	k1|∇x	PROPN
ejpam-4931	270	3	√	√	NUM
ejpam-4931	270	4	ξ0|2	ξ0|2	NOUN
ejpam-4931	270	5	+	+	CCONJ
ejpam-4931	270	6	δ	δ	NOUN
ejpam-4931	270	7	2	2	NUM
ejpam-4931	270	8	|∇x∆	|∇x∆	NOUN
ejpam-4931	270	9	2	2	NUM
ejpam-4931	270	10	xξ0|2	xξ0|2	X
ejpam-4931	270	11	)	)	PUNCT
ejpam-4931	270	12	dx	dx	PROPN
ejpam-4931	270	13	.	.	PUNCT
ejpam-4931	271	1	thus	thus	ADV
ejpam-4931	271	2	the	the	DET
ejpam-4931	271	3	energy	energy	NOUN
ejpam-4931	271	4	equality	equality	NOUN
ejpam-4931	271	5	(	(	PUNCT
ejpam-4931	271	6	30	30	NUM
ejpam-4931	271	7	)	)	PUNCT
ejpam-4931	271	8	gives∫	gives∫	NOUN
ejpam-4931	271	9	τ	τ	PROPN
ejpam-4931	271	10	0	0	NUM
ejpam-4931	271	11	∥∆xun∥2l2(ω)dt	∥∆xun∥2l2(ω)dt	PROPN
ejpam-4931	271	12	≤	≤	PROPN
ejpam-4931	271	13	e0(ξn	e0(ξn	PROPN
ejpam-4931	271	14	,	,	PUNCT
ejpam-4931	271	15	un	un	PROPN
ejpam-4931	271	16	)	)	PUNCT
ejpam-4931	271	17	<	<	X
ejpam-4931	272	1	+	+	PRON
ejpam-4931	272	2	∞.	∞.	PROPN
ejpam-4931	272	3	(	(	PUNCT
ejpam-4931	272	4	31	31	NUM
ejpam-4931	272	5	)	)	PUNCT
ejpam-4931	272	6	from	from	ADP
ejpam-4931	272	7	dimxn	dimxn	NOUN
ejpam-4931	272	8	<	<	X
ejpam-4931	272	9	∞	∞	NUM
ejpam-4931	272	10	and	and	CCONJ
ejpam-4931	272	11	(	(	PUNCT
ejpam-4931	272	12	20	20	NUM
ejpam-4931	272	13	)	)	PUNCT
ejpam-4931	272	14	,	,	PUNCT
ejpam-4931	272	15	the	the	DET
ejpam-4931	272	16	density	density	NOUN
ejpam-4931	272	17	is	be	AUX
ejpam-4931	272	18	bounded	bound	VERB
ejpam-4931	272	19	with	with	ADP
ejpam-4931	272	20	a	a	DET
ejpam-4931	272	21	positive	positive	ADJ
ejpam-4931	272	22	constant	constant	NOUN
ejpam-4931	272	23	,	,	PUNCT
ejpam-4931	272	24	which	which	PRON
ejpam-4931	272	25	means	mean	VERB
ejpam-4931	272	26	that	that	SCONJ
ejpam-4931	272	27	there	there	PRON
ejpam-4931	272	28	exists	exist	VERB
ejpam-4931	272	29	a	a	DET
ejpam-4931	272	30	constant	constant	ADJ
ejpam-4931	272	31	η	η	NOUN
ejpam-4931	272	32	>	>	X
ejpam-4931	272	33	0	0	NUM
ejpam-4931	272	34	such	such	ADJ
ejpam-4931	272	35	that	that	SCONJ
ejpam-4931	272	36	0	0	NUM
ejpam-4931	272	37	<	<	X
ejpam-4931	272	38	η	η	PROPN
ejpam-4931	272	39	≤	≤	PROPN
ejpam-4931	272	40	ξn(t	ξn(t	NUM
ejpam-4931	272	41	,	,	PUNCT
ejpam-4931	272	42	x	x	NOUN
ejpam-4931	272	43	)	)	PUNCT
ejpam-4931	272	44	≤	≤	NUM
ejpam-4931	272	45	1	1	NUM
ejpam-4931	272	46	η	η	NOUN
ejpam-4931	272	47	,	,	PUNCT
ejpam-4931	272	48	(	(	PUNCT
ejpam-4931	272	49	32	32	NUM
ejpam-4931	272	50	)	)	PUNCT
ejpam-4931	272	51	for	for	ADP
ejpam-4931	272	52	any	any	DET
ejpam-4931	272	53	t	t	NOUN
ejpam-4931	272	54	∈	∈	PROPN
ejpam-4931	273	1	[	[	X
ejpam-4931	273	2	0	0	NUM
ejpam-4931	273	3	,	,	PUNCT
ejpam-4931	273	4	τ	τ	PROPN
ejpam-4931	273	5	]	]	PUNCT
ejpam-4931	273	6	and	and	CCONJ
ejpam-4931	273	7	(	(	PUNCT
ejpam-4931	273	8	x	x	NOUN
ejpam-4931	273	9	,	,	PUNCT
ejpam-4931	273	10	y	y	NOUN
ejpam-4931	273	11	)	)	PUNCT
ejpam-4931	273	12	∈	∈	PROPN
ejpam-4931	273	13	ω	ω	PROPN
ejpam-4931	273	14	.	.	PUNCT
ejpam-4931	274	1	furthermore	furthermore	ADV
ejpam-4931	274	2	,	,	PUNCT
ejpam-4931	274	3	from	from	ADP
ejpam-4931	274	4	the	the	DET
ejpam-4931	274	5	basic	basic	ADJ
ejpam-4931	274	6	energy	energy	NOUN
ejpam-4931	274	7	equality	equality	NOUN
ejpam-4931	274	8	(	(	PUNCT
ejpam-4931	274	9	30	30	NUM
ejpam-4931	274	10	)	)	PUNCT
ejpam-4931	274	11	and	and	CCONJ
ejpam-4931	274	12	using	use	VERB
ejpam-4931	274	13	(	(	PUNCT
ejpam-4931	274	14	32	32	NUM
ejpam-4931	274	15	)	)	PUNCT
ejpam-4931	274	16	,	,	PUNCT
ejpam-4931	274	17	we	we	PRON
ejpam-4931	274	18	also	also	ADV
ejpam-4931	274	19	obtain	obtain	VERB
ejpam-4931	274	20	sup	sup	NOUN
ejpam-4931	274	21	t∈[0,τ	t∈[0,τ	X
ejpam-4931	274	22	]	]	PUNCT
ejpam-4931	274	23	∫	∫	PROPN
ejpam-4931	274	24	ω	ω	PROPN
ejpam-4931	274	25	ξnu	ξnu	PROPN
ejpam-4931	274	26	2	2	NUM
ejpam-4931	274	27	ndx	ndx	NOUN
ejpam-4931	274	28	≤	≤	NOUN
ejpam-4931	274	29	e0(ξn	e0(ξn	PROPN
ejpam-4931	274	30	,	,	PUNCT
ejpam-4931	274	31	un	un	PROPN
ejpam-4931	274	32	)	)	PUNCT
ejpam-4931	274	33	≤	≤	PUNCT
ejpam-4931	275	1	c	c	X
ejpam-4931	275	2	<	<	X
ejpam-4931	275	3	∞.	∞.	PROPN
ejpam-4931	275	4	(	(	PUNCT
ejpam-4931	275	5	33	33	NUM
ejpam-4931	275	6	)	)	PUNCT
ejpam-4931	275	7	from	from	ADP
ejpam-4931	275	8	(	(	PUNCT
ejpam-4931	275	9	30	30	NUM
ejpam-4931	275	10	)	)	PUNCT
ejpam-4931	275	11	,	,	PUNCT
ejpam-4931	275	12	we	we	PRON
ejpam-4931	275	13	get	get	VERB
ejpam-4931	275	14	sup	sup	NOUN
ejpam-4931	275	15	t∈[0,τ	t∈[0,τ	X
ejpam-4931	275	16	]	]	PUNCT
ejpam-4931	275	17	∫	∫	PROPN
ejpam-4931	275	18	ω	ω	PROPN
ejpam-4931	275	19	ξn|dx(un)|2dx	ξn|dx(un)|2dx	PROPN
ejpam-4931	275	20	≤	≤	PROPN
ejpam-4931	275	21	e0(ξn	e0(ξn	PROPN
ejpam-4931	275	22	,	,	PUNCT
ejpam-4931	275	23	un	un	PROPN
ejpam-4931	275	24	)	)	PUNCT
ejpam-4931	275	25	.	.	PUNCT
ejpam-4931	276	1	(	(	PUNCT
ejpam-4931	276	2	34	34	NUM
ejpam-4931	276	3	)	)	PUNCT
ejpam-4931	276	4	as	as	SCONJ
ejpam-4931	276	5	all	all	DET
ejpam-4931	276	6	norms	norm	NOUN
ejpam-4931	276	7	are	be	AUX
ejpam-4931	276	8	equivalent	equivalent	ADJ
ejpam-4931	276	9	on	on	ADP
ejpam-4931	276	10	xn	xn	PROPN
ejpam-4931	276	11	,	,	PUNCT
ejpam-4931	276	12	from	from	ADP
ejpam-4931	276	13	(	(	PUNCT
ejpam-4931	276	14	31	31	NUM
ejpam-4931	276	15	)	)	PUNCT
ejpam-4931	276	16	-(33	-(33	PROPN
ejpam-4931	276	17	)	)	PUNCT
ejpam-4931	276	18	,	,	PUNCT
ejpam-4931	276	19	we	we	PRON
ejpam-4931	276	20	obtain	obtain	VERB
ejpam-4931	276	21	sup	sup	NOUN
ejpam-4931	276	22	t∈[0,τ	t∈[0,τ	X
ejpam-4931	276	23	]	]	PUNCT
ejpam-4931	276	24	∥un∥l∞(ω)≤	∥un∥l∞(ω)≤	ADP
ejpam-4931	276	25	c	c	X
ejpam-4931	276	26	<	<	X
ejpam-4931	276	27	+	+	NOUN
ejpam-4931	276	28	∞	∞	PROPN
ejpam-4931	276	29	,	,	PUNCT
ejpam-4931	276	30	(	(	PUNCT
ejpam-4931	276	31	35	35	NUM
ejpam-4931	276	32	)	)	PUNCT
ejpam-4931	276	33	sup	sup	NOUN
ejpam-4931	276	34	t∈[0,τ	t∈[0,τ	X
ejpam-4931	276	35	]	]	PUNCT
ejpam-4931	276	36	∥∇xun∥l∞(ω)≤	∥∇xun∥l∞(ω)≤	PROPN
ejpam-4931	276	37	c	c	NOUN
ejpam-4931	276	38	and	and	CCONJ
ejpam-4931	276	39	sup	sup	NOUN
ejpam-4931	276	40	t∈[0,τ	t∈[0,τ	PROPN
ejpam-4931	276	41	]	]	PUNCT
ejpam-4931	276	42	∥∆xun∥l∞(ω)≤	∥∆xun∥l∞(ω)≤	PROPN
ejpam-4931	276	43	c.	c.	NOUN
ejpam-4931	276	44	(	(	PUNCT
ejpam-4931	276	45	36	36	NUM
ejpam-4931	276	46	)	)	PUNCT
ejpam-4931	276	47	then	then	ADV
ejpam-4931	276	48	,	,	PUNCT
ejpam-4931	276	49	we	we	PRON
ejpam-4931	276	50	can	can	AUX
ejpam-4931	276	51	extend	extend	VERB
ejpam-4931	276	52	τ	τ	PROPN
ejpam-4931	276	53	to	to	ADP
ejpam-4931	276	54	t	t	NOUN
ejpam-4931	276	55	by	by	ADP
ejpam-4931	276	56	repeating	repeat	VERB
ejpam-4931	276	57	the	the	DET
ejpam-4931	276	58	above	above	ADJ
ejpam-4931	276	59	argument	argument	NOUN
ejpam-4931	276	60	several	several	ADJ
ejpam-4931	276	61	times	time	NOUN
ejpam-4931	276	62	and	and	CCONJ
ejpam-4931	276	63	obtain	obtain	VERB
ejpam-4931	276	64	un	un	PROPN
ejpam-4931	276	65	∈	∈	PROPN
ejpam-4931	276	66	c	c	PROPN
ejpam-4931	276	67	(	(	PUNCT
ejpam-4931	276	68	[	[	X
ejpam-4931	276	69	0	0	NUM
ejpam-4931	276	70	,	,	PUNCT
ejpam-4931	276	71	t	t	X
ejpam-4931	276	72	]	]	PUNCT
ejpam-4931	276	73	;	;	PUNCT
ejpam-4931	276	74	xn	xn	NUM
ejpam-4931	276	75	)	)	PUNCT
ejpam-4931	276	76	.	.	PUNCT
ejpam-4931	277	1	in	in	ADP
ejpam-4931	277	2	other	other	ADJ
ejpam-4931	277	3	words	word	NOUN
ejpam-4931	277	4	,	,	PUNCT
ejpam-4931	277	5	we	we	PRON
ejpam-4931	277	6	obtain	obtain	VERB
ejpam-4931	277	7	a	a	DET
ejpam-4931	277	8	global	global	ADJ
ejpam-4931	277	9	solution	solution	NOUN
ejpam-4931	277	10	(	(	PUNCT
ejpam-4931	277	11	ξn	ξn	PROPN
ejpam-4931	277	12	,	,	PUNCT
ejpam-4931	277	13	un	un	PROPN
ejpam-4931	277	14	,	,	PUNCT
ejpam-4931	277	15	vn	vn	NOUN
ejpam-4931	277	16	)	)	PUNCT
ejpam-4931	277	17	of	of	ADP
ejpam-4931	277	18	(	(	PUNCT
ejpam-4931	277	19	19	19	NUM
ejpam-4931	277	20	)	)	PUNCT
ejpam-4931	277	21	and	and	CCONJ
ejpam-4931	277	22	(	(	PUNCT
ejpam-4931	277	23	24	24	NUM
ejpam-4931	277	24	)	)	PUNCT
ejpam-4931	277	25	for	for	ADP
ejpam-4931	277	26	any	any	DET
ejpam-4931	277	27	t	t	PROPN
ejpam-4931	277	28	>	>	X
ejpam-4931	277	29	0	0	X
ejpam-4931	277	30	.	.	PUNCT
ejpam-4931	278	1	moreover	moreover	ADV
ejpam-4931	278	2	,	,	PUNCT
ejpam-4931	278	3	from	from	ADP
ejpam-4931	278	4	(	(	PUNCT
ejpam-4931	278	5	30	30	NUM
ejpam-4931	278	6	)	)	PUNCT
ejpam-4931	278	7	,	,	PUNCT
ejpam-4931	278	8	we	we	PRON
ejpam-4931	278	9	have	have	VERB
ejpam-4931	278	10	sup	sup	NOUN
ejpam-4931	278	11	t∈[0,t	t∈[0,t	PROPN
ejpam-4931	278	12	]	]	PUNCT
ejpam-4931	278	13	∫	∫	PROPN
ejpam-4931	279	1	ω	ω	NUM
ejpam-4931	279	2	√	√	PROPN
ejpam-4931	279	3	ξnu	ξnu	VERB
ejpam-4931	279	4	2	2	NUM
ejpam-4931	279	5	ndx	ndx	NOUN
ejpam-4931	279	6	≤	≤	NOUN
ejpam-4931	279	7	e0(ξn	e0(ξn	PROPN
ejpam-4931	279	8	,	,	PUNCT
ejpam-4931	279	9	un	un	PROPN
ejpam-4931	279	10	)	)	PUNCT
ejpam-4931	279	11	.	.	PUNCT
ejpam-4931	280	1	(	(	PUNCT
ejpam-4931	280	2	37	37	NUM
ejpam-4931	280	3	)	)	PUNCT
ejpam-4931	280	4	also	also	ADV
ejpam-4931	280	5	,	,	PUNCT
ejpam-4931	280	6	e(ξn	e(ξn	PROPN
ejpam-4931	280	7	,	,	PUNCT
ejpam-4931	280	8	un	un	NOUN
ejpam-4931	280	9	)	)	PUNCT
ejpam-4931	280	10	≤	≤	NOUN
ejpam-4931	280	11	e0(ξn	e0(ξn	PROPN
ejpam-4931	280	12	,	,	PUNCT
ejpam-4931	280	13	un	un	PROPN
ejpam-4931	280	14	)	)	PUNCT
ejpam-4931	280	15	,	,	PUNCT
ejpam-4931	280	16	(	(	PUNCT
ejpam-4931	280	17	38	38	NUM
ejpam-4931	280	18	)	)	PUNCT
ejpam-4931	280	19	which	which	PRON
ejpam-4931	280	20	gives	give	VERB
ejpam-4931	280	21	∥ξn∥l∞(0,t	∥ξn∥l∞(0,t	NOUN
ejpam-4931	280	22	;	;	PUNCT
ejpam-4931	280	23	h5(ω))≤	h5(ω))≤	PROPN
ejpam-4931	280	24	c	c	X
ejpam-4931	280	25	(	(	PUNCT
ejpam-4931	280	26	e0(ξn	e0(ξn	PROPN
ejpam-4931	280	27	,	,	PUNCT
ejpam-4931	280	28	un	un	PROPN
ejpam-4931	280	29	)	)	PUNCT
ejpam-4931	280	30	,	,	PUNCT
ejpam-4931	280	31	δ	δ	PROPN
ejpam-4931	280	32	)	)	PUNCT
ejpam-4931	280	33	and	and	CCONJ
ejpam-4931	280	34	∥ξ2n∥l∞(0,t	∥ξ2n∥l∞(0,t	PROPN
ejpam-4931	280	35	;	;	PUNCT
ejpam-4931	280	36	l2(ω))≤	l2(ω))≤	ADJ
ejpam-4931	280	37	c.	c.	NOUN
ejpam-4931	280	38	(	(	PUNCT
ejpam-4931	280	39	39	39	NUM
ejpam-4931	280	40	)	)	PUNCT
ejpam-4931	280	41	using	use	VERB
ejpam-4931	280	42	hölder	hölder	NOUN
ejpam-4931	280	43	’s	’s	PART
ejpam-4931	280	44	inequality	inequality	NOUN
ejpam-4931	280	45	we	we	PRON
ejpam-4931	280	46	have:∫	have:∫	VERB
ejpam-4931	281	1	ω	ω	NUM
ejpam-4931	281	2	ξnū	ξnū	NOUN
ejpam-4931	281	3	2	2	NUM
ejpam-4931	281	4	ndxdy	ndxdy	NOUN
ejpam-4931	281	5	=	=	SYM
ejpam-4931	281	6	∫	∫	PROPN
ejpam-4931	282	1	ω	ω	PROPN
ejpam-4931	282	2	ξn	ξn	PROPN
ejpam-4931	282	3	(	(	PUNCT
ejpam-4931	282	4	∫	∫	PROPN
ejpam-4931	282	5	1	1	NUM
ejpam-4931	282	6	0	0	NUM
ejpam-4931	282	7	un(τ)dτ	un(τ)dτ	ADJ
ejpam-4931	282	8	)	)	PUNCT
ejpam-4931	282	9	2	2	NUM
ejpam-4931	282	10	dxdy	dxdy	PROPN
ejpam-4931	282	11	j.	j.	PROPN
ejpam-4931	282	12	ouya	ouya	PROPN
ejpam-4931	282	13	,	,	PUNCT
ejpam-4931	282	14	a.	a.	NOUN
ejpam-4931	282	15	ouédraogo	ouédraogo	PROPN
ejpam-4931	282	16	/	/	SYM
ejpam-4931	282	17	eur	eur	PROPN
ejpam-4931	282	18	.	.	PUNCT
ejpam-4931	283	1	j.	j.	PROPN
ejpam-4931	283	2	pure	pure	PROPN
ejpam-4931	283	3	appl	appl	PROPN
ejpam-4931	283	4	.	.	PROPN
ejpam-4931	283	5	math	math	PROPN
ejpam-4931	283	6	,	,	PUNCT
ejpam-4931	283	7	16	16	NUM
ejpam-4931	283	8	(	(	PUNCT
ejpam-4931	283	9	4	4	NUM
ejpam-4931	283	10	)	)	PUNCT
ejpam-4931	283	11	(	(	PUNCT
ejpam-4931	283	12	2023	2023	NUM
ejpam-4931	283	13	)	)	PUNCT
ejpam-4931	283	14	,	,	PUNCT
ejpam-4931	283	15	2247	2247	NUM
ejpam-4931	283	16	-	-	SYM
ejpam-4931	283	17	2285	2285	NUM
ejpam-4931	283	18	2258	2258	NUM
ejpam-4931	283	19	≤	≤	NUM
ejpam-4931	283	20	∫	∫	PROPN
ejpam-4931	283	21	ω	ω	PROPN
ejpam-4931	283	22	ξn	ξn	PROPN
ejpam-4931	283	23	(	(	PUNCT
ejpam-4931	283	24	∫	∫	PROPN
ejpam-4931	283	25	1	1	NUM
ejpam-4931	283	26	0	0	NUM
ejpam-4931	283	27	|un(τ)|2dτ	|un(τ)|2dτ	NUM
ejpam-4931	283	28	)	)	PUNCT
ejpam-4931	283	29	dxdy	dxdy	PROPN
ejpam-4931	283	30	≤	≤	NUM
ejpam-4931	283	31	∫	∫	PROPN
ejpam-4931	283	32	1	1	NUM
ejpam-4931	283	33	0	0	NUM
ejpam-4931	283	34	(	(	PUNCT
ejpam-4931	284	1	sup	sup	NOUN
ejpam-4931	284	2	t∈[0,t	t∈[0,t	NOUN
ejpam-4931	284	3	]	]	PUNCT
ejpam-4931	284	4	∫	∫	PROPN
ejpam-4931	284	5	ω	ω	PROPN
ejpam-4931	284	6	ξnu	ξnu	PROPN
ejpam-4931	284	7	2	2	NUM
ejpam-4931	284	8	ndxdy	ndxdy	NOUN
ejpam-4931	284	9	)	)	PUNCT
ejpam-4931	284	10	dτ	dτ	PROPN
ejpam-4931	285	1	≤	≤	NUM
ejpam-4931	285	2	∫	∫	PROPN
ejpam-4931	285	3	1	1	NUM
ejpam-4931	285	4	0	0	NUM
ejpam-4931	285	5	e0(ξn	e0(ξn	PROPN
ejpam-4931	285	6	,	,	PUNCT
ejpam-4931	285	7	un)dτ	un)dτ	PROPN
ejpam-4931	285	8	≤	≤	PROPN
ejpam-4931	285	9	e0(ξn	e0(ξn	PROPN
ejpam-4931	285	10	,	,	PUNCT
ejpam-4931	285	11	un	un	PROPN
ejpam-4931	285	12	)	)	PUNCT
ejpam-4931	285	13	(	(	PUNCT
ejpam-4931	285	14	40	40	NUM
ejpam-4931	285	15	)	)	PUNCT
ejpam-4931	285	16	and	and	CCONJ
ejpam-4931	285	17	∫	∫	PROPN
ejpam-4931	285	18	ω	ω	PROPN
ejpam-4931	285	19	ξnũ	ξnũ	PROPN
ejpam-4931	285	20	2	2	NUM
ejpam-4931	285	21	ndxdy	ndxdy	NOUN
ejpam-4931	285	22	=	=	SYM
ejpam-4931	285	23	∫	∫	PROPN
ejpam-4931	286	1	ω	ω	PROPN
ejpam-4931	286	2	ξn	ξn	PROPN
ejpam-4931	286	3	(	(	PUNCT
ejpam-4931	286	4	∫	∫	PROPN
ejpam-4931	286	5	y	y	PROPN
ejpam-4931	286	6	0	0	NUM
ejpam-4931	286	7	un(τ)dτ	un(τ)dτ	ADJ
ejpam-4931	286	8	)	)	PUNCT
ejpam-4931	286	9	2	2	NUM
ejpam-4931	286	10	dxdy	dxdy	PROPN
ejpam-4931	286	11	≤	≤	PROPN
ejpam-4931	286	12	∫	∫	PROPN
ejpam-4931	286	13	ω	ω	PROPN
ejpam-4931	286	14	ξn	ξn	PROPN
ejpam-4931	286	15	(	(	PUNCT
ejpam-4931	286	16	∫	∫	PROPN
ejpam-4931	286	17	y	y	PROPN
ejpam-4931	286	18	0	0	PROPN
ejpam-4931	286	19	|un(τ)|2dτ	|un(τ)|2dτ	X
ejpam-4931	286	20	)	)	PUNCT
ejpam-4931	286	21	dxdy	dxdy	PROPN
ejpam-4931	286	22	≤	≤	PROPN
ejpam-4931	286	23	∫	∫	PROPN
ejpam-4931	287	1	ω	ω	PROPN
ejpam-4931	287	2	ξn	ξn	PROPN
ejpam-4931	287	3	(	(	PUNCT
ejpam-4931	287	4	∫	∫	PROPN
ejpam-4931	287	5	1	1	NUM
ejpam-4931	287	6	0	0	NUM
ejpam-4931	287	7	|un(τ)|2dτ	|un(τ)|2dτ	NUM
ejpam-4931	287	8	)	)	PUNCT
ejpam-4931	287	9	dxdy	dxdy	PROPN
ejpam-4931	287	10	≤	≤	PROPN
ejpam-4931	287	11	∫	∫	PROPN
ejpam-4931	287	12	ω	ω	PROPN
ejpam-4931	287	13	ξn	ξn	PROPN
ejpam-4931	287	14	(	(	PUNCT
ejpam-4931	287	15	∫	∫	PROPN
ejpam-4931	287	16	1	1	NUM
ejpam-4931	287	17	0	0	NUM
ejpam-4931	287	18	12dτ	12dτ	NOUN
ejpam-4931	287	19	)	)	PUNCT
ejpam-4931	287	20	(	(	PUNCT
ejpam-4931	287	21	∫	∫	PROPN
ejpam-4931	287	22	1	1	NUM
ejpam-4931	287	23	0	0	NUM
ejpam-4931	287	24	u2n(τ)dτ	u2n(τ)dτ	ADJ
ejpam-4931	287	25	)	)	PUNCT
ejpam-4931	287	26	dxdz	dxdz	VERB
ejpam-4931	287	27	≤	≤	PROPN
ejpam-4931	287	28	e0(ξn	e0(ξn	PROPN
ejpam-4931	287	29	,	,	PUNCT
ejpam-4931	287	30	un	un	PROPN
ejpam-4931	287	31	)	)	PUNCT
ejpam-4931	287	32	.	.	PUNCT
ejpam-4931	288	1	(	(	PUNCT
ejpam-4931	288	2	41	41	NUM
ejpam-4931	288	3	)	)	PUNCT
ejpam-4931	288	4	in	in	ADP
ejpam-4931	288	5	addition	addition	NOUN
ejpam-4931	288	6	,	,	PUNCT
ejpam-4931	288	7	the	the	DET
ejpam-4931	288	8	basic	basic	ADJ
ejpam-4931	288	9	energy	energy	NOUN
ejpam-4931	288	10	(	(	PUNCT
ejpam-4931	288	11	30	30	NUM
ejpam-4931	288	12	)	)	PUNCT
ejpam-4931	288	13	also	also	ADV
ejpam-4931	288	14	gives∫	gives∫	VERB
ejpam-4931	288	15	t	t	PROPN
ejpam-4931	288	16	0	0	NUM
ejpam-4931	288	17	∫	∫	PROPN
ejpam-4931	289	1	ω	ω	NUM
ejpam-4931	289	2	ξn|∇2	ξn|∇2	PROPN
ejpam-4931	289	3	x	x	SYM
ejpam-4931	289	4	ln	ln	PROPN
ejpam-4931	289	5	ξn|2dxdt	ξn|2dxdt	PROPN
ejpam-4931	289	6	≤	≤	PROPN
ejpam-4931	289	7	e0(ξn	e0(ξn	PROPN
ejpam-4931	289	8	,	,	PUNCT
ejpam-4931	289	9	un	un	PROPN
ejpam-4931	289	10	)	)	PUNCT
ejpam-4931	289	11	(	(	PUNCT
ejpam-4931	289	12	42	42	NUM
ejpam-4931	289	13	)	)	PUNCT
ejpam-4931	289	14	and	and	CCONJ
ejpam-4931	289	15	sup	sup	NOUN
ejpam-4931	289	16	t∈[0,t	t∈[0,t	PROPN
ejpam-4931	289	17	]	]	PUNCT
ejpam-4931	290	1	∫	∫	PROPN
ejpam-4931	290	2	ω	ω	PROPN
ejpam-4931	290	3	δ|∇x∆	δ|∇x∆	PROPN
ejpam-4931	290	4	2	2	NUM
ejpam-4931	290	5	xξn|2dx	xξn|2dx	SYM
ejpam-4931	290	6	≤	≤	NUM
ejpam-4931	290	7	e0(ξn	e0(ξn	PROPN
ejpam-4931	290	8	,	,	PUNCT
ejpam-4931	290	9	un	un	PROPN
ejpam-4931	290	10	)	)	PUNCT
ejpam-4931	290	11	,	,	PUNCT
ejpam-4931	290	12	(	(	PUNCT
ejpam-4931	290	13	43	43	NUM
ejpam-4931	290	14	)	)	PUNCT
ejpam-4931	290	15	which	which	PRON
ejpam-4931	290	16	,	,	PUNCT
ejpam-4931	290	17	with	with	ADP
ejpam-4931	290	18	(	(	PUNCT
ejpam-4931	290	19	32	32	NUM
ejpam-4931	290	20	)	)	PUNCT
ejpam-4931	290	21	,	,	PUNCT
ejpam-4931	290	22	implies	imply	VERB
ejpam-4931	290	23	that	that	SCONJ
ejpam-4931	290	24	ξn	ξn	PROPN
ejpam-4931	290	25	is	be	AUX
ejpam-4931	290	26	a	a	DET
ejpam-4931	290	27	positive	positive	ADJ
ejpam-4931	290	28	regular	regular	ADJ
ejpam-4931	290	29	function	function	NOUN
ejpam-4931	290	30	.	.	PUNCT
ejpam-4931	291	1	we	we	PRON
ejpam-4931	291	2	need	need	VERB
ejpam-4931	291	3	the	the	DET
ejpam-4931	291	4	following	follow	VERB
ejpam-4931	291	5	lemma	lemma	PROPN
ejpam-4931	291	6	from	from	ADP
ejpam-4931	291	7	jüngel	jüngel	NOUN
ejpam-4931	291	8	[	[	X
ejpam-4931	291	9	9	9	NUM
ejpam-4931	291	10	]	]	PUNCT
ejpam-4931	291	11	.	.	PUNCT
ejpam-4931	292	1	lemma	lemma	PROPN
ejpam-4931	292	2	4	4	NUM
ejpam-4931	292	3	.	.	X
ejpam-4931	293	1	for	for	ADP
ejpam-4931	293	2	any	any	DET
ejpam-4931	293	3	positive	positive	ADJ
ejpam-4931	293	4	regular	regular	ADJ
ejpam-4931	293	5	function	function	NOUN
ejpam-4931	293	6	ξ(x	ξ(x	NOUN
ejpam-4931	293	7	,	,	PUNCT
ejpam-4931	293	8	y	y	PROPN
ejpam-4931	293	9	)	)	PUNCT
ejpam-4931	293	10	,	,	PUNCT
ejpam-4931	293	11	we	we	PRON
ejpam-4931	293	12	have∫	have∫	VERB
ejpam-4931	293	13	ω	ω	PROPN
ejpam-4931	293	14	|∇2	|∇2	PROPN
ejpam-4931	294	1	√	√	PROPN
ejpam-4931	294	2	ξ|2dxdy	ξ|2dxdy	PROPN
ejpam-4931	294	3	≤	≤	ADV
ejpam-4931	294	4	7	7	NUM
ejpam-4931	294	5	∫	∫	PROPN
ejpam-4931	294	6	ω	ω	PROPN
ejpam-4931	294	7	ξ|∇2	ξ|∇2	PROPN
ejpam-4931	294	8	ln	ln	ADJ
ejpam-4931	294	9	ξ|2dxdy	ξ|2dxdy	NOUN
ejpam-4931	294	10	(	(	PUNCT
ejpam-4931	294	11	44	44	NUM
ejpam-4931	294	12	)	)	PUNCT
ejpam-4931	294	13	and	and	CCONJ
ejpam-4931	294	14	∫	∫	PROPN
ejpam-4931	294	15	ω	ω	NUM
ejpam-4931	294	16	|∇ξ	|∇ξ	ADJ
ejpam-4931	294	17	1	1	NUM
ejpam-4931	294	18	4	4	NUM
ejpam-4931	294	19	|4dxdy	|4dxdy	PROPN
ejpam-4931	294	20	≤	≤	NOUN
ejpam-4931	294	21	8	8	NUM
ejpam-4931	294	22	∫	∫	PROPN
ejpam-4931	294	23	ω	ω	PROPN
ejpam-4931	294	24	ξ|∇2	ξ|∇2	PROPN
ejpam-4931	294	25	ln	ln	ADJ
ejpam-4931	294	26	ξ|2dxdy	ξ|2dxdy	NOUN
ejpam-4931	294	27	.	.	PUNCT
ejpam-4931	295	1	(	(	PUNCT
ejpam-4931	295	2	45	45	NUM
ejpam-4931	295	3	)	)	PUNCT
ejpam-4931	295	4	therefore	therefore	ADV
ejpam-4931	295	5	,	,	PUNCT
ejpam-4931	295	6	the	the	DET
ejpam-4931	295	7	energy	energy	NOUN
ejpam-4931	295	8	equality	equality	NOUN
ejpam-4931	295	9	(	(	PUNCT
ejpam-4931	295	10	30	30	NUM
ejpam-4931	295	11	)	)	PUNCT
ejpam-4931	295	12	and	and	CCONJ
ejpam-4931	295	13	the	the	DET
ejpam-4931	295	14	lemma	lemma	PROPN
ejpam-4931	295	15	(	(	PUNCT
ejpam-4931	295	16	4	4	X
ejpam-4931	295	17	)	)	PUNCT
ejpam-4931	295	18	allow	allow	VERB
ejpam-4931	295	19	us	we	PRON
ejpam-4931	295	20	to	to	PART
ejpam-4931	295	21	state	state	VERB
ejpam-4931	295	22	the	the	DET
ejpam-4931	295	23	following	follow	VERB
ejpam-4931	295	24	lemma	lemma	PROPN
ejpam-4931	295	25	.	.	PUNCT
ejpam-4931	296	1	lemma	lemma	PROPN
ejpam-4931	296	2	5	5	NUM
ejpam-4931	296	3	.	.	PUNCT
ejpam-4931	297	1	for	for	ADP
ejpam-4931	297	2	any	any	DET
ejpam-4931	297	3	smooth	smooth	ADJ
ejpam-4931	297	4	positive	positive	ADJ
ejpam-4931	297	5	function	function	NOUN
ejpam-4931	297	6	ξ(t	ξ(t	NOUN
ejpam-4931	297	7	,	,	PUNCT
ejpam-4931	297	8	x	x	NOUN
ejpam-4931	297	9	,	,	PUNCT
ejpam-4931	297	10	y	y	PROPN
ejpam-4931	297	11	)	)	PUNCT
ejpam-4931	297	12	,	,	PUNCT
ejpam-4931	297	13	we	we	PRON
ejpam-4931	297	14	have	have	VERB
ejpam-4931	297	15	the	the	DET
ejpam-4931	297	16	following	follow	VERB
ejpam-4931	297	17	estimate	estimate	NOUN
ejpam-4931	297	18	:	:	PUNCT
ejpam-4931	297	19	(	(	PUNCT
ejpam-4931	297	20	kϵ	kϵ	NOUN
ejpam-4931	297	21	)	)	PUNCT
ejpam-4931	297	22	1	1	NUM
ejpam-4931	297	23	2	2	NUM
ejpam-4931	297	24	∥	∥	NUM
ejpam-4931	297	25	√	√	PUNCT
ejpam-4931	298	1	ξn∥l2([0,t	ξn∥l2([0,t	NOUN
ejpam-4931	298	2	]	]	X
ejpam-4931	298	3	;	;	PUNCT
ejpam-4931	298	4	h2(ω))+(kϵ	h2(ω))+(kϵ	PROPN
ejpam-4931	298	5	)	)	PUNCT
ejpam-4931	298	6	1	1	NUM
ejpam-4931	298	7	4	4	NUM
ejpam-4931	298	8	∥∇xξ	∥∇xξ	NOUN
ejpam-4931	298	9	1	1	NUM
ejpam-4931	298	10	4	4	NUM
ejpam-4931	298	11	n	n	ADV
ejpam-4931	298	12	∥l4([0,t	∥l4([0,t	VERB
ejpam-4931	298	13	]	]	X
ejpam-4931	298	14	;	;	PUNCT
ejpam-4931	298	15	l4(ω))≤	l4(ω))≤	PROPN
ejpam-4931	298	16	c	c	NOUN
ejpam-4931	298	17	,	,	PUNCT
ejpam-4931	298	18	(	(	PUNCT
ejpam-4931	298	19	46	46	NUM
ejpam-4931	298	20	)	)	PUNCT
ejpam-4931	298	21	for	for	ADP
ejpam-4931	298	22	a	a	DET
ejpam-4931	298	23	constant	constant	ADJ
ejpam-4931	298	24	c	c	NOUN
ejpam-4931	298	25	>	>	X
ejpam-4931	298	26	0	0	PUNCT
ejpam-4931	298	27	independent	independent	ADJ
ejpam-4931	298	28	on	on	ADP
ejpam-4931	298	29	n.	n.	PROPN
ejpam-4931	298	30	j.	j.	PROPN
ejpam-4931	298	31	ouya	ouya	PROPN
ejpam-4931	298	32	,	,	PUNCT
ejpam-4931	298	33	a.	a.	NOUN
ejpam-4931	298	34	ouédraogo	ouédraogo	PROPN
ejpam-4931	298	35	/	/	SYM
ejpam-4931	298	36	eur	eur	PROPN
ejpam-4931	298	37	.	.	PUNCT
ejpam-4931	299	1	j.	j.	PROPN
ejpam-4931	299	2	pure	pure	PROPN
ejpam-4931	299	3	appl	appl	PROPN
ejpam-4931	299	4	.	.	PROPN
ejpam-4931	299	5	math	math	PROPN
ejpam-4931	299	6	,	,	PUNCT
ejpam-4931	299	7	16	16	NUM
ejpam-4931	299	8	(	(	PUNCT
ejpam-4931	299	9	4	4	NUM
ejpam-4931	299	10	)	)	PUNCT
ejpam-4931	299	11	(	(	PUNCT
ejpam-4931	299	12	2023	2023	NUM
ejpam-4931	299	13	)	)	PUNCT
ejpam-4931	299	14	,	,	PUNCT
ejpam-4931	299	15	2247	2247	NUM
ejpam-4931	299	16	-	-	SYM
ejpam-4931	299	17	2285	2285	NUM
ejpam-4931	299	18	2259	2259	NUM
ejpam-4931	299	19	to	to	PART
ejpam-4931	299	20	close	close	VERB
ejpam-4931	299	21	this	this	DET
ejpam-4931	299	22	section	section	NOUN
ejpam-4931	299	23	,	,	PUNCT
ejpam-4931	299	24	we	we	PRON
ejpam-4931	299	25	give	give	VERB
ejpam-4931	299	26	a	a	DET
ejpam-4931	299	27	summary	summary	NOUN
ejpam-4931	299	28	of	of	ADP
ejpam-4931	299	29	the	the	DET
ejpam-4931	299	30	approximate	approximate	ADJ
ejpam-4931	299	31	solution	solution	NOUN
ejpam-4931	299	32	(	(	PUNCT
ejpam-4931	299	33	ξn	ξn	PROPN
ejpam-4931	299	34	,	,	PUNCT
ejpam-4931	299	35	un	un	PROPN
ejpam-4931	299	36	,	,	PUNCT
ejpam-4931	299	37	vn	vn	NOUN
ejpam-4931	299	38	)	)	PUNCT
ejpam-4931	299	39	as	as	SCONJ
ejpam-4931	299	40	follows	follow	VERB
ejpam-4931	299	41	.	.	PUNCT
ejpam-4931	300	1	proposition	proposition	NOUN
ejpam-4931	300	2	3.1	3.1	NUM
ejpam-4931	300	3	.	.	PUNCT
ejpam-4931	301	1	assume	assume	VERB
ejpam-4931	301	2	that	that	SCONJ
ejpam-4931	301	3	(	(	PUNCT
ejpam-4931	301	4	ξn	ξn	PROPN
ejpam-4931	301	5	,	,	PUNCT
ejpam-4931	301	6	un	un	PROPN
ejpam-4931	301	7	,	,	PUNCT
ejpam-4931	301	8	vn	vn	NOUN
ejpam-4931	301	9	)	)	PUNCT
ejpam-4931	301	10	is	be	AUX
ejpam-4931	301	11	the	the	DET
ejpam-4931	301	12	solution	solution	NOUN
ejpam-4931	301	13	of	of	ADP
ejpam-4931	301	14	(	(	PUNCT
ejpam-4931	301	15	19	19	NUM
ejpam-4931	301	16	)	)	PUNCT
ejpam-4931	301	17	and	and	CCONJ
ejpam-4931	301	18	(	(	PUNCT
ejpam-4931	301	19	24	24	NUM
ejpam-4931	301	20	)	)	PUNCT
ejpam-4931	301	21	on	on	ADP
ejpam-4931	301	22	[	[	X
ejpam-4931	301	23	0	0	NUM
ejpam-4931	301	24	,	,	PUNCT
ejpam-4931	301	25	t	t	X
ejpam-4931	301	26	]	]	PUNCT
ejpam-4931	301	27	×ω	×ω	PRON
ejpam-4931	301	28	constructed	construct	VERB
ejpam-4931	301	29	above	above	ADV
ejpam-4931	301	30	.	.	PUNCT
ejpam-4931	302	1	then	then	ADV
ejpam-4931	302	2	the	the	DET
ejpam-4931	302	3	solution	solution	NOUN
ejpam-4931	302	4	satisfies	satisfy	VERB
ejpam-4931	302	5	the	the	DET
ejpam-4931	302	6	energy	energy	NOUN
ejpam-4931	302	7	inequality	inequality	NOUN
ejpam-4931	302	8	e(ξn	e(ξn	PROPN
ejpam-4931	302	9	,	,	PUNCT
ejpam-4931	302	10	un	un	PROPN
ejpam-4931	302	11	)	)	PUNCT
ejpam-4931	302	12	+	+	NUM
ejpam-4931	303	1	2ϵ	2ϵ	NUM
ejpam-4931	303	2	∫	∫	PROPN
ejpam-4931	303	3	t	t	NOUN
ejpam-4931	303	4	0	0	NUM
ejpam-4931	303	5	∫	∫	PROPN
ejpam-4931	303	6	ω	ω	PROPN
ejpam-4931	303	7	|∇xξn|2dxdt+	|∇xξn|2dxdt+	PROPN
ejpam-4931	303	8	r1	r1	PROPN
ejpam-4931	303	9	∫	∫	PROPN
ejpam-4931	303	10	t	t	PROPN
ejpam-4931	303	11	0	0	NUM
ejpam-4931	304	1	∫	∫	PROPN
ejpam-4931	305	1	ω	ω	NUM
ejpam-4931	305	2	u2ndxdt+	u2ndxdt+	NOUN
ejpam-4931	305	3	r	r	NOUN
ejpam-4931	305	4	∫	∫	PROPN
ejpam-4931	305	5	t	t	PROPN
ejpam-4931	305	6	0	0	NUM
ejpam-4931	305	7	∫	∫	PROPN
ejpam-4931	305	8	ω	ω	NUM
ejpam-4931	305	9	ξn|un|3dxdt	ξn|un|3dxdt	PROPN
ejpam-4931	305	10	+	+	CCONJ
ejpam-4931	305	11	∫	∫	PROPN
ejpam-4931	305	12	t	t	PROPN
ejpam-4931	305	13	0	0	NUM
ejpam-4931	305	14	∫	∫	PROPN
ejpam-4931	305	15	ω	ω	PROPN
ejpam-4931	305	16	2ξn|dx(un)|2dx	2ξn|dx(un)|2dx	PROPN
ejpam-4931	306	1	+	+	CCONJ
ejpam-4931	306	2	α	α	PROPN
ejpam-4931	306	3	∫	∫	PROPN
ejpam-4931	306	4	t	t	PROPN
ejpam-4931	306	5	0	0	NUM
ejpam-4931	306	6	∫	∫	PROPN
ejpam-4931	306	7	ω	ω	PROPN
ejpam-4931	306	8	|∆xun|2dxdt+	|∆xun|2dxdt+	NOUN
ejpam-4931	306	9	4ϵr2	4ϵr2	NUM
ejpam-4931	306	10	β	β	PROPN
ejpam-4931	306	11	∫	∫	PROPN
ejpam-4931	306	12	t	t	PROPN
ejpam-4931	306	13	0	0	NUM
ejpam-4931	306	14	∫	∫	PROPN
ejpam-4931	306	15	ω	ω	PROPN
ejpam-4931	306	16	|∇xξ	|∇xξ	PROPN
ejpam-4931	306	17	−β	−β	ADJ
ejpam-4931	306	18	2	2	NUM
ejpam-4931	306	19	n	n	NOUN
ejpam-4931	306	20	|2dxdt	|2dxdt	PROPN
ejpam-4931	306	21	+	+	CCONJ
ejpam-4931	306	22	δϵ	δϵ	NOUN
ejpam-4931	306	23	∫	∫	PROPN
ejpam-4931	306	24	t	t	PROPN
ejpam-4931	306	25	0	0	NUM
ejpam-4931	306	26	∫	∫	PROPN
ejpam-4931	306	27	ω	ω	PROPN
ejpam-4931	306	28	|∆3	|∆3	PROPN
ejpam-4931	306	29	xξn|2dxdt+	xξn|2dxdt+	PROPN
ejpam-4931	306	30	∫	∫	PROPN
ejpam-4931	306	31	t	t	PROPN
ejpam-4931	306	32	0	0	NUM
ejpam-4931	306	33	∫	∫	PROPN
ejpam-4931	306	34	ω	ω	X
ejpam-4931	306	35	ξn|∂yun|2dxdt+	ξn|∂yun|2dxdt+	X
ejpam-4931	306	36	ϵk1	ϵk1	NOUN
ejpam-4931	306	37	2	2	NUM
ejpam-4931	306	38	∫	∫	NOUN
ejpam-4931	306	39	t	t	PROPN
ejpam-4931	306	40	0	0	NUM
ejpam-4931	306	41	∫	∫	PROPN
ejpam-4931	307	1	ω	ω	NUM
ejpam-4931	307	2	ξn|∇2	ξn|∇2	PROPN
ejpam-4931	307	3	x	x	SYM
ejpam-4931	307	4	ln	ln	PROPN
ejpam-4931	307	5	ξn|2dxdt	ξn|2dxdt	PROPN
ejpam-4931	307	6	≤	≤	PROPN
ejpam-4931	307	7	e(ξ0	e(ξ0	NOUN
ejpam-4931	307	8	,	,	PUNCT
ejpam-4931	307	9	u0	u0	ADJ
ejpam-4931	307	10	)	)	PUNCT
ejpam-4931	307	11	,	,	PUNCT
ejpam-4931	307	12	(	(	PUNCT
ejpam-4931	307	13	47	47	NUM
ejpam-4931	307	14	)	)	PUNCT
ejpam-4931	307	15	with	with	ADP
ejpam-4931	307	16	e(ξn	e(ξn	PROPN
ejpam-4931	307	17	,	,	PUNCT
ejpam-4931	307	18	un	un	PROPN
ejpam-4931	307	19	)	)	PUNCT
ejpam-4931	307	20	=	=	SYM
ejpam-4931	308	1	∫	∫	PROPN
ejpam-4931	308	2	ω	ω	PROPN
ejpam-4931	308	3	(	(	PUNCT
ejpam-4931	308	4	1	1	NUM
ejpam-4931	308	5	2	2	NUM
ejpam-4931	308	6	ξnu	ξnu	NOUN
ejpam-4931	308	7	2	2	NUM
ejpam-4931	308	8	n	n	NOUN
ejpam-4931	308	9	+	+	CCONJ
ejpam-4931	308	10	ξ2n	ξ2n	PROPN
ejpam-4931	308	11	+	+	CCONJ
ejpam-4931	308	12	r2	r2	PROPN
ejpam-4931	308	13	β	β	X
ejpam-4931	308	14	+	+	CCONJ
ejpam-4931	308	15	1	1	NUM
ejpam-4931	308	16	ξ−β	ξ−β	VERB
ejpam-4931	308	17	n	n	NOUN
ejpam-4931	308	18	+	+	CCONJ
ejpam-4931	308	19	k1|∇x	k1|∇x	PROPN
ejpam-4931	308	20	√	√	X
ejpam-4931	309	1	ξn|2	ξn|2	PROPN
ejpam-4931	309	2	+	+	CCONJ
ejpam-4931	309	3	δ	δ	NOUN
ejpam-4931	309	4	2	2	NUM
ejpam-4931	309	5	|∇x∆	|∇x∆	NOUN
ejpam-4931	309	6	2	2	NUM
ejpam-4931	309	7	xξn|2	xξn|2	PUNCT
ejpam-4931	309	8	)	)	PUNCT
ejpam-4931	309	9	dx	dx	PROPN
ejpam-4931	309	10	.	.	PUNCT
ejpam-4931	310	1	in	in	ADP
ejpam-4931	310	2	particular	particular	ADJ
ejpam-4931	310	3	,	,	PUNCT
ejpam-4931	310	4	we	we	PRON
ejpam-4931	310	5	have	have	VERB
ejpam-4931	310	6	the	the	DET
ejpam-4931	310	7	following	follow	VERB
ejpam-4931	310	8	estimates	estimates	PROPN
ejpam-4931	310	9	√	√	PROPN
ejpam-4931	310	10	ξnun	ξnun	PROPN
ejpam-4931	310	11	∈	∈	PROPN
ejpam-4931	310	12	l∞	l∞	NOUN
ejpam-4931	310	13	(	(	PUNCT
ejpam-4931	311	1	[	[	X
ejpam-4931	311	2	0	0	NUM
ejpam-4931	311	3	,	,	PUNCT
ejpam-4931	311	4	t	t	X
ejpam-4931	311	5	]	]	PUNCT
ejpam-4931	311	6	;	;	PUNCT
ejpam-4931	311	7	l2(ω	l2(ω	NUM
ejpam-4931	311	8	)	)	PUNCT
ejpam-4931	311	9	)	)	PUNCT
ejpam-4931	311	10	,	,	PUNCT
ejpam-4931	311	11	ξn	ξn	PROPN
ejpam-4931	311	12	∈	∈	PROPN
ejpam-4931	311	13	l2	l2	NOUN
ejpam-4931	311	14	(	(	PUNCT
ejpam-4931	311	15	[	[	X
ejpam-4931	311	16	0	0	NUM
ejpam-4931	311	17	,	,	PUNCT
ejpam-4931	311	18	t	t	X
ejpam-4931	311	19	]	]	PUNCT
ejpam-4931	311	20	;	;	PUNCT
ejpam-4931	311	21	l2(ω	l2(ω	NUM
ejpam-4931	311	22	)	)	PUNCT
ejpam-4931	311	23	)	)	PUNCT
ejpam-4931	311	24	,	,	PUNCT
ejpam-4931	311	25	r2ξ	r2ξ	NOUN
ejpam-4931	311	26	−β	−β	PROPN
ejpam-4931	311	27	n	n	PROPN
ejpam-4931	311	28	∈	∈	PROPN
ejpam-4931	311	29	l∞	l∞	NOUN
ejpam-4931	311	30	(	(	PUNCT
ejpam-4931	311	31	[	[	X
ejpam-4931	311	32	0	0	NUM
ejpam-4931	311	33	,	,	PUNCT
ejpam-4931	311	34	t	t	X
ejpam-4931	311	35	]	]	PUNCT
ejpam-4931	311	36	;	;	PUNCT
ejpam-4931	311	37	l1(ω	l1(ω	X
ejpam-4931	311	38	)	)	PUNCT
ejpam-4931	311	39	)	)	PUNCT
ejpam-4931	311	40	,	,	PUNCT
ejpam-4931	311	41	√	√	NUM
ejpam-4931	311	42	ξndxun	ξndxun	PROPN
ejpam-4931	311	43	∈	∈	PROPN
ejpam-4931	311	44	l2	l2	NOUN
ejpam-4931	311	45	(	(	PUNCT
ejpam-4931	311	46	[	[	X
ejpam-4931	311	47	0	0	NUM
ejpam-4931	311	48	,	,	PUNCT
ejpam-4931	311	49	t	t	X
ejpam-4931	311	50	]	]	PUNCT
ejpam-4931	311	51	;	;	PUNCT
ejpam-4931	311	52	l2(ω	l2(ω	NUM
ejpam-4931	311	53	)	)	PUNCT
ejpam-4931	311	54	)	)	PUNCT
ejpam-4931	311	55	,	,	PUNCT
ejpam-4931	311	56	√	√	NUM
ejpam-4931	311	57	α∆xun	α∆xun	PROPN
ejpam-4931	311	58	∈	∈	PROPN
ejpam-4931	311	59	l2	l2	NOUN
ejpam-4931	311	60	(	(	PUNCT
ejpam-4931	311	61	[	[	X
ejpam-4931	311	62	0	0	NUM
ejpam-4931	311	63	,	,	PUNCT
ejpam-4931	311	64	t	t	X
ejpam-4931	311	65	]	]	PUNCT
ejpam-4931	311	66	;	;	PUNCT
ejpam-4931	311	67	l2(ω	l2(ω	NUM
ejpam-4931	311	68	)	)	PUNCT
ejpam-4931	311	69	)	)	PUNCT
ejpam-4931	311	70	,	,	PUNCT
ejpam-4931	311	71	√	√	PROPN
ejpam-4931	311	72	k1	k1	PROPN
ejpam-4931	311	73	√	√	PROPN
ejpam-4931	311	74	ξn	ξn	PROPN
ejpam-4931	311	75	∈	∈	PROPN
ejpam-4931	311	76	l∞	l∞	NOUN
ejpam-4931	311	77	(	(	PUNCT
ejpam-4931	311	78	[	[	X
ejpam-4931	311	79	0	0	NUM
ejpam-4931	311	80	,	,	PUNCT
ejpam-4931	311	81	t	t	X
ejpam-4931	311	82	]	]	PUNCT
ejpam-4931	311	83	;	;	PUNCT
ejpam-4931	311	84	h1(ω	h1(ω	PROPN
ejpam-4931	311	85	)	)	PUNCT
ejpam-4931	311	86	)	)	PUNCT
ejpam-4931	311	87	,	,	PUNCT
ejpam-4931	311	88	√	√	NUM
ejpam-4931	311	89	δξn	δξn	VERB
ejpam-4931	311	90	∈	∈	PROPN
ejpam-4931	311	91	l∞	l∞	NOUN
ejpam-4931	311	92	(	(	PUNCT
ejpam-4931	311	93	[	[	X
ejpam-4931	311	94	0	0	NUM
ejpam-4931	311	95	,	,	PUNCT
ejpam-4931	311	96	t	t	X
ejpam-4931	311	97	]	]	PUNCT
ejpam-4931	311	98	;	;	PUNCT
ejpam-4931	311	99	h5(ω	h5(ω	NUM
ejpam-4931	311	100	)	)	PUNCT
ejpam-4931	311	101	)	)	PUNCT
ejpam-4931	311	102	,	,	PUNCT
ejpam-4931	311	103	√	√	VERB
ejpam-4931	311	104	ϵ∇x	ϵ∇x	PRON
ejpam-4931	311	105	√	√	PROPN
ejpam-4931	311	106	ξn	ξn	PROPN
ejpam-4931	311	107	∈	∈	PROPN
ejpam-4931	311	108	l2	l2	NOUN
ejpam-4931	311	109	(	(	PUNCT
ejpam-4931	311	110	[	[	X
ejpam-4931	311	111	0	0	NUM
ejpam-4931	311	112	,	,	PUNCT
ejpam-4931	311	113	t	t	X
ejpam-4931	311	114	]	]	PUNCT
ejpam-4931	311	115	;	;	PUNCT
ejpam-4931	311	116	l2(ω	l2(ω	NUM
ejpam-4931	311	117	)	)	PUNCT
ejpam-4931	311	118	)	)	PUNCT
ejpam-4931	311	119	;	;	PUNCT
ejpam-4931	311	120	√	√	NUM
ejpam-4931	311	121	ξn∂yun	ξn∂yun	NUM
ejpam-4931	311	122	∈	∈	NOUN
ejpam-4931	311	123	l2	l2	NOUN
ejpam-4931	311	124	(	(	PUNCT
ejpam-4931	311	125	[	[	X
ejpam-4931	311	126	0	0	NUM
ejpam-4931	311	127	,	,	PUNCT
ejpam-4931	311	128	t	t	X
ejpam-4931	311	129	]	]	PUNCT
ejpam-4931	311	130	;	;	PUNCT
ejpam-4931	311	131	l2(ω	l2(ω	NUM
ejpam-4931	311	132	)	)	PUNCT
ejpam-4931	311	133	)	)	PUNCT
ejpam-4931	311	134	,	,	PUNCT
ejpam-4931	311	135	√	√	PROPN
ejpam-4931	311	136	ϵr2∇xξ	ϵr2∇xξ	VERB
ejpam-4931	311	137	−β	−β	PROPN
ejpam-4931	311	138	2	2	NUM
ejpam-4931	311	139	n	n	CCONJ
ejpam-4931	311	140	∈	∈	NOUN
ejpam-4931	311	141	l2	l2	NOUN
ejpam-4931	311	142	(	(	PUNCT
ejpam-4931	311	143	[	[	X
ejpam-4931	311	144	0	0	NUM
ejpam-4931	311	145	,	,	PUNCT
ejpam-4931	311	146	t	t	X
ejpam-4931	311	147	]	]	PUNCT
ejpam-4931	311	148	;	;	PUNCT
ejpam-4931	311	149	l2(ω	l2(ω	NUM
ejpam-4931	311	150	)	)	PUNCT
ejpam-4931	311	151	)	)	PUNCT
ejpam-4931	311	152	,	,	PUNCT
ejpam-4931	311	153	√	√	NUM
ejpam-4931	311	154	δϵξn	δϵξn	NOUN
ejpam-4931	311	155	∈	∈	NOUN
ejpam-4931	311	156	l2	l2	NOUN
ejpam-4931	311	157	(	(	PUNCT
ejpam-4931	311	158	[	[	X
ejpam-4931	311	159	0	0	NUM
ejpam-4931	311	160	,	,	PUNCT
ejpam-4931	311	161	t	t	X
ejpam-4931	311	162	]	]	PUNCT
ejpam-4931	311	163	;	;	PUNCT
ejpam-4931	311	164	h6(ω	h6(ω	X
ejpam-4931	311	165	)	)	PUNCT
ejpam-4931	311	166	)	)	PUNCT
ejpam-4931	311	167	,	,	PUNCT
ejpam-4931	311	168	√	√	NUM
ejpam-4931	311	169	r1un	r1un	PUNCT
ejpam-4931	311	170	∈	∈	PROPN
ejpam-4931	311	171	l2	l2	NOUN
ejpam-4931	311	172	(	(	PUNCT
ejpam-4931	311	173	[	[	X
ejpam-4931	311	174	0	0	NUM
ejpam-4931	311	175	,	,	PUNCT
ejpam-4931	311	176	t	t	X
ejpam-4931	311	177	]	]	PUNCT
ejpam-4931	311	178	;	;	PUNCT
ejpam-4931	311	179	l2(ω	l2(ω	NUM
ejpam-4931	311	180	)	)	PUNCT
ejpam-4931	311	181	)	)	PUNCT
ejpam-4931	311	182	,	,	PUNCT
ejpam-4931	312	1	ξ	ξ	PROPN
ejpam-4931	312	2	1	1	NUM
ejpam-4931	312	3	3	3	NUM
ejpam-4931	312	4	n	n	NOUN
ejpam-4931	312	5	un	un	PROPN
ejpam-4931	312	6	∈	∈	PROPN
ejpam-4931	312	7	l3	l3	PROPN
ejpam-4931	312	8	(	(	PUNCT
ejpam-4931	312	9	[	[	X
ejpam-4931	312	10	0	0	NUM
ejpam-4931	312	11	,	,	PUNCT
ejpam-4931	312	12	t	t	X
ejpam-4931	312	13	]	]	PUNCT
ejpam-4931	312	14	;	;	PUNCT
ejpam-4931	312	15	l3(ω	l3(ω	X
ejpam-4931	312	16	)	)	PUNCT
ejpam-4931	312	17	)	)	PUNCT
ejpam-4931	312	18	,	,	PUNCT
ejpam-4931	312	19	√	√	PUNCT
ejpam-4931	313	1	ϵk1	ϵk1	NOUN
ejpam-4931	313	2	√	√	NUM
ejpam-4931	313	3	ξn	ξn	PROPN
ejpam-4931	313	4	∈	∈	PROPN
ejpam-4931	313	5	l2	l2	NOUN
ejpam-4931	313	6	(	(	PUNCT
ejpam-4931	313	7	[	[	X
ejpam-4931	313	8	0	0	NUM
ejpam-4931	313	9	,	,	PUNCT
ejpam-4931	313	10	t	t	X
ejpam-4931	313	11	]	]	PUNCT
ejpam-4931	313	12	;	;	PUNCT
ejpam-4931	313	13	h2(ω	h2(ω	NUM
ejpam-4931	313	14	)	)	PUNCT
ejpam-4931	313	15	)	)	PUNCT
ejpam-4931	313	16	,	,	PUNCT
ejpam-4931	313	17	4	4	NUM
ejpam-4931	313	18	√	√	NOUN
ejpam-4931	313	19	k1ϵ∇xξ	k1ϵ∇xξ	PROPN
ejpam-4931	313	20	1	1	NUM
ejpam-4931	313	21	4	4	NUM
ejpam-4931	313	22	n	n	PRON
ejpam-4931	313	23	∈	∈	PROPN
ejpam-4931	313	24	l4	l4	PROPN
ejpam-4931	313	25	(	(	PUNCT
ejpam-4931	313	26	[	[	X
ejpam-4931	313	27	0	0	NUM
ejpam-4931	313	28	,	,	PUNCT
ejpam-4931	313	29	t	t	X
ejpam-4931	313	30	]	]	PUNCT
ejpam-4931	313	31	;	;	PUNCT
ejpam-4931	313	32	l4(ω	l4(ω	X
ejpam-4931	313	33	)	)	PUNCT
ejpam-4931	313	34	)	)	PUNCT
ejpam-4931	313	35	,	,	PUNCT
ejpam-4931	313	36	ξ2	ξ2	PROPN
ejpam-4931	313	37	∈	∈	PROPN
ejpam-4931	313	38	l∞	l∞	NOUN
ejpam-4931	313	39	(	(	PUNCT
ejpam-4931	313	40	[	[	X
ejpam-4931	313	41	0	0	NUM
ejpam-4931	313	42	,	,	PUNCT
ejpam-4931	313	43	t	t	X
ejpam-4931	313	44	]	]	PUNCT
ejpam-4931	313	45	;	;	PUNCT
ejpam-4931	313	46	l1(ω	l1(ω	X
ejpam-4931	313	47	)	)	PUNCT
ejpam-4931	313	48	)	)	PUNCT
ejpam-4931	313	49	,	,	PUNCT
ejpam-4931	313	50	√	√	NUM
ejpam-4931	313	51	ξnūn	ξnūn	NUM
ejpam-4931	313	52	∈	∈	NOUN
ejpam-4931	313	53	l∞	l∞	NOUN
ejpam-4931	313	54	(	(	PUNCT
ejpam-4931	313	55	[	[	X
ejpam-4931	313	56	0	0	NUM
ejpam-4931	313	57	,	,	PUNCT
ejpam-4931	313	58	t	t	X
ejpam-4931	313	59	]	]	PUNCT
ejpam-4931	313	60	;	;	PUNCT
ejpam-4931	313	61	l2(ω	l2(ω	NUM
ejpam-4931	313	62	)	)	PUNCT
ejpam-4931	313	63	)	)	PUNCT
ejpam-4931	313	64	,	,	PUNCT
ejpam-4931	313	65	√	√	NUM
ejpam-4931	313	66	ξnũn	ξnũn	PROPN
ejpam-4931	313	67	∈	∈	PROPN
ejpam-4931	313	68	l∞	l∞	NOUN
ejpam-4931	313	69	(	(	PUNCT
ejpam-4931	313	70	[	[	X
ejpam-4931	313	71	0	0	NUM
ejpam-4931	313	72	,	,	PUNCT
ejpam-4931	313	73	t	t	X
ejpam-4931	313	74	]	]	PUNCT
ejpam-4931	313	75	;	;	PUNCT
ejpam-4931	313	76	l2(ω	l2(ω	NUM
ejpam-4931	313	77	)	)	PUNCT
ejpam-4931	313	78	)	)	PUNCT
ejpam-4931	313	79	.	.	PUNCT
ejpam-4931	314	1	(	(	PUNCT
ejpam-4931	314	2	48	48	NUM
ejpam-4931	314	3	)	)	PUNCT
ejpam-4931	314	4	now	now	ADV
ejpam-4931	314	5	,	,	PUNCT
ejpam-4931	314	6	we	we	PRON
ejpam-4931	314	7	want	want	VERB
ejpam-4931	314	8	to	to	PART
ejpam-4931	314	9	pass	pass	VERB
ejpam-4931	314	10	to	to	ADP
ejpam-4931	314	11	the	the	DET
ejpam-4931	314	12	limit	limit	NOUN
ejpam-4931	314	13	in	in	ADP
ejpam-4931	314	14	(	(	PUNCT
ejpam-4931	314	15	47	47	NUM
ejpam-4931	314	16	)	)	PUNCT
ejpam-4931	315	1	when	when	SCONJ
ejpam-4931	315	2	n	n	PRON
ejpam-4931	315	3	−→	−→	NOUN
ejpam-4931	315	4	+	+	NOUN
ejpam-4931	315	5	∞.	∞.	PROPN
ejpam-4931	315	6	we	we	PRON
ejpam-4931	315	7	then	then	ADV
ejpam-4931	315	8	state	state	VERB
ejpam-4931	315	9	a	a	DET
ejpam-4931	315	10	series	series	NOUN
ejpam-4931	315	11	of	of	ADP
ejpam-4931	315	12	convergence	convergence	NOUN
ejpam-4931	315	13	lemmas	lemmas	ADJ
ejpam-4931	315	14	.	.	PUNCT
ejpam-4931	316	1	3.3	3.3	NUM
ejpam-4931	316	2	.	.	PUNCT
ejpam-4931	317	1	convergence	convergence	NOUN
ejpam-4931	317	2	results	result	NOUN
ejpam-4931	317	3	we	we	PRON
ejpam-4931	317	4	fix	fix	VERB
ejpam-4931	317	5	ϵ	ϵ	ADP
ejpam-4931	317	6	,	,	PUNCT
ejpam-4931	317	7	r	r	NOUN
ejpam-4931	317	8	,	,	PUNCT
ejpam-4931	317	9	r1	r1	NOUN
ejpam-4931	317	10	,	,	PUNCT
ejpam-4931	317	11	k1	k1	PROPN
ejpam-4931	317	12	,	,	PUNCT
ejpam-4931	317	13	α	α	NOUN
ejpam-4931	317	14	,	,	PUNCT
ejpam-4931	317	15	δ	δ	PROPN
ejpam-4931	317	16	,	,	PUNCT
ejpam-4931	317	17	r2	r2	PROPN
ejpam-4931	317	18	>	>	PUNCT
ejpam-4931	317	19	0	0	PUNCT
ejpam-4931	318	1	and	and	CCONJ
ejpam-4931	318	2	let	let	VERB
ejpam-4931	318	3	us	we	PRON
ejpam-4931	318	4	first	first	ADV
ejpam-4931	318	5	take	take	VERB
ejpam-4931	318	6	the	the	DET
ejpam-4931	318	7	limits	limit	NOUN
ejpam-4931	319	1	when	when	SCONJ
ejpam-4931	319	2	n	n	PRON
ejpam-4931	319	3	−→	−→	NOUN
ejpam-4931	319	4	+	+	PROPN
ejpam-4931	319	5	∞.	∞.	PROPN
ejpam-4931	319	6	lemma	lemma	PROPN
ejpam-4931	319	7	6	6	NUM
ejpam-4931	319	8	.	.	PUNCT
ejpam-4931	320	1	(	(	PUNCT
ejpam-4931	320	2	convergence	convergence	NOUN
ejpam-4931	320	3	of	of	ADP
ejpam-4931	320	4	ξn	ξn	PROPN
ejpam-4931	320	5	)	)	PUNCT
ejpam-4931	320	6	.	.	PUNCT
ejpam-4931	321	1	for	for	ADP
ejpam-4931	321	2	any	any	DET
ejpam-4931	321	3	fixed	fix	VERB
ejpam-4931	321	4	positive	positive	ADJ
ejpam-4931	321	5	constants	constant	NOUN
ejpam-4931	321	6	ϵ	ϵ	ADP
ejpam-4931	321	7	,	,	PUNCT
ejpam-4931	321	8	r1	r1	PROPN
ejpam-4931	321	9	,	,	PUNCT
ejpam-4931	321	10	k1	k1	PROPN
ejpam-4931	321	11	,	,	PUNCT
ejpam-4931	321	12	α	α	NOUN
ejpam-4931	321	13	,	,	PUNCT
ejpam-4931	321	14	δ	δ	PROPN
ejpam-4931	321	15	and	and	CCONJ
ejpam-4931	321	16	r	r	PROPN
ejpam-4931	321	17	,	,	PUNCT
ejpam-4931	321	18	j.	j.	PROPN
ejpam-4931	321	19	ouya	ouya	PROPN
ejpam-4931	321	20	,	,	PUNCT
ejpam-4931	321	21	a.	a.	NOUN
ejpam-4931	321	22	ouédraogo	ouédraogo	PROPN
ejpam-4931	321	23	/	/	SYM
ejpam-4931	321	24	eur	eur	PROPN
ejpam-4931	321	25	.	.	PUNCT
ejpam-4931	322	1	j.	j.	PROPN
ejpam-4931	322	2	pure	pure	PROPN
ejpam-4931	322	3	appl	appl	PROPN
ejpam-4931	322	4	.	.	PROPN
ejpam-4931	322	5	math	math	PROPN
ejpam-4931	322	6	,	,	PUNCT
ejpam-4931	322	7	16	16	NUM
ejpam-4931	322	8	(	(	PUNCT
ejpam-4931	322	9	4	4	NUM
ejpam-4931	322	10	)	)	PUNCT
ejpam-4931	322	11	(	(	PUNCT
ejpam-4931	322	12	2023	2023	NUM
ejpam-4931	322	13	)	)	PUNCT
ejpam-4931	322	14	,	,	PUNCT
ejpam-4931	322	15	2247	2247	NUM
ejpam-4931	322	16	-	-	SYM
ejpam-4931	322	17	2285	2285	NUM
ejpam-4931	322	18	2260	2260	NUM
ejpam-4931	322	19	the	the	DET
ejpam-4931	322	20	following	follow	VERB
ejpam-4931	322	21	estimates	estimate	NOUN
ejpam-4931	322	22	hold:	hold:	PROPN
ejpam-4931	322	23	∥∂t	∥∂t	PROPN
ejpam-4931	322	24	√	√	PROPN
ejpam-4931	322	25	ξn∥	ξn∥	PROPN
ejpam-4931	322	26	l∞	l∞	NOUN
ejpam-4931	322	27	(	(	PUNCT
ejpam-4931	322	28	[	[	X
ejpam-4931	322	29	0,t	0,t	X
ejpam-4931	322	30	]	]	X
ejpam-4931	322	31	;	;	PUNCT
ejpam-4931	322	32	w−1	w−1	PROPN
ejpam-4931	322	33	,	,	PUNCT
ejpam-4931	322	34	32	32	NUM
ejpam-4931	322	35	(	(	PUNCT
ejpam-4931	322	36	ω	ω	NOUN
ejpam-4931	322	37	)	)	PUNCT
ejpam-4931	322	38	)	)	PUNCT
ejpam-4931	323	1	+	+	VERB
ejpam-4931	323	2	∥	∥	PRON
ejpam-4931	323	3	√	√	VERB
ejpam-4931	323	4	ξn∥l2	ξn∥l2	NOUN
ejpam-4931	323	5	(	(	PUNCT
ejpam-4931	323	6	[	[	X
ejpam-4931	323	7	0,t	0,t	X
ejpam-4931	323	8	]	]	X
ejpam-4931	323	9	;	;	PUNCT
ejpam-4931	323	10	h2(ω	h2(ω	NUM
ejpam-4931	323	11	)	)	PUNCT
ejpam-4931	323	12	)	)	PUNCT
ejpam-4931	323	13	≤	≤	NUM
ejpam-4931	323	14	k	k	NOUN
ejpam-4931	323	15	,	,	PUNCT
ejpam-4931	323	16	∥ξn∥l∞	∥ξn∥l∞	PUNCT
ejpam-4931	323	17	(	(	PUNCT
ejpam-4931	323	18	[	[	X
ejpam-4931	323	19	0,t	0,t	X
ejpam-4931	323	20	]	]	X
ejpam-4931	323	21	;	;	PUNCT
ejpam-4931	323	22	h5(ω	h5(ω	NUM
ejpam-4931	323	23	)	)	PUNCT
ejpam-4931	323	24	)	)	PUNCT
ejpam-4931	324	1	+	+	X
ejpam-4931	324	2	∥∂tξn∥	∥∂tξn∥	ADJ
ejpam-4931	324	3	l∞	l∞	NOUN
ejpam-4931	324	4	(	(	PUNCT
ejpam-4931	324	5	[	[	X
ejpam-4931	324	6	0,t	0,t	X
ejpam-4931	324	7	]	]	X
ejpam-4931	324	8	;	;	PUNCT
ejpam-4931	324	9	w−1	w−1	PROPN
ejpam-4931	324	10	,	,	PUNCT
ejpam-4931	324	11	32	32	NUM
ejpam-4931	324	12	(	(	PUNCT
ejpam-4931	324	13	ω	ω	NOUN
ejpam-4931	324	14	)	)	PUNCT
ejpam-4931	324	15	)	)	PUNCT
ejpam-4931	324	16	≤	≤	NOUN
ejpam-4931	325	1	k	k	NOUN
ejpam-4931	325	2	,	,	PUNCT
ejpam-4931	325	3	∥ξ−β	∥ξ−β	NOUN
ejpam-4931	325	4	n	n	CCONJ
ejpam-4931	325	5	∥	∥	NUM
ejpam-4931	325	6	l	l	NOUN
ejpam-4931	325	7	5	5	NUM
ejpam-4931	325	8	3	3	NUM
ejpam-4931	325	9	(	(	PUNCT
ejpam-4931	325	10	[	[	X
ejpam-4931	325	11	0,t	0,t	X
ejpam-4931	325	12	]	]	X
ejpam-4931	325	13	;	;	PUNCT
ejpam-4931	325	14	l	l	NOUN
ejpam-4931	325	15	5	5	NUM
ejpam-4931	325	16	3	3	NUM
ejpam-4931	325	17	(	(	PUNCT
ejpam-4931	325	18	ω	ω	NOUN
ejpam-4931	325	19	)	)	PUNCT
ejpam-4931	325	20	)	)	PUNCT
ejpam-4931	325	21	≤	≤	PUNCT
ejpam-4931	326	1	k	k	NOUN
ejpam-4931	326	2	,	,	PUNCT
ejpam-4931	326	3	∥ξ2n∥l	∥ξ2n∥l	PROPN
ejpam-4931	326	4	5	5	NUM
ejpam-4931	326	5	3	3	NUM
ejpam-4931	326	6	(	(	PUNCT
ejpam-4931	326	7	[	[	X
ejpam-4931	326	8	0,t	0,t	X
ejpam-4931	326	9	]	]	X
ejpam-4931	326	10	;	;	PUNCT
ejpam-4931	326	11	l	l	NOUN
ejpam-4931	326	12	5	5	NUM
ejpam-4931	326	13	3	3	NUM
ejpam-4931	326	14	(	(	PUNCT
ejpam-4931	326	15	ω	ω	NOUN
ejpam-4931	326	16	)	)	PUNCT
ejpam-4931	326	17	)	)	PUNCT
ejpam-4931	326	18	≤	≤	PUNCT
ejpam-4931	327	1	k	k	X
ejpam-4931	327	2	,	,	PUNCT
ejpam-4931	327	3	(	(	PUNCT
ejpam-4931	327	4	49	49	NUM
ejpam-4931	327	5	)	)	PUNCT
ejpam-4931	327	6	where	where	SCONJ
ejpam-4931	327	7	k	k	PROPN
ejpam-4931	327	8	is	be	AUX
ejpam-4931	327	9	independent	independent	ADJ
ejpam-4931	327	10	of	of	ADP
ejpam-4931	327	11	n	n	NUM
ejpam-4931	327	12	,	,	PUNCT
ejpam-4931	327	13	depends	depend	VERB
ejpam-4931	327	14	on	on	ADP
ejpam-4931	327	15	ϵ	ϵ	PRON
ejpam-4931	327	16	,	,	PUNCT
ejpam-4931	327	17	r2	r2	PROPN
ejpam-4931	327	18	,	,	PUNCT
ejpam-4931	327	19	δ	δ	PROPN
ejpam-4931	327	20	,	,	PUNCT
ejpam-4931	327	21	r1	r1	PROPN
ejpam-4931	327	22	,	,	PUNCT
ejpam-4931	327	23	initial	initial	ADJ
ejpam-4931	327	24	data	datum	NOUN
ejpam-4931	327	25	and	and	CCONJ
ejpam-4931	327	26	t	t	PROPN
ejpam-4931	327	27	.	.	PUNCT
ejpam-4931	328	1	moreover	moreover	ADV
ejpam-4931	328	2	,	,	PUNCT
ejpam-4931	328	3	up	up	ADP
ejpam-4931	328	4	to	to	ADP
ejpam-4931	328	5	an	an	DET
ejpam-4931	328	6	extracted	extract	VERB
ejpam-4931	328	7	subsequence	subsequence	NOUN
ejpam-4931	328	8	ξn	ξn	NOUN
ejpam-4931	328	9	,	,	PUNCT
ejpam-4931	328	10	when	when	SCONJ
ejpam-4931	328	11	n	n	PRON
ejpam-4931	328	12	−→	−→	VERB
ejpam-4931	329	1	+	+	NOUN
ejpam-4931	329	2	∞	∞	NUM
ejpam-4931	329	3	we	we	PRON
ejpam-4931	329	4	have:	have:	VERB
ejpam-4931	329	5	√	√	VERB
ejpam-4931	329	6	ξn	ξn	PROPN
ejpam-4931	329	7	−→	−→	NOUN
ejpam-4931	329	8	√	√	PROPN
ejpam-4931	329	9	ξ	ξ	ADP
ejpam-4931	329	10	strongly	strongly	ADV
ejpam-4931	329	11	in	in	ADP
ejpam-4931	329	12	l2	l2	NOUN
ejpam-4931	329	13	(	(	PUNCT
ejpam-4931	329	14	[	[	X
ejpam-4931	329	15	0	0	NUM
ejpam-4931	329	16	,	,	PUNCT
ejpam-4931	329	17	t	t	X
ejpam-4931	329	18	]	]	PUNCT
ejpam-4931	329	19	;	;	PUNCT
ejpam-4931	329	20	h1(ω	h1(ω	PROPN
ejpam-4931	329	21	)	)	PUNCT
ejpam-4931	329	22	)	)	PUNCT
ejpam-4931	330	1	and	and	CCONJ
ejpam-4931	330	2	√	√	VERB
ejpam-4931	330	3	ξn	ξn	VERB
ejpam-4931	330	4	−→	−→	ADJ
ejpam-4931	330	5	√	√	NUM
ejpam-4931	330	6	ξ	ξ	DET
ejpam-4931	330	7	a.e	a.e	PROPN
ejpam-4931	330	8	,	,	PUNCT
ejpam-4931	330	9	ξn	ξn	PROPN
ejpam-4931	330	10	−→	−→	NOUN
ejpam-4931	330	11	ξ	ξ	X
ejpam-4931	330	12	strongly	strongly	ADV
ejpam-4931	330	13	in	in	ADP
ejpam-4931	330	14	c	c	PROPN
ejpam-4931	330	15	(	(	PUNCT
ejpam-4931	330	16	[	[	X
ejpam-4931	330	17	0	0	NUM
ejpam-4931	330	18	,	,	PUNCT
ejpam-4931	330	19	t	t	X
ejpam-4931	330	20	]	]	PUNCT
ejpam-4931	330	21	;	;	PUNCT
ejpam-4931	330	22	h5(ω	h5(ω	NUM
ejpam-4931	330	23	)	)	PUNCT
ejpam-4931	330	24	)	)	PUNCT
ejpam-4931	330	25	and	and	CCONJ
ejpam-4931	330	26	ξn	ξn	PROPN
ejpam-4931	330	27	−→	−→	NOUN
ejpam-4931	330	28	ξ	ξ	PROPN
ejpam-4931	330	29	a.e	a.e	PROPN
ejpam-4931	330	30	,	,	PUNCT
ejpam-4931	330	31	ξ−β	ξ−β	NOUN
ejpam-4931	330	32	n	n	PRON
ejpam-4931	330	33	−→	−→	NOUN
ejpam-4931	330	34	ξ−β	ξ−β	VERB
ejpam-4931	330	35	strongly	strongly	ADV
ejpam-4931	330	36	in	in	ADP
ejpam-4931	330	37	l1	l1	PROPN
ejpam-4931	330	38	(	(	PUNCT
ejpam-4931	330	39	[	[	X
ejpam-4931	330	40	0	0	NUM
ejpam-4931	330	41	,	,	PUNCT
ejpam-4931	330	42	t	t	X
ejpam-4931	330	43	]	]	PUNCT
ejpam-4931	330	44	;	;	PUNCT
ejpam-4931	330	45	l1(ω	l1(ω	X
ejpam-4931	330	46	)	)	PUNCT
ejpam-4931	330	47	)	)	PUNCT
ejpam-4931	330	48	and	and	CCONJ
ejpam-4931	330	49	ξ−β	ξ−β	NOUN
ejpam-4931	330	50	n	n	PRON
ejpam-4931	330	51	−→	−→	VERB
ejpam-4931	330	52	ξ−β	ξ−β	VERB
ejpam-4931	330	53	a.e	a.e	PROPN
ejpam-4931	330	54	.	.	PUNCT
ejpam-4931	330	55	(	(	PUNCT
ejpam-4931	330	56	50	50	NUM
ejpam-4931	330	57	)	)	PUNCT
ejpam-4931	330	58	proof	proof	NOUN
ejpam-4931	330	59	.	.	PUNCT
ejpam-4931	331	1	the	the	DET
ejpam-4931	331	2	proof	proof	NOUN
ejpam-4931	331	3	of	of	ADP
ejpam-4931	331	4	(	(	PUNCT
ejpam-4931	331	5	49	49	NUM
ejpam-4931	331	6	)	)	PUNCT
ejpam-4931	331	7	is	be	AUX
ejpam-4931	331	8	done	do	VERB
ejpam-4931	331	9	in	in	ADP
ejpam-4931	331	10	lemma	lemma	PROPN
ejpam-4931	331	11	2.2	2.2	NUM
ejpam-4931	331	12	of	of	ADP
ejpam-4931	331	13	[	[	X
ejpam-4931	331	14	18	18	NUM
ejpam-4931	331	15	]	]	PUNCT
ejpam-4931	331	16	.	.	PUNCT
ejpam-4931	332	1	it	it	PRON
ejpam-4931	332	2	remains	remain	VERB
ejpam-4931	332	3	to	to	PART
ejpam-4931	332	4	prove	prove	VERB
ejpam-4931	332	5	(	(	PUNCT
ejpam-4931	332	6	50	50	NUM
ejpam-4931	332	7	)	)	PUNCT
ejpam-4931	332	8	.	.	PUNCT
ejpam-4931	333	1	since	since	SCONJ
ejpam-4931	333	2	√	√	NUM
ejpam-4931	333	3	ξn	ξn	PROPN
ejpam-4931	333	4	∈	∈	PROPN
ejpam-4931	333	5	l∞	l∞	NOUN
ejpam-4931	333	6	(	(	PUNCT
ejpam-4931	333	7	[	[	X
ejpam-4931	333	8	0	0	NUM
ejpam-4931	333	9	,	,	PUNCT
ejpam-4931	333	10	t	t	X
ejpam-4931	333	11	]	]	PUNCT
ejpam-4931	333	12	;	;	PUNCT
ejpam-4931	333	13	h1(ω	h1(ω	PROPN
ejpam-4931	333	14	)	)	PUNCT
ejpam-4931	333	15	)	)	PUNCT
ejpam-4931	333	16	,	,	PUNCT
ejpam-4931	333	17	using	use	VERB
ejpam-4931	333	18	sobolev	sobolev	NOUN
ejpam-4931	333	19	embedding	embed	VERB
ejpam-4931	333	20	theorem	theorem	NOUN
ejpam-4931	333	21	(	(	PUNCT
ejpam-4931	333	22	since	since	SCONJ
ejpam-4931	333	23	k	k	PROPN
ejpam-4931	333	24	=	=	SYM
ejpam-4931	333	25	1	1	NUM
ejpam-4931	333	26	,	,	PUNCT
ejpam-4931	333	27	d	d	NOUN
ejpam-4931	333	28	=	=	SYM
ejpam-4931	333	29	3	3	NUM
ejpam-4931	333	30	,	,	PUNCT
ejpam-4931	333	31	p	p	NOUN
ejpam-4931	333	32	=	=	NOUN
ejpam-4931	333	33	2	2	NUM
ejpam-4931	333	34	<	<	X
ejpam-4931	333	35	d	d	NOUN
ejpam-4931	333	36	,	,	PUNCT
ejpam-4931	333	37	then	then	ADV
ejpam-4931	333	38	w	w	PROPN
ejpam-4931	333	39	1,2(ω	1,2(ω	NUM
ejpam-4931	333	40	)	)	PUNCT
ejpam-4931	333	41	=	=	SYM
ejpam-4931	333	42	h1(ω	h1(ω	X
ejpam-4931	333	43	)	)	PUNCT
ejpam-4931	333	44	↪	↪	PROPN
ejpam-4931	333	45	→	→	SYM
ejpam-4931	333	46	lp∗(ω	lp∗(ω	ADJ
ejpam-4931	333	47	)	)	PUNCT
ejpam-4931	333	48	with	with	ADP
ejpam-4931	333	49	p∗	p∗	ADJ
ejpam-4931	333	50	=	=	PUNCT
ejpam-4931	333	51	dp	dp	PROPN
ejpam-4931	333	52	d−p	d−p	NOUN
ejpam-4931	333	53	=	=	NOUN
ejpam-4931	333	54	6	6	NUM
ejpam-4931	333	55	)	)	PUNCT
ejpam-4931	333	56	we	we	PRON
ejpam-4931	333	57	deduce	deduce	VERB
ejpam-4931	333	58	that	that	PRON
ejpam-4931	333	59	√	√	VERB
ejpam-4931	333	60	ξn	ξn	PROPN
ejpam-4931	333	61	∈	∈	PROPN
ejpam-4931	333	62	l∞	l∞	NOUN
ejpam-4931	333	63	(	(	PUNCT
ejpam-4931	333	64	[	[	X
ejpam-4931	333	65	0	0	NUM
ejpam-4931	333	66	,	,	PUNCT
ejpam-4931	333	67	t	t	X
ejpam-4931	333	68	]	]	PUNCT
ejpam-4931	333	69	;	;	PUNCT
ejpam-4931	333	70	l6(ω	l6(ω	PROPN
ejpam-4931	333	71	)	)	PUNCT
ejpam-4931	333	72	)	)	PUNCT
ejpam-4931	333	73	.	.	PUNCT
ejpam-4931	334	1	then	then	ADV
ejpam-4931	334	2	,	,	PUNCT
ejpam-4931	334	3	since	since	SCONJ
ejpam-4931	334	4	√	√	NUM
ejpam-4931	334	5	ξn	ξn	PROPN
ejpam-4931	334	6	∈	∈	PROPN
ejpam-4931	334	7	l∞	l∞	NOUN
ejpam-4931	334	8	(	(	PUNCT
ejpam-4931	334	9	[	[	X
ejpam-4931	334	10	0	0	NUM
ejpam-4931	334	11	,	,	PUNCT
ejpam-4931	334	12	t	t	X
ejpam-4931	334	13	]	]	PUNCT
ejpam-4931	334	14	;	;	PUNCT
ejpam-4931	334	15	l6(ω	l6(ω	PROPN
ejpam-4931	334	16	)	)	PUNCT
ejpam-4931	334	17	)	)	PUNCT
ejpam-4931	335	1	and√	and√	PRON
ejpam-4931	335	2	ξnūn	ξnūn	NUM
ejpam-4931	335	3	∈	∈	PROPN
ejpam-4931	335	4	l∞	l∞	NOUN
ejpam-4931	335	5	(	(	PUNCT
ejpam-4931	335	6	[	[	X
ejpam-4931	335	7	0	0	NUM
ejpam-4931	335	8	,	,	PUNCT
ejpam-4931	335	9	t	t	X
ejpam-4931	335	10	]	]	PUNCT
ejpam-4931	335	11	;	;	PUNCT
ejpam-4931	335	12	l2(ω	l2(ω	NUM
ejpam-4931	335	13	)	)	PUNCT
ejpam-4931	335	14	)	)	PUNCT
ejpam-4931	335	15	,	,	PUNCT
ejpam-4931	335	16	the	the	DET
ejpam-4931	335	17	hölder	hölder	NOUN
ejpam-4931	335	18	inequality	inequality	NOUN
ejpam-4931	335	19	allows	allow	VERB
ejpam-4931	335	20	us	we	PRON
ejpam-4931	335	21	to	to	PART
ejpam-4931	335	22	conclude	conclude	VERB
ejpam-4931	335	23	that	that	DET
ejpam-4931	335	24	ξnūn	ξnūn	NOUN
ejpam-4931	335	25	=	=	SYM
ejpam-4931	336	1	√	√	ADP
ejpam-4931	336	2	ξn	ξn	NOUN
ejpam-4931	336	3	√	√	NUM
ejpam-4931	336	4	ξnūn	ξnūn	NUM
ejpam-4931	336	5	∈	∈	NOUN
ejpam-4931	336	6	l∞	l∞	NOUN
ejpam-4931	336	7	(	(	PUNCT
ejpam-4931	336	8	[	[	X
ejpam-4931	336	9	0	0	NUM
ejpam-4931	336	10	,	,	PUNCT
ejpam-4931	336	11	t	t	X
ejpam-4931	336	12	]	]	PUNCT
ejpam-4931	336	13	;	;	PUNCT
ejpam-4931	336	14	l	l	NOUN
ejpam-4931	336	15	3	3	NUM
ejpam-4931	336	16	2	2	NUM
ejpam-4931	336	17	(	(	PUNCT
ejpam-4931	336	18	ω	ω	NOUN
ejpam-4931	336	19	)	)	PUNCT
ejpam-4931	336	20	)	)	PUNCT
ejpam-4931	336	21	.	.	PUNCT
ejpam-4931	337	1	by	by	ADP
ejpam-4931	337	2	(	(	PUNCT
ejpam-4931	337	3	19	19	NUM
ejpam-4931	337	4	)	)	PUNCT
ejpam-4931	337	5	,	,	PUNCT
ejpam-4931	337	6	we	we	PRON
ejpam-4931	337	7	have	have	VERB
ejpam-4931	337	8	∂tξn	∂tξn	PUNCT
ejpam-4931	337	9	=	=	SYM
ejpam-4931	337	10	ϵ∆xξn	ϵ∆xξn	PROPN
ejpam-4931	337	11	−	−	PROPN
ejpam-4931	337	12	divx(ξnun)−	divx(ξnun)−	PROPN
ejpam-4931	337	13	∂y(ξnvn	∂y(ξnvn	PROPN
ejpam-4931	337	14	)	)	PUNCT
ejpam-4931	338	1	=	=	SYM
ejpam-4931	338	2	ϵ∆xξn	ϵ∆xξn	X
ejpam-4931	339	1	−	−	PROPN
ejpam-4931	339	2	divx	divx	PROPN
ejpam-4931	339	3	(	(	PUNCT
ejpam-4931	339	4	√	√	PROPN
ejpam-4931	339	5	ξn	ξn	PROPN
ejpam-4931	339	6	√	√	NUM
ejpam-4931	339	7	ξnūn	ξnūn	NUM
ejpam-4931	339	8	)	)	PUNCT
ejpam-4931	339	9	∈	∈	NOUN
ejpam-4931	339	10	l∞	l∞	NOUN
ejpam-4931	339	11	(	(	PUNCT
ejpam-4931	339	12	[	[	X
ejpam-4931	339	13	0	0	NUM
ejpam-4931	339	14	,	,	PUNCT
ejpam-4931	339	15	t	t	X
ejpam-4931	339	16	]	]	PUNCT
ejpam-4931	339	17	;	;	PUNCT
ejpam-4931	339	18	w−1	w−1	PROPN
ejpam-4931	339	19	,	,	PUNCT
ejpam-4931	339	20	3	3	NUM
ejpam-4931	339	21	2	2	NUM
ejpam-4931	339	22	(	(	PUNCT
ejpam-4931	339	23	ω	ω	NOUN
ejpam-4931	339	24	)	)	PUNCT
ejpam-4931	339	25	)	)	PUNCT
ejpam-4931	339	26	.	.	PUNCT
ejpam-4931	340	1	(	(	PUNCT
ejpam-4931	340	2	51	51	NUM
ejpam-4931	340	3	)	)	PUNCT
ejpam-4931	340	4	using	use	VERB
ejpam-4931	340	5	(	(	PUNCT
ejpam-4931	340	6	51	51	NUM
ejpam-4931	340	7	)	)	PUNCT
ejpam-4931	340	8	,	,	PUNCT
ejpam-4931	340	9	we	we	PRON
ejpam-4931	340	10	get	get	VERB
ejpam-4931	340	11	ξn	ξn	PRON
ejpam-4931	340	12	∈	∈	PROPN
ejpam-4931	340	13	l∞	l∞	NOUN
ejpam-4931	340	14	(	(	PUNCT
ejpam-4931	340	15	[	[	X
ejpam-4931	340	16	0	0	NUM
ejpam-4931	340	17	,	,	PUNCT
ejpam-4931	340	18	t	t	X
ejpam-4931	340	19	]	]	PUNCT
ejpam-4931	340	20	;	;	PUNCT
ejpam-4931	340	21	h5(ω	h5(ω	NUM
ejpam-4931	340	22	)	)	PUNCT
ejpam-4931	340	23	)	)	PUNCT
ejpam-4931	341	1	∩l2	∩l2	PROPN
ejpam-4931	341	2	(	(	PUNCT
ejpam-4931	341	3	[	[	X
ejpam-4931	341	4	0	0	NUM
ejpam-4931	341	5	,	,	PUNCT
ejpam-4931	341	6	t	t	X
ejpam-4931	341	7	]	]	PUNCT
ejpam-4931	341	8	;	;	PUNCT
ejpam-4931	341	9	h6(ω	h6(ω	X
ejpam-4931	341	10	)	)	PUNCT
ejpam-4931	341	11	)	)	PUNCT
ejpam-4931	341	12	.	.	PUNCT
ejpam-4931	342	1	from	from	ADP
ejpam-4931	342	2	aubin	aubin	PROPN
ejpam-4931	342	3	-	-	PUNCT
ejpam-4931	342	4	lions	lion	NOUN
ejpam-4931	342	5	lemma	lemma	PROPN
ejpam-4931	342	6	1	1	NUM
ejpam-4931	342	7	,	,	PUNCT
ejpam-4931	342	8	we	we	PRON
ejpam-4931	342	9	deduce	deduce	VERB
ejpam-4931	342	10	that	that	SCONJ
ejpam-4931	342	11	ξn	ξn	PROPN
ejpam-4931	342	12	∈	∈	PROPN
ejpam-4931	342	13	c	c	NOUN
ejpam-4931	342	14	(	(	PUNCT
ejpam-4931	342	15	[	[	X
ejpam-4931	342	16	0	0	NUM
ejpam-4931	342	17	,	,	PUNCT
ejpam-4931	342	18	t	t	X
ejpam-4931	342	19	]	]	PUNCT
ejpam-4931	342	20	;	;	PUNCT
ejpam-4931	342	21	h5(ω	h5(ω	NUM
ejpam-4931	342	22	)	)	PUNCT
ejpam-4931	342	23	)	)	PUNCT
ejpam-4931	342	24	.	.	PUNCT
ejpam-4931	343	1	so	so	ADV
ejpam-4931	343	2	,	,	PUNCT
ejpam-4931	343	3	up	up	ADP
ejpam-4931	343	4	to	to	ADP
ejpam-4931	343	5	a	a	DET
ejpam-4931	343	6	subsequence	subsequence	NOUN
ejpam-4931	343	7	,	,	PUNCT
ejpam-4931	343	8	we	we	PRON
ejpam-4931	343	9	have	have	VERB
ejpam-4931	343	10	ξn	ξn	NOUN
ejpam-4931	343	11	−→	−→	NOUN
ejpam-4931	343	12	ξ	ξ	X
ejpam-4931	343	13	strongly	strongly	ADV
ejpam-4931	343	14	in	in	ADP
ejpam-4931	343	15	c	c	PROPN
ejpam-4931	343	16	(	(	PUNCT
ejpam-4931	343	17	[	[	X
ejpam-4931	343	18	0	0	NUM
ejpam-4931	343	19	,	,	PUNCT
ejpam-4931	343	20	t	t	X
ejpam-4931	343	21	]	]	PUNCT
ejpam-4931	343	22	;	;	PUNCT
ejpam-4931	343	23	h5(ω	h5(ω	NUM
ejpam-4931	343	24	)	)	PUNCT
ejpam-4931	343	25	)	)	PUNCT
ejpam-4931	344	1	and	and	CCONJ
ejpam-4931	344	2	ξn	ξn	PROPN
ejpam-4931	344	3	−→	−→	NOUN
ejpam-4931	344	4	ξ	ξ	PROPN
ejpam-4931	344	5	a.e	a.e	PROPN
ejpam-4931	344	6	.	.	PROPN
ejpam-4931	345	1	next	next	ADV
ejpam-4931	345	2	,	,	PUNCT
ejpam-4931	345	3	we	we	PRON
ejpam-4931	345	4	claim	claim	VERB
ejpam-4931	345	5	that	that	SCONJ
ejpam-4931	345	6	ξ−β	ξ−β	PROPN
ejpam-4931	345	7	n	n	PRON
ejpam-4931	345	8	is	be	AUX
ejpam-4931	345	9	bounded	bound	VERB
ejpam-4931	345	10	in	in	ADP
ejpam-4931	345	11	l	l	PROPN
ejpam-4931	345	12	5	5	NUM
ejpam-4931	345	13	3	3	NUM
ejpam-4931	345	14	(	(	PUNCT
ejpam-4931	345	15	[	[	X
ejpam-4931	345	16	0	0	NUM
ejpam-4931	345	17	,	,	PUNCT
ejpam-4931	345	18	t	t	X
ejpam-4931	345	19	]	]	PUNCT
ejpam-4931	345	20	;	;	PUNCT
ejpam-4931	345	21	l	l	NOUN
ejpam-4931	345	22	5	5	NUM
ejpam-4931	345	23	3	3	NUM
ejpam-4931	345	24	(	(	PUNCT
ejpam-4931	345	25	ω	ω	NOUN
ejpam-4931	345	26	)	)	PUNCT
ejpam-4931	345	27	)	)	PUNCT
ejpam-4931	345	28	.	.	PUNCT
ejpam-4931	346	1	indeed	indeed	ADV
ejpam-4931	346	2	,	,	PUNCT
ejpam-4931	346	3	using	use	VERB
ejpam-4931	346	4	the	the	DET
ejpam-4931	346	5	fact	fact	NOUN
ejpam-4931	346	6	that	that	SCONJ
ejpam-4931	346	7	∇xξ	∇xξ	NOUN
ejpam-4931	346	8	−β/2	−β/2	PRON
ejpam-4931	346	9	n	n	CCONJ
ejpam-4931	346	10	is	be	AUX
ejpam-4931	346	11	bounded	bound	VERB
ejpam-4931	346	12	in	in	ADP
ejpam-4931	346	13	l2	l2	NOUN
ejpam-4931	346	14	(	(	PUNCT
ejpam-4931	346	15	[	[	X
ejpam-4931	346	16	0	0	NUM
ejpam-4931	346	17	,	,	PUNCT
ejpam-4931	346	18	t	t	X
ejpam-4931	346	19	]	]	PUNCT
ejpam-4931	346	20	;	;	PUNCT
ejpam-4931	346	21	l2(ω	l2(ω	NUM
ejpam-4931	346	22	)	)	PUNCT
ejpam-4931	346	23	)	)	PUNCT
ejpam-4931	346	24	and	and	CCONJ
ejpam-4931	346	25	the	the	DET
ejpam-4931	346	26	sobolev	sobolev	NOUN
ejpam-4931	346	27	embedding	embed	VERB
ejpam-4931	346	28	theorem	theorem	VERB
ejpam-4931	346	29	,	,	PUNCT
ejpam-4931	346	30	we	we	PRON
ejpam-4931	346	31	deduce	deduce	VERB
ejpam-4931	346	32	that	that	SCONJ
ejpam-4931	346	33	ξ−β	ξ−β	PROPN
ejpam-4931	346	34	n	n	PRON
ejpam-4931	346	35	is	be	AUX
ejpam-4931	346	36	bounded	bound	VERB
ejpam-4931	346	37	in	in	ADP
ejpam-4931	346	38	l1	l1	PROPN
ejpam-4931	346	39	(	(	PUNCT
ejpam-4931	346	40	[	[	X
ejpam-4931	346	41	0	0	NUM
ejpam-4931	346	42	,	,	PUNCT
ejpam-4931	346	43	t	t	X
ejpam-4931	346	44	]	]	PUNCT
ejpam-4931	346	45	;	;	PUNCT
ejpam-4931	346	46	l3(ω	l3(ω	X
ejpam-4931	346	47	)	)	PUNCT
ejpam-4931	346	48	)	)	PUNCT
ejpam-4931	346	49	.	.	PUNCT
ejpam-4931	347	1	then	then	ADV
ejpam-4931	347	2	we	we	PRON
ejpam-4931	347	3	apply	apply	VERB
ejpam-4931	347	4	hölder	hölder	NOUN
ejpam-4931	347	5	inequality	inequality	NOUN
ejpam-4931	347	6	to	to	PART
ejpam-4931	347	7	get	get	VERB
ejpam-4931	347	8	∥ξ−β	∥ξ−β	ADJ
ejpam-4931	347	9	n	n	CCONJ
ejpam-4931	347	10	∥	∥	NUM
ejpam-4931	347	11	l	l	NOUN
ejpam-4931	347	12	5	5	NUM
ejpam-4931	347	13	3	3	NUM
ejpam-4931	347	14	(	(	PUNCT
ejpam-4931	347	15	[	[	X
ejpam-4931	347	16	0,t	0,t	X
ejpam-4931	347	17	]	]	X
ejpam-4931	347	18	;	;	PUNCT
ejpam-4931	347	19	l	l	NOUN
ejpam-4931	347	20	5	5	NUM
ejpam-4931	347	21	3	3	NUM
ejpam-4931	347	22	(	(	PUNCT
ejpam-4931	347	23	ω	ω	NOUN
ejpam-4931	347	24	)	)	PUNCT
ejpam-4931	347	25	)	)	PUNCT
ejpam-4931	347	26	≤	≤	NOUN
ejpam-4931	347	27	∥ξ−β	∥ξ−β	NOUN
ejpam-4931	347	28	n	n	NOUN
ejpam-4931	347	29	∥	∥	NUM
ejpam-4931	347	30	2	2	NUM
ejpam-4931	347	31	5	5	NUM
ejpam-4931	347	32	l∞	l∞	NOUN
ejpam-4931	347	33	(	(	PUNCT
ejpam-4931	347	34	[	[	X
ejpam-4931	347	35	0,t	0,t	X
ejpam-4931	347	36	]	]	X
ejpam-4931	347	37	;	;	PUNCT
ejpam-4931	347	38	l1(ω	l1(ω	X
ejpam-4931	347	39	)	)	PUNCT
ejpam-4931	347	40	)	)	PUNCT
ejpam-4931	347	41	∥ξ−β	∥ξ−β	VERB
ejpam-4931	347	42	n	n	NOUN
ejpam-4931	347	43	∥	∥	NUM
ejpam-4931	347	44	3	3	NUM
ejpam-4931	347	45	5	5	NUM
ejpam-4931	347	46	l1	l1	PROPN
ejpam-4931	347	47	(	(	PUNCT
ejpam-4931	347	48	[	[	X
ejpam-4931	347	49	0,t	0,t	X
ejpam-4931	347	50	]	]	X
ejpam-4931	347	51	;	;	PUNCT
ejpam-4931	347	52	l3(ω	l3(ω	X
ejpam-4931	347	53	)	)	PUNCT
ejpam-4931	347	54	)	)	PUNCT
ejpam-4931	347	55	≤	≤	PROPN
ejpam-4931	348	1	k.	k.	NOUN
ejpam-4931	348	2	(	(	PUNCT
ejpam-4931	348	3	52	52	NUM
ejpam-4931	348	4	)	)	PUNCT
ejpam-4931	348	5	now	now	ADV
ejpam-4931	348	6	,	,	PUNCT
ejpam-4931	348	7	using	use	VERB
ejpam-4931	348	8	the	the	DET
ejpam-4931	348	9	following	follow	VERB
ejpam-4931	348	10	sobolev	sobolev	NOUN
ejpam-4931	348	11	inequality	inequality	NOUN
ejpam-4931	348	12	,	,	PUNCT
ejpam-4931	348	13	∥ξ−1	∥ξ−1	ADJ
ejpam-4931	348	14	n	n	CCONJ
ejpam-4931	348	15	∥l∞(ω)≤	∥l∞(ω)≤	ADV
ejpam-4931	348	16	c	c	NOUN
ejpam-4931	348	17	(	(	PUNCT
ejpam-4931	348	18	1+∥ξ−1	1+∥ξ−1	NUM
ejpam-4931	348	19	n	n	PRON
ejpam-4931	348	20	∥l3(ω	∥l3(ω	NOUN
ejpam-4931	348	21	)	)	PUNCT
ejpam-4931	348	22	)	)	PUNCT
ejpam-4931	348	23	3	3	X
ejpam-4931	348	24	(	(	PUNCT
ejpam-4931	348	25	1+∥ξn∥hk+2(ω	1+∥ξn∥hk+2(ω	NUM
ejpam-4931	348	26	)	)	PUNCT
ejpam-4931	348	27	)	)	PUNCT
ejpam-4931	348	28	2	2	NUM
ejpam-4931	348	29	for	for	ADP
ejpam-4931	348	30	k	k	PROPN
ejpam-4931	348	31	≥	≥	NUM
ejpam-4931	348	32	3	3	NUM
ejpam-4931	348	33	2	2	NUM
ejpam-4931	348	34	(	(	PUNCT
ejpam-4931	348	35	see	see	VERB
ejpam-4931	348	36	[	[	X
ejpam-4931	348	37	[	[	X
ejpam-4931	348	38	1	1	NUM
ejpam-4931	348	39	]	]	PUNCT
ejpam-4931	348	40	,	,	PUNCT
ejpam-4931	348	41	lemma	lemma	PROPN
ejpam-4931	348	42	2.1	2.1	NUM
ejpam-4931	348	43	]	]	PUNCT
ejpam-4931	348	44	)	)	PUNCT
ejpam-4931	348	45	,	,	PUNCT
ejpam-4931	348	46	and	and	CCONJ
ejpam-4931	348	47	the	the	DET
ejpam-4931	348	48	estimates	estimate	NOUN
ejpam-4931	348	49	of	of	ADP
ejpam-4931	348	50	density	density	NOUN
ejpam-4931	348	51	in	in	ADP
ejpam-4931	348	52	(	(	PUNCT
ejpam-4931	348	53	48	48	NUM
ejpam-4931	348	54	)	)	PUNCT
ejpam-4931	348	55	,	,	PUNCT
ejpam-4931	348	56	we	we	PRON
ejpam-4931	348	57	get	get	VERB
ejpam-4931	348	58	∥ξ−β	∥ξ−β	ADJ
ejpam-4931	348	59	n	n	PRON
ejpam-4931	348	60	∥l∞(ω)≤	∥l∞(ω)≤	ADJ
ejpam-4931	348	61	c(r2	c(r2	NOUN
ejpam-4931	348	62	,	,	PUNCT
ejpam-4931	348	63	δ	δ	PROPN
ejpam-4931	348	64	)	)	PUNCT
ejpam-4931	348	65	a.e	a.e	NOUN
ejpam-4931	348	66	on	on	ADP
ejpam-4931	348	67	[	[	X
ejpam-4931	348	68	0	0	NUM
ejpam-4931	348	69	,	,	PUNCT
ejpam-4931	348	70	t	t	X
ejpam-4931	348	71	]	]	PUNCT
ejpam-4931	348	72	.	.	PUNCT
ejpam-4931	349	1	(	(	PUNCT
ejpam-4931	349	2	53	53	NUM
ejpam-4931	349	3	)	)	PUNCT
ejpam-4931	349	4	j.	j.	PROPN
ejpam-4931	349	5	ouya	ouya	PROPN
ejpam-4931	349	6	,	,	PUNCT
ejpam-4931	349	7	a.	a.	NOUN
ejpam-4931	349	8	ouédraogo	ouédraogo	PROPN
ejpam-4931	349	9	/	/	SYM
ejpam-4931	349	10	eur	eur	PROPN
ejpam-4931	349	11	.	.	PUNCT
ejpam-4931	350	1	j.	j.	PROPN
ejpam-4931	350	2	pure	pure	PROPN
ejpam-4931	350	3	appl	appl	PROPN
ejpam-4931	350	4	.	.	PROPN
ejpam-4931	350	5	math	math	PROPN
ejpam-4931	350	6	,	,	PUNCT
ejpam-4931	350	7	16	16	NUM
ejpam-4931	350	8	(	(	PUNCT
ejpam-4931	350	9	4	4	NUM
ejpam-4931	350	10	)	)	PUNCT
ejpam-4931	350	11	(	(	PUNCT
ejpam-4931	350	12	2023	2023	NUM
ejpam-4931	350	13	)	)	PUNCT
ejpam-4931	350	14	,	,	PUNCT
ejpam-4931	350	15	2247	2247	NUM
ejpam-4931	350	16	-	-	SYM
ejpam-4931	350	17	2285	2285	NUM
ejpam-4931	350	18	2261	2261	NUM
ejpam-4931	350	19	thus	thus	ADV
ejpam-4931	350	20	,	,	PUNCT
ejpam-4931	350	21	we	we	PRON
ejpam-4931	350	22	have	have	AUX
ejpam-4931	350	23	ξ−β	ξ−β	VERB
ejpam-4931	350	24	n	n	PRON
ejpam-4931	350	25	converges	converge	VERB
ejpam-4931	350	26	a.e	a.e	PRON
ejpam-4931	350	27	to	to	ADP
ejpam-4931	350	28	ξ−β	ξ−β	NOUN
ejpam-4931	350	29	.	.	PUNCT
ejpam-4931	351	1	thanks	thank	NOUN
ejpam-4931	351	2	to	to	ADP
ejpam-4931	351	3	(	(	PUNCT
ejpam-4931	351	4	52	52	NUM
ejpam-4931	351	5	)	)	PUNCT
ejpam-4931	351	6	and	and	CCONJ
ejpam-4931	351	7	lemma	lemma	PROPN
ejpam-4931	351	8	2	2	NUM
ejpam-4931	351	9	,	,	PUNCT
ejpam-4931	351	10	we	we	PRON
ejpam-4931	351	11	have	have	VERB
ejpam-4931	351	12	ξ−β	ξ−β	VERB
ejpam-4931	351	13	n	n	PRON
ejpam-4931	351	14	−→	−→	NOUN
ejpam-4931	351	15	ξ−β	ξ−β	VERB
ejpam-4931	351	16	strongly	strongly	ADV
ejpam-4931	351	17	in	in	ADP
ejpam-4931	351	18	l1	l1	PROPN
ejpam-4931	351	19	(	(	PUNCT
ejpam-4931	351	20	[	[	X
ejpam-4931	351	21	0	0	NUM
ejpam-4931	351	22	,	,	PUNCT
ejpam-4931	351	23	t	t	X
ejpam-4931	351	24	]	]	PUNCT
ejpam-4931	351	25	;	;	PUNCT
ejpam-4931	351	26	l1(ω	l1(ω	X
ejpam-4931	351	27	)	)	PUNCT
ejpam-4931	351	28	)	)	PUNCT
ejpam-4931	351	29	.	.	PUNCT
ejpam-4931	352	1	using	use	VERB
ejpam-4931	352	2	again	again	ADV
ejpam-4931	352	3	the	the	DET
ejpam-4931	352	4	mass	mass	ADJ
ejpam-4931	352	5	equation	equation	NOUN
ejpam-4931	352	6	(	(	PUNCT
ejpam-4931	352	7	19	19	NUM
ejpam-4931	352	8	)	)	PUNCT
ejpam-4931	352	9	,	,	PUNCT
ejpam-4931	352	10	we	we	PRON
ejpam-4931	352	11	have	have	VERB
ejpam-4931	352	12	∂t	∂t	PROPN
ejpam-4931	352	13	√	√	PROPN
ejpam-4931	352	14	ξn	ξn	NOUN
ejpam-4931	352	15	=	=	SYM
ejpam-4931	352	16	1	1	NUM
ejpam-4931	352	17	2	2	NUM
ejpam-4931	352	18	1√	1√	PROPN
ejpam-4931	352	19	ξn	ξn	NOUN
ejpam-4931	352	20	∂tξn	∂tξn	PUNCT
ejpam-4931	352	21	=	=	SYM
ejpam-4931	352	22	1	1	NUM
ejpam-4931	352	23	2	2	NUM
ejpam-4931	352	24	1√	1√	PROPN
ejpam-4931	352	25	ξn	ξn	NOUN
ejpam-4931	352	26	(	(	PUNCT
ejpam-4931	352	27	ϵ∆xξn	ϵ∆xξn	NUM
ejpam-4931	352	28	−	−	PROPN
ejpam-4931	352	29	divx	divx	PROPN
ejpam-4931	352	30	(	(	PUNCT
ejpam-4931	352	31	√	√	PROPN
ejpam-4931	352	32	ξn	ξn	PROPN
ejpam-4931	352	33	√	√	NUM
ejpam-4931	352	34	ξnūn	ξnūn	NUM
ejpam-4931	352	35	)	)	PUNCT
ejpam-4931	352	36	)	)	PUNCT
ejpam-4931	352	37	.	.	PUNCT
ejpam-4931	353	1	by	by	ADP
ejpam-4931	353	2	using	use	VERB
ejpam-4931	353	3	(	(	PUNCT
ejpam-4931	353	4	53	53	NUM
ejpam-4931	353	5	)	)	PUNCT
ejpam-4931	353	6	and	and	CCONJ
ejpam-4931	353	7	the	the	DET
ejpam-4931	353	8	fact	fact	NOUN
ejpam-4931	353	9	that	that	SCONJ
ejpam-4931	353	10	∂tξn	∂tξn	PUNCT
ejpam-4931	353	11	∈	∈	PROPN
ejpam-4931	353	12	l∞	l∞	NOUN
ejpam-4931	353	13	(	(	PUNCT
ejpam-4931	353	14	[	[	X
ejpam-4931	353	15	0	0	NUM
ejpam-4931	353	16	,	,	PUNCT
ejpam-4931	353	17	t	t	X
ejpam-4931	353	18	]	]	PUNCT
ejpam-4931	353	19	;	;	PUNCT
ejpam-4931	353	20	w−1	w−1	PROPN
ejpam-4931	353	21	,	,	PUNCT
ejpam-4931	353	22	3	3	NUM
ejpam-4931	353	23	2	2	NUM
ejpam-4931	353	24	)	)	PUNCT
ejpam-4931	353	25	,	,	PUNCT
ejpam-4931	353	26	we	we	PRON
ejpam-4931	353	27	have	have	AUX
ejpam-4931	353	28	∂t	∂t	PROPN
ejpam-4931	353	29	√	√	PROPN
ejpam-4931	353	30	ξn	ξn	PROPN
ejpam-4931	353	31	∈	∈	PROPN
ejpam-4931	353	32	l∞	l∞	NOUN
ejpam-4931	353	33	(	(	PUNCT
ejpam-4931	353	34	[	[	X
ejpam-4931	353	35	0	0	NUM
ejpam-4931	353	36	,	,	PUNCT
ejpam-4931	353	37	t	t	X
ejpam-4931	353	38	]	]	PUNCT
ejpam-4931	353	39	;	;	PUNCT
ejpam-4931	353	40	w−1	w−1	PROPN
ejpam-4931	353	41	,	,	PUNCT
ejpam-4931	353	42	3	3	NUM
ejpam-4931	353	43	2	2	NUM
ejpam-4931	353	44	)	)	PUNCT
ejpam-4931	353	45	.	.	PUNCT
ejpam-4931	354	1	note	note	VERB
ejpam-4931	354	2	that	that	SCONJ
ejpam-4931	354	3	√	√	VERB
ejpam-4931	354	4	ξn	ξn	PROPN
ejpam-4931	354	5	∈	∈	PROPN
ejpam-4931	354	6	l2	l2	NOUN
ejpam-4931	354	7	(	(	PUNCT
ejpam-4931	354	8	[	[	X
ejpam-4931	354	9	0	0	NUM
ejpam-4931	354	10	,	,	PUNCT
ejpam-4931	354	11	t	t	X
ejpam-4931	354	12	]	]	PUNCT
ejpam-4931	354	13	;	;	PUNCT
ejpam-4931	354	14	h2(ω	h2(ω	NUM
ejpam-4931	354	15	)	)	PUNCT
ejpam-4931	354	16	)	)	PUNCT
ejpam-4931	354	17	which	which	PRON
ejpam-4931	354	18	is	be	AUX
ejpam-4931	354	19	reflexive	reflexive	ADJ
ejpam-4931	354	20	,	,	PUNCT
ejpam-4931	354	21	so	so	ADV
ejpam-4931	354	22	using	use	VERB
ejpam-4931	354	23	the	the	DET
ejpam-4931	354	24	aubin	aubin	PROPN
ejpam-4931	354	25	-	-	PUNCT
ejpam-4931	354	26	lions	lion	NOUN
ejpam-4931	354	27	lemma	lemma	PROPN
ejpam-4931	354	28	,	,	PUNCT
ejpam-4931	354	29	we	we	PRON
ejpam-4931	354	30	obtain√	obtain√	VERB
ejpam-4931	354	31	ξn	ξn	INTJ
ejpam-4931	354	32	−→	−→	ADJ
ejpam-4931	354	33	√	√	PROPN
ejpam-4931	354	34	ξ	ξ	ADP
ejpam-4931	354	35	strongly	strongly	ADV
ejpam-4931	354	36	in	in	ADP
ejpam-4931	354	37	l2	l2	NOUN
ejpam-4931	354	38	(	(	PUNCT
ejpam-4931	354	39	[	[	X
ejpam-4931	354	40	0	0	NUM
ejpam-4931	354	41	,	,	PUNCT
ejpam-4931	354	42	t	t	X
ejpam-4931	354	43	]	]	PUNCT
ejpam-4931	354	44	;	;	PUNCT
ejpam-4931	354	45	h1(ω	h1(ω	PROPN
ejpam-4931	354	46	)	)	PUNCT
ejpam-4931	354	47	)	)	PUNCT
ejpam-4931	355	1	and	and	CCONJ
ejpam-4931	355	2	√	√	VERB
ejpam-4931	355	3	ξn	ξn	VERB
ejpam-4931	355	4	−→	−→	ADJ
ejpam-4931	355	5	√	√	NUM
ejpam-4931	355	6	ξ	ξ	PROPN
ejpam-4931	355	7	a.e	a.e	NOUN
ejpam-4931	355	8	in	in	ADP
ejpam-4931	355	9	[	[	X
ejpam-4931	355	10	0	0	NUM
ejpam-4931	355	11	,	,	PUNCT
ejpam-4931	355	12	t	t	X
ejpam-4931	355	13	]	]	X
ejpam-4931	355	14	×	×	PROPN
ejpam-4931	355	15	ω	ω	X
ejpam-4931	355	16	.	.	PUNCT
ejpam-4931	356	1	furthermore	furthermore	ADV
ejpam-4931	356	2	,	,	PUNCT
ejpam-4931	356	3	as	as	ADP
ejpam-4931	356	4	in	in	ADP
ejpam-4931	356	5	[	[	X
ejpam-4931	356	6	5	5	NUM
ejpam-4931	356	7	]	]	PUNCT
ejpam-4931	356	8	we	we	PRON
ejpam-4931	356	9	show	show	VERB
ejpam-4931	356	10	that	that	NUM
ejpam-4931	356	11	∥∇xξn∥l2	∥∇xξn∥l2	ADJ
ejpam-4931	356	12	(	(	PUNCT
ejpam-4931	356	13	[	[	X
ejpam-4931	356	14	0,t	0,t	X
ejpam-4931	356	15	]	]	X
ejpam-4931	356	16	×ω	×ω	X
ejpam-4931	356	17	)	)	PUNCT
ejpam-4931	356	18	≤	≤	NUM
ejpam-4931	357	1	k	k	NOUN
ejpam-4931	357	2	,	,	PUNCT
ejpam-4931	357	3	∥ξ2n∥l	∥ξ2n∥l	PROPN
ejpam-4931	357	4	5	5	NUM
ejpam-4931	357	5	3	3	NUM
ejpam-4931	357	6	(	(	PUNCT
ejpam-4931	357	7	[	[	X
ejpam-4931	357	8	0,t	0,t	X
ejpam-4931	357	9	]	]	X
ejpam-4931	357	10	;	;	PUNCT
ejpam-4931	357	11	l	l	NOUN
ejpam-4931	357	12	5	5	NUM
ejpam-4931	357	13	3	3	NUM
ejpam-4931	357	14	(	(	PUNCT
ejpam-4931	357	15	ω	ω	NOUN
ejpam-4931	357	16	)	)	PUNCT
ejpam-4931	357	17	)	)	PUNCT
ejpam-4931	357	18	≤	≤	NUM
ejpam-4931	357	19	∥ξ2n∥	∥ξ2n∥	VERB
ejpam-4931	357	20	2	2	NUM
ejpam-4931	357	21	5	5	NUM
ejpam-4931	357	22	l∞	l∞	NOUN
ejpam-4931	357	23	(	(	PUNCT
ejpam-4931	357	24	[	[	X
ejpam-4931	357	25	0,t	0,t	X
ejpam-4931	357	26	]	]	X
ejpam-4931	357	27	;	;	PUNCT
ejpam-4931	357	28	l1(ω	l1(ω	X
ejpam-4931	357	29	)	)	PUNCT
ejpam-4931	357	30	)	)	PUNCT
ejpam-4931	357	31	∥ξ2n∥	∥ξ2n∥	VERB
ejpam-4931	357	32	3	3	NUM
ejpam-4931	357	33	5	5	NUM
ejpam-4931	357	34	l1	l1	PROPN
ejpam-4931	357	35	(	(	PUNCT
ejpam-4931	357	36	[	[	X
ejpam-4931	357	37	0,t	0,t	X
ejpam-4931	357	38	]	]	X
ejpam-4931	357	39	;	;	PUNCT
ejpam-4931	357	40	l3(ω	l3(ω	X
ejpam-4931	357	41	)	)	PUNCT
ejpam-4931	357	42	)	)	PUNCT
ejpam-4931	357	43	≤	≤	PROPN
ejpam-4931	358	1	k.	k.	PROPN
ejpam-4931	359	1	(	(	PUNCT
ejpam-4931	359	2	54	54	NUM
ejpam-4931	359	3	)	)	PUNCT
ejpam-4931	359	4	using	use	VERB
ejpam-4931	359	5	(	(	PUNCT
ejpam-4931	359	6	49	49	NUM
ejpam-4931	359	7	)	)	PUNCT
ejpam-4931	359	8	and	and	CCONJ
ejpam-4931	359	9	the	the	DET
ejpam-4931	359	10	fact	fact	NOUN
ejpam-4931	359	11	that	that	SCONJ
ejpam-4931	359	12	ξ2n	ξ2n	PROPN
ejpam-4931	359	13	converges	converge	VERB
ejpam-4931	359	14	almost	almost	ADV
ejpam-4931	359	15	everywhere	everywhere	ADV
ejpam-4931	359	16	to	to	ADP
ejpam-4931	359	17	ξ2	ξ2	NOUN
ejpam-4931	359	18	,	,	PUNCT
ejpam-4931	359	19	we	we	PRON
ejpam-4931	359	20	obtain	obtain	VERB
ejpam-4931	359	21	ξ2n	ξ2n	PROPN
ejpam-4931	359	22	−→	−→	ADJ
ejpam-4931	359	23	ξ2	ξ2	NOUN
ejpam-4931	359	24	strongly	strongly	ADV
ejpam-4931	359	25	in	in	ADP
ejpam-4931	359	26	l1	l1	PROPN
ejpam-4931	359	27	(	(	PUNCT
ejpam-4931	359	28	[	[	X
ejpam-4931	359	29	0	0	NUM
ejpam-4931	359	30	,	,	PUNCT
ejpam-4931	359	31	t	t	X
ejpam-4931	359	32	]	]	PUNCT
ejpam-4931	359	33	;	;	PUNCT
ejpam-4931	359	34	l1(ω	l1(ω	X
ejpam-4931	359	35	)	)	PUNCT
ejpam-4931	359	36	)	)	PUNCT
ejpam-4931	359	37	.	.	PUNCT
ejpam-4931	360	1	lemma	lemma	PROPN
ejpam-4931	360	2	7	7	NUM
ejpam-4931	360	3	.	.	PUNCT
ejpam-4931	361	1	(	(	PUNCT
ejpam-4931	361	2	convergence	convergence	NOUN
ejpam-4931	361	3	of	of	ADP
ejpam-4931	361	4	momentum	momentum	NOUN
ejpam-4931	361	5	ξnun	ξnun	PROPN
ejpam-4931	361	6	)	)	PUNCT
ejpam-4931	361	7	.	.	PUNCT
ejpam-4931	362	1	up	up	ADP
ejpam-4931	362	2	to	to	ADP
ejpam-4931	362	3	an	an	DET
ejpam-4931	362	4	extracted	extract	VERB
ejpam-4931	362	5	subsequence	subsequence	NOUN
ejpam-4931	362	6	,	,	PUNCT
ejpam-4931	362	7	we	we	PRON
ejpam-4931	362	8	have	have	VERB
ejpam-4931	362	9	ξnun	ξnun	VERB
ejpam-4931	362	10	−→	−→	ADV
ejpam-4931	362	11	ξu	ξu	NOUN
ejpam-4931	362	12	strongly	strongly	ADV
ejpam-4931	362	13	in	in	ADP
ejpam-4931	362	14	l2	l2	NOUN
ejpam-4931	362	15	(	(	PUNCT
ejpam-4931	362	16	[	[	X
ejpam-4931	362	17	0	0	NUM
ejpam-4931	362	18	,	,	PUNCT
ejpam-4931	362	19	t	t	X
ejpam-4931	362	20	]	]	PUNCT
ejpam-4931	362	21	;	;	PUNCT
ejpam-4931	362	22	l2(ω	l2(ω	NUM
ejpam-4931	362	23	)	)	PUNCT
ejpam-4931	362	24	)	)	PUNCT
ejpam-4931	362	25	and	and	CCONJ
ejpam-4931	362	26	ξnun	ξnun	VERB
ejpam-4931	362	27	−→	−→	ADV
ejpam-4931	362	28	ξu	ξu	INTJ
ejpam-4931	362	29	a.e	a.e	VERB
ejpam-4931	362	30	in	in	ADP
ejpam-4931	362	31	[	[	X
ejpam-4931	362	32	0	0	NUM
ejpam-4931	362	33	,	,	PUNCT
ejpam-4931	362	34	t	t	X
ejpam-4931	362	35	]	]	X
ejpam-4931	362	36	×	×	PROPN
ejpam-4931	362	37	ω	ω	NOUN
ejpam-4931	362	38	.	.	PUNCT
ejpam-4931	363	1	proof	proof	NOUN
ejpam-4931	363	2	.	.	PUNCT
ejpam-4931	364	1	according	accord	VERB
ejpam-4931	364	2	to	to	ADP
ejpam-4931	364	3	estimates	estimate	NOUN
ejpam-4931	364	4	(	(	PUNCT
ejpam-4931	364	5	48	48	NUM
ejpam-4931	364	6	)	)	PUNCT
ejpam-4931	364	7	,	,	PUNCT
ejpam-4931	364	8	we	we	PRON
ejpam-4931	364	9	know	know	VERB
ejpam-4931	364	10	that	that	SCONJ
ejpam-4931	364	11	un	un	PROPN
ejpam-4931	364	12	is	be	AUX
ejpam-4931	364	13	bounded	bound	VERB
ejpam-4931	364	14	in	in	ADP
ejpam-4931	364	15	l2	l2	NOUN
ejpam-4931	364	16	(	(	PUNCT
ejpam-4931	364	17	[	[	X
ejpam-4931	364	18	0	0	NUM
ejpam-4931	364	19	,	,	PUNCT
ejpam-4931	364	20	t	t	X
ejpam-4931	364	21	]	]	PUNCT
ejpam-4931	364	22	;	;	PUNCT
ejpam-4931	364	23	l2(ω	l2(ω	NUM
ejpam-4931	364	24	)	)	PUNCT
ejpam-4931	364	25	)	)	PUNCT
ejpam-4931	364	26	which	which	PRON
ejpam-4931	364	27	is	be	AUX
ejpam-4931	364	28	reflexive	reflexive	ADJ
ejpam-4931	364	29	.	.	PUNCT
ejpam-4931	365	1	so	so	ADV
ejpam-4931	365	2	,	,	PUNCT
ejpam-4931	365	3	up	up	ADP
ejpam-4931	365	4	to	to	ADP
ejpam-4931	365	5	a	a	DET
ejpam-4931	365	6	subsequence	subsequence	NOUN
ejpam-4931	365	7	,	,	PUNCT
ejpam-4931	365	8	we	we	PRON
ejpam-4931	365	9	have	have	AUX
ejpam-4931	365	10	un	un	PROPN
ejpam-4931	365	11	⇀	⇀	NUM
ejpam-4931	365	12	u	u	NOUN
ejpam-4931	365	13	weakly	weakly	ADJ
ejpam-4931	365	14	in	in	ADP
ejpam-4931	365	15	l2	l2	NOUN
ejpam-4931	365	16	(	(	PUNCT
ejpam-4931	365	17	[	[	X
ejpam-4931	365	18	0	0	NUM
ejpam-4931	365	19	,	,	PUNCT
ejpam-4931	365	20	t	t	X
ejpam-4931	365	21	]	]	PUNCT
ejpam-4931	365	22	;	;	PUNCT
ejpam-4931	365	23	l2(ω	l2(ω	NUM
ejpam-4931	365	24	)	)	PUNCT
ejpam-4931	365	25	)	)	PUNCT
ejpam-4931	365	26	.	.	PUNCT
ejpam-4931	366	1	recalling	recall	VERB
ejpam-4931	366	2	that	that	SCONJ
ejpam-4931	366	3	ξn	ξn	PROPN
ejpam-4931	366	4	−→	−→	NOUN
ejpam-4931	366	5	ξ	ξ	X
ejpam-4931	366	6	strongly	strongly	ADV
ejpam-4931	366	7	in	in	ADP
ejpam-4931	366	8	c	c	PROPN
ejpam-4931	366	9	(	(	PUNCT
ejpam-4931	366	10	[	[	X
ejpam-4931	366	11	0	0	NUM
ejpam-4931	366	12	,	,	PUNCT
ejpam-4931	366	13	t	t	X
ejpam-4931	366	14	]	]	PUNCT
ejpam-4931	366	15	;	;	PUNCT
ejpam-4931	366	16	h5(ω	h5(ω	NUM
ejpam-4931	366	17	)	)	PUNCT
ejpam-4931	366	18	)	)	PUNCT
ejpam-4931	366	19	,	,	PUNCT
ejpam-4931	366	20	we	we	PRON
ejpam-4931	366	21	have	have	VERB
ejpam-4931	366	22	ξnun	ξnun	VERB
ejpam-4931	366	23	−→	−→	ADV
ejpam-4931	366	24	ξu	ξu	NOUN
ejpam-4931	366	25	strongly	strongly	ADV
ejpam-4931	366	26	in	in	ADP
ejpam-4931	366	27	l1	l1	PROPN
ejpam-4931	366	28	(	(	PUNCT
ejpam-4931	366	29	[	[	X
ejpam-4931	366	30	0	0	NUM
ejpam-4931	366	31	,	,	PUNCT
ejpam-4931	366	32	t	t	X
ejpam-4931	366	33	]	]	PUNCT
ejpam-4931	366	34	;	;	PUNCT
ejpam-4931	366	35	l1(ω	l1(ω	X
ejpam-4931	366	36	)	)	PUNCT
ejpam-4931	366	37	)	)	PUNCT
ejpam-4931	366	38	.	.	PUNCT
ejpam-4931	367	1	moreover	moreover	ADV
ejpam-4931	367	2	,	,	PUNCT
ejpam-4931	367	3	since	since	SCONJ
ejpam-4931	367	4	ξn	ξn	PROPN
ejpam-4931	367	5	∈	∈	PROPN
ejpam-4931	367	6	l∞	l∞	NOUN
ejpam-4931	367	7	(	(	PUNCT
ejpam-4931	367	8	[	[	X
ejpam-4931	367	9	0	0	NUM
ejpam-4931	367	10	,	,	PUNCT
ejpam-4931	367	11	t	t	X
ejpam-4931	367	12	]	]	PUNCT
ejpam-4931	367	13	;	;	PUNCT
ejpam-4931	367	14	h5(ω	h5(ω	NUM
ejpam-4931	367	15	)	)	PUNCT
ejpam-4931	367	16	)	)	PUNCT
ejpam-4931	367	17	,	,	PUNCT
ejpam-4931	367	18	un	un	PROPN
ejpam-4931	367	19	∈	∈	PROPN
ejpam-4931	367	20	l2	l2	NOUN
ejpam-4931	367	21	(	(	PUNCT
ejpam-4931	367	22	[	[	X
ejpam-4931	367	23	0	0	NUM
ejpam-4931	367	24	,	,	PUNCT
ejpam-4931	367	25	t	t	X
ejpam-4931	367	26	]	]	PUNCT
ejpam-4931	367	27	;	;	PUNCT
ejpam-4931	367	28	h2(ω	h2(ω	NUM
ejpam-4931	367	29	)	)	PUNCT
ejpam-4931	367	30	)	)	PUNCT
ejpam-4931	367	31	,	,	PUNCT
ejpam-4931	367	32	√	√	NUM
ejpam-4931	367	33	ξn∂yun	ξn∂yun	NUM
ejpam-4931	367	34	∈	∈	NOUN
ejpam-4931	367	35	l2	l2	NOUN
ejpam-4931	367	36	(	(	PUNCT
ejpam-4931	367	37	[	[	X
ejpam-4931	367	38	0	0	NUM
ejpam-4931	367	39	,	,	PUNCT
ejpam-4931	367	40	t	t	X
ejpam-4931	367	41	]	]	PUNCT
ejpam-4931	367	42	;	;	PUNCT
ejpam-4931	367	43	l2(ω	l2(ω	NUM
ejpam-4931	367	44	)	)	PUNCT
ejpam-4931	367	45	)	)	PUNCT
ejpam-4931	367	46	,	,	PUNCT
ejpam-4931	367	47	we	we	PRON
ejpam-4931	367	48	deduce	deduce	VERB
ejpam-4931	367	49	∇(ξnun	∇(ξnun	NOUN
ejpam-4931	367	50	)	)	PUNCT
ejpam-4931	367	51	=	=	SYM
ejpam-4931	367	52	un.∇xξn	un.∇xξn	PROPN
ejpam-4931	368	1	+	+	CCONJ
ejpam-4931	368	2	ξn∇xun	ξn∇xun	NOUN
ejpam-4931	369	1	+	+	CCONJ
ejpam-4931	369	2	ξn∂yun	ξn∂yun	NUM
ejpam-4931	369	3	∈	∈	NOUN
ejpam-4931	369	4	l2	l2	NOUN
ejpam-4931	369	5	(	(	PUNCT
ejpam-4931	369	6	[	[	X
ejpam-4931	369	7	0	0	NUM
ejpam-4931	369	8	,	,	PUNCT
ejpam-4931	369	9	t	t	X
ejpam-4931	369	10	]	]	PUNCT
ejpam-4931	369	11	;	;	PUNCT
ejpam-4931	369	12	l2(ω	l2(ω	NUM
ejpam-4931	369	13	)	)	PUNCT
ejpam-4931	369	14	)	)	PUNCT
ejpam-4931	369	15	.	.	PUNCT
ejpam-4931	370	1	this	this	DET
ejpam-4931	370	2	last	last	ADJ
ejpam-4931	370	3	identity	identity	NOUN
ejpam-4931	370	4	and	and	CCONJ
ejpam-4931	370	5	the	the	DET
ejpam-4931	370	6	fact	fact	NOUN
ejpam-4931	370	7	that	that	SCONJ
ejpam-4931	370	8	ξnun	ξnun	PROPN
ejpam-4931	370	9	∈	∈	PROPN
ejpam-4931	370	10	l2	l2	NOUN
ejpam-4931	370	11	(	(	PUNCT
ejpam-4931	370	12	[	[	X
ejpam-4931	370	13	0	0	NUM
ejpam-4931	370	14	,	,	PUNCT
ejpam-4931	370	15	t	t	X
ejpam-4931	370	16	]	]	PUNCT
ejpam-4931	370	17	;	;	PUNCT
ejpam-4931	370	18	l2(ω	l2(ω	NUM
ejpam-4931	370	19	)	)	PUNCT
ejpam-4931	370	20	)	)	PUNCT
ejpam-4931	370	21	give	give	VERB
ejpam-4931	370	22	ξnun	ξnun	PROPN
ejpam-4931	370	23	∈	∈	PROPN
ejpam-4931	370	24	l2	l2	NOUN
ejpam-4931	370	25	(	(	PUNCT
ejpam-4931	370	26	[	[	X
ejpam-4931	370	27	0	0	NUM
ejpam-4931	370	28	,	,	PUNCT
ejpam-4931	370	29	t	t	X
ejpam-4931	370	30	]	]	PUNCT
ejpam-4931	370	31	;	;	PUNCT
ejpam-4931	370	32	h1(ω	h1(ω	PROPN
ejpam-4931	370	33	)	)	PUNCT
ejpam-4931	370	34	)	)	PUNCT
ejpam-4931	370	35	.	.	PUNCT
ejpam-4931	371	1	next	next	ADV
ejpam-4931	371	2	,	,	PUNCT
ejpam-4931	371	3	we	we	PRON
ejpam-4931	371	4	claim	claim	VERB
ejpam-4931	371	5	that	that	SCONJ
ejpam-4931	371	6	∂y(ξnun	∂y(ξnun	PROPN
ejpam-4931	371	7	)	)	PUNCT
ejpam-4931	371	8	∈	∈	NOUN
ejpam-4931	371	9	l2	l2	NOUN
ejpam-4931	371	10	(	(	PUNCT
ejpam-4931	371	11	[	[	X
ejpam-4931	371	12	0	0	NUM
ejpam-4931	371	13	,	,	PUNCT
ejpam-4931	371	14	t	t	X
ejpam-4931	371	15	]	]	PUNCT
ejpam-4931	371	16	;	;	PUNCT
ejpam-4931	371	17	h−s(ω	h−s(ω	NOUN
ejpam-4931	371	18	)	)	PUNCT
ejpam-4931	371	19	)	)	PUNCT
ejpam-4931	371	20	,	,	PUNCT
ejpam-4931	371	21	for	for	SCONJ
ejpam-4931	371	22	some	some	PRON
ejpam-4931	371	23	s	s	VERB
ejpam-4931	371	24	>	>	X
ejpam-4931	371	25	0	0	X
ejpam-4931	371	26	.	.	PUNCT
ejpam-4931	372	1	indeed	indeed	ADV
ejpam-4931	372	2	,	,	PUNCT
ejpam-4931	372	3	∂t(ξnun	∂t(ξnun	ADJ
ejpam-4931	372	4	)	)	PUNCT
ejpam-4931	373	1	=	=	NOUN
ejpam-4931	373	2	−	−	PROPN
ejpam-4931	374	1	divx(ξnun	divx(ξnun	PROPN
ejpam-4931	374	2	⊗	⊗	PROPN
ejpam-4931	374	3	un)−	un)−	X
ejpam-4931	374	4	∂y(ξnunvn)−∇xξ	∂y(ξnunvn)−∇xξ	PROPN
ejpam-4931	374	5	2	2	NUM
ejpam-4931	374	6	n	n	NUM
ejpam-4931	374	7	−	−	PROPN
ejpam-4931	374	8	r1un	r1un	NOUN
ejpam-4931	374	9	−	−	PROPN
ejpam-4931	375	1	rξ|un|un	rξ|un|un	ADV
ejpam-4931	375	2	−	−	PROPN
ejpam-4931	375	3	α∆2un	α∆2un	PROPN
ejpam-4931	375	4	+	+	CCONJ
ejpam-4931	375	5	2divx	2divx	NUM
ejpam-4931	375	6	(	(	PUNCT
ejpam-4931	375	7	ξndx(un	ξndx(un	PROPN
ejpam-4931	375	8	)	)	PUNCT
ejpam-4931	375	9	)	)	PUNCT
ejpam-4931	376	1	+	+	PUNCT
ejpam-4931	376	2	∂y(ξn∂yun	∂y(ξn∂yun	NOUN
ejpam-4931	376	3	)	)	PUNCT
ejpam-4931	376	4	j.	j.	PROPN
ejpam-4931	376	5	ouya	ouya	PROPN
ejpam-4931	376	6	,	,	PUNCT
ejpam-4931	376	7	a.	a.	NOUN
ejpam-4931	376	8	ouédraogo	ouédraogo	PROPN
ejpam-4931	376	9	/	/	SYM
ejpam-4931	376	10	eur	eur	PROPN
ejpam-4931	376	11	.	.	PUNCT
ejpam-4931	377	1	j.	j.	PROPN
ejpam-4931	377	2	pure	pure	PROPN
ejpam-4931	377	3	appl	appl	PROPN
ejpam-4931	377	4	.	.	PROPN
ejpam-4931	377	5	math	math	PROPN
ejpam-4931	377	6	,	,	PUNCT
ejpam-4931	377	7	16	16	NUM
ejpam-4931	377	8	(	(	PUNCT
ejpam-4931	377	9	4	4	NUM
ejpam-4931	377	10	)	)	PUNCT
ejpam-4931	377	11	(	(	PUNCT
ejpam-4931	377	12	2023	2023	NUM
ejpam-4931	377	13	)	)	PUNCT
ejpam-4931	377	14	,	,	PUNCT
ejpam-4931	377	15	2247	2247	NUM
ejpam-4931	377	16	-	-	SYM
ejpam-4931	377	17	2285	2285	NUM
ejpam-4931	377	18	2262	2262	NUM
ejpam-4931	377	19	+	+	CCONJ
ejpam-4931	377	20	ε∇xξn	ε∇xξn	X
ejpam-4931	377	21	·	·	PUNCT
ejpam-4931	378	1	∇xun	∇xun	ADJ
ejpam-4931	378	2	+	+	CCONJ
ejpam-4931	378	3	r2∇xξ	r2∇xξ	NOUN
ejpam-4931	378	4	−β	−β	NOUN
ejpam-4931	378	5	n	n	PROPN
ejpam-4931	378	6	+	+	CCONJ
ejpam-4931	378	7	k1ξn∇x	k1ξn∇x	NOUN
ejpam-4931	378	8	(	(	PUNCT
ejpam-4931	378	9	∆x	∆x	PROPN
ejpam-4931	378	10	√	√	NUM
ejpam-4931	378	11	ξn√	ξn√	PROPN
ejpam-4931	378	12	ξn	ξn	NOUN
ejpam-4931	378	13	)	)	PUNCT
ejpam-4931	379	1	+	+	CCONJ
ejpam-4931	379	2	δξn∇x∆	δξn∇x∆	NOUN
ejpam-4931	379	3	5	5	NUM
ejpam-4931	379	4	xξn	xξn	PROPN
ejpam-4931	379	5	.	.	PUNCT
ejpam-4931	380	1	(	(	PUNCT
ejpam-4931	380	2	55	55	NUM
ejpam-4931	380	3	)	)	PUNCT
ejpam-4931	380	4	where	where	SCONJ
ejpam-4931	380	5	∂y(ξnunvn	∂y(ξnunvn	NOUN
ejpam-4931	380	6	)	)	PUNCT
ejpam-4931	381	1	=	=	PUNCT
ejpam-4931	381	2	∂y	∂y	NOUN
ejpam-4931	381	3	(	(	PUNCT
ejpam-4931	381	4	ξnun	ξnun	PROPN
ejpam-4931	381	5	(	(	PUNCT
ejpam-4931	381	6	−	−	PROPN
ejpam-4931	381	7	divx(ξnũn	divx(ξnũn	NOUN
ejpam-4931	381	8	)	)	PUNCT
ejpam-4931	381	9	ξn	ξn	PROPN
ejpam-4931	382	1	+	+	CCONJ
ejpam-4931	382	2	y	y	PROPN
ejpam-4931	382	3	divx(ξnūn	divx(ξnūn	PROPN
ejpam-4931	382	4	)	)	PUNCT
ejpam-4931	382	5	ξn	ξn	NOUN
ejpam-4931	382	6	)	)	PUNCT
ejpam-4931	382	7	)	)	PUNCT
ejpam-4931	383	1	=	=	PUNCT
ejpam-4931	383	2	∂y	∂y	NOUN
ejpam-4931	383	3	(	(	PUNCT
ejpam-4931	383	4	−	−	PROPN
ejpam-4931	383	5	divx(ξnũn	divx(ξnũn	PROPN
ejpam-4931	383	6	⊗	⊗	PROPN
ejpam-4931	383	7	un	un	PROPN
ejpam-4931	383	8	)	)	PUNCT
ejpam-4931	383	9	+	+	CCONJ
ejpam-4931	383	10	ξnũn.∇xun	ξnũn.∇xun	PROPN
ejpam-4931	383	11	+	+	NUM
ejpam-4931	383	12	ydivx(ξnūn	ydivx(ξnūn	PROPN
ejpam-4931	383	13	⊗	⊗	PROPN
ejpam-4931	383	14	un)−	un)−	PART
ejpam-4931	383	15	yξnūn.∇xun	yξnūn.∇xun	PROPN
ejpam-4931	383	16	)	)	PUNCT
ejpam-4931	383	17	.	.	PUNCT
ejpam-4931	384	1	(	(	PUNCT
ejpam-4931	384	2	56	56	NUM
ejpam-4931	384	3	)	)	PUNCT
ejpam-4931	384	4	based	base	VERB
ejpam-4931	384	5	on	on	ADP
ejpam-4931	384	6	the	the	DET
ejpam-4931	384	7	energy	energy	NOUN
ejpam-4931	384	8	estimates	estimate	NOUN
ejpam-4931	384	9	(	(	PUNCT
ejpam-4931	384	10	48	48	NUM
ejpam-4931	384	11	)	)	PUNCT
ejpam-4931	384	12	,	,	PUNCT
ejpam-4931	384	13	we	we	PRON
ejpam-4931	384	14	get	get	VERB
ejpam-4931	384	15	∂y(ξnun	∂y(ξnun	NOUN
ejpam-4931	384	16	)	)	PUNCT
ejpam-4931	384	17	∈	∈	NOUN
ejpam-4931	384	18	l2	l2	NOUN
ejpam-4931	384	19	(	(	PUNCT
ejpam-4931	384	20	[	[	X
ejpam-4931	384	21	0	0	NUM
ejpam-4931	384	22	,	,	PUNCT
ejpam-4931	384	23	t	t	X
ejpam-4931	384	24	]	]	PUNCT
ejpam-4931	384	25	;	;	PUNCT
ejpam-4931	384	26	h−5(ω	h−5(ω	PROPN
ejpam-4931	384	27	)	)	PUNCT
ejpam-4931	384	28	)	)	PUNCT
ejpam-4931	384	29	.	.	PUNCT
ejpam-4931	385	1	then	then	ADV
ejpam-4931	385	2	,	,	PUNCT
ejpam-4931	385	3	thanks	thank	NOUN
ejpam-4931	385	4	to	to	ADP
ejpam-4931	385	5	the	the	DET
ejpam-4931	385	6	aubin	aubin	PROPN
ejpam-4931	385	7	-	-	PUNCT
ejpam-4931	385	8	lions	lion	NOUN
ejpam-4931	385	9	lemma	lemma	PROPN
ejpam-4931	385	10	1	1	NUM
ejpam-4931	385	11	,	,	PUNCT
ejpam-4931	385	12	ξnun	ξnun	PROPN
ejpam-4931	385	13	converges	converge	VERB
ejpam-4931	385	14	strongly	strongly	ADV
ejpam-4931	385	15	in	in	ADP
ejpam-4931	385	16	l2	l2	NOUN
ejpam-4931	385	17	(	(	PUNCT
ejpam-4931	385	18	[	[	X
ejpam-4931	385	19	0	0	NUM
ejpam-4931	385	20	,	,	PUNCT
ejpam-4931	385	21	t	t	X
ejpam-4931	385	22	]	]	PUNCT
ejpam-4931	385	23	;	;	PUNCT
ejpam-4931	385	24	l2(ω	l2(ω	NUM
ejpam-4931	385	25	)	)	PUNCT
ejpam-4931	385	26	)	)	PUNCT
ejpam-4931	385	27	to	to	ADP
ejpam-4931	385	28	a	a	DET
ejpam-4931	385	29	function	function	NOUN
ejpam-4931	385	30	f	f	PROPN
ejpam-4931	385	31	∈	∈	PROPN
ejpam-4931	385	32	l2	l2	NOUN
ejpam-4931	385	33	(	(	PUNCT
ejpam-4931	385	34	[	[	X
ejpam-4931	385	35	0	0	NUM
ejpam-4931	385	36	,	,	PUNCT
ejpam-4931	385	37	t	t	X
ejpam-4931	385	38	]	]	PUNCT
ejpam-4931	385	39	;	;	PUNCT
ejpam-4931	385	40	l2(ω	l2(ω	NUM
ejpam-4931	385	41	)	)	PUNCT
ejpam-4931	385	42	)	)	PUNCT
ejpam-4931	385	43	.	.	PUNCT
ejpam-4931	386	1	also	also	ADV
ejpam-4931	386	2	,	,	PUNCT
ejpam-4931	386	3	since	since	SCONJ
ejpam-4931	386	4	ξnun	ξnun	PROPN
ejpam-4931	386	5	−→	−→	ADV
ejpam-4931	386	6	ξu	ξu	VERB
ejpam-4931	386	7	strongly	strongly	ADV
ejpam-4931	386	8	in	in	ADP
ejpam-4931	386	9	l1	l1	PROPN
ejpam-4931	386	10	(	(	PUNCT
ejpam-4931	386	11	[	[	X
ejpam-4931	386	12	0	0	NUM
ejpam-4931	386	13	,	,	PUNCT
ejpam-4931	386	14	t	t	X
ejpam-4931	386	15	]	]	PUNCT
ejpam-4931	386	16	;	;	PUNCT
ejpam-4931	386	17	l1(ω	l1(ω	X
ejpam-4931	386	18	)	)	PUNCT
ejpam-4931	386	19	)	)	PUNCT
ejpam-4931	386	20	,	,	PUNCT
ejpam-4931	386	21	we	we	PRON
ejpam-4931	386	22	have	have	VERB
ejpam-4931	386	23	ξnun	ξnun	VERB
ejpam-4931	386	24	−→	−→	ADV
ejpam-4931	386	25	ξu	ξu	NOUN
ejpam-4931	386	26	strongly	strongly	ADV
ejpam-4931	386	27	in	in	ADP
ejpam-4931	386	28	l2	l2	NOUN
ejpam-4931	386	29	(	(	PUNCT
ejpam-4931	386	30	[	[	X
ejpam-4931	386	31	0	0	NUM
ejpam-4931	386	32	,	,	PUNCT
ejpam-4931	386	33	t	t	X
ejpam-4931	386	34	]	]	PUNCT
ejpam-4931	386	35	;	;	PUNCT
ejpam-4931	386	36	l2(ω	l2(ω	NUM
ejpam-4931	386	37	)	)	PUNCT
ejpam-4931	386	38	)	)	PUNCT
ejpam-4931	386	39	.	.	PUNCT
ejpam-4931	387	1	we	we	PRON
ejpam-4931	387	2	have	have	VERB
ejpam-4931	387	3	the	the	DET
ejpam-4931	387	4	following	follow	VERB
ejpam-4931	387	5	result	result	NOUN
ejpam-4931	387	6	.	.	PUNCT
ejpam-4931	388	1	lemma	lemma	PROPN
ejpam-4931	388	2	8	8	NUM
ejpam-4931	388	3	.	.	PUNCT
ejpam-4931	389	1	(	(	PUNCT
ejpam-4931	389	2	see	see	VERB
ejpam-4931	389	3	[	[	X
ejpam-4931	389	4	19	19	NUM
ejpam-4931	389	5	]	]	PUNCT
ejpam-4931	389	6	,	,	PUNCT
ejpam-4931	389	7	lemma	lemma	PROPN
ejpam-4931	389	8	3.5	3.5	NUM
ejpam-4931	389	9	)	)	PUNCT
ejpam-4931	389	10	.	.	PUNCT
ejpam-4931	390	1	up	up	ADP
ejpam-4931	390	2	to	to	ADP
ejpam-4931	390	3	an	an	DET
ejpam-4931	390	4	extracted	extract	VERB
ejpam-4931	390	5	subsequence	subsequence	NOUN
ejpam-4931	390	6	,	,	PUNCT
ejpam-4931	390	7	we	we	PRON
ejpam-4931	390	8	have	have	VERB
ejpam-4931	390	9	√	√	VERB
ejpam-4931	390	10	ξnun	ξnun	ADJ
ejpam-4931	390	11	−→	−→	ADV
ejpam-4931	390	12	√	√	PROPN
ejpam-4931	390	13	ξu	ξu	VERB
ejpam-4931	390	14	strongly	strongly	ADV
ejpam-4931	390	15	in	in	ADP
ejpam-4931	390	16	l2	l2	NOUN
ejpam-4931	390	17	(	(	PUNCT
ejpam-4931	390	18	[	[	X
ejpam-4931	390	19	0	0	NUM
ejpam-4931	390	20	,	,	PUNCT
ejpam-4931	390	21	t	t	X
ejpam-4931	390	22	]	]	PUNCT
ejpam-4931	390	23	;	;	PUNCT
ejpam-4931	390	24	l2(ω	l2(ω	NUM
ejpam-4931	390	25	)	)	PUNCT
ejpam-4931	390	26	)	)	PUNCT
ejpam-4931	390	27	,	,	PUNCT
ejpam-4931	390	28	√	√	NUM
ejpam-4931	390	29	ξnũn	ξnũn	NUM
ejpam-4931	390	30	−→	−→	NOUN
ejpam-4931	390	31	√	√	PROPN
ejpam-4931	390	32	ξũ	ξũ	ADV
ejpam-4931	390	33	strongly	strongly	ADV
ejpam-4931	390	34	in	in	ADP
ejpam-4931	390	35	l2	l2	NOUN
ejpam-4931	390	36	(	(	PUNCT
ejpam-4931	390	37	[	[	X
ejpam-4931	390	38	0	0	NUM
ejpam-4931	390	39	,	,	PUNCT
ejpam-4931	390	40	t	t	X
ejpam-4931	390	41	]	]	PUNCT
ejpam-4931	390	42	;	;	PUNCT
ejpam-4931	390	43	l2(ω	l2(ω	NUM
ejpam-4931	390	44	)	)	PUNCT
ejpam-4931	390	45	)	)	PUNCT
ejpam-4931	390	46	,	,	PUNCT
ejpam-4931	390	47	√	√	NUM
ejpam-4931	390	48	ξnūn	ξnūn	NOUN
ejpam-4931	390	49	−→	−→	NOUN
ejpam-4931	390	50	√	√	PRON
ejpam-4931	390	51	ξū	ξū	ADV
ejpam-4931	390	52	strongly	strongly	ADV
ejpam-4931	390	53	in	in	ADP
ejpam-4931	390	54	l2	l2	NOUN
ejpam-4931	390	55	(	(	PUNCT
ejpam-4931	390	56	[	[	X
ejpam-4931	390	57	0	0	NUM
ejpam-4931	390	58	,	,	PUNCT
ejpam-4931	390	59	t	t	X
ejpam-4931	390	60	]	]	PUNCT
ejpam-4931	390	61	;	;	PUNCT
ejpam-4931	390	62	l2(ω	l2(ω	NUM
ejpam-4931	390	63	)	)	PUNCT
ejpam-4931	390	64	)	)	PUNCT
ejpam-4931	390	65	.	.	PUNCT
ejpam-4931	391	1	by	by	ADP
ejpam-4931	391	2	lemma	lemma	PROPN
ejpam-4931	391	3	8	8	NUM
ejpam-4931	391	4	,	,	PUNCT
ejpam-4931	391	5	we	we	PRON
ejpam-4931	391	6	conclude	conclude	VERB
ejpam-4931	391	7	that	that	SCONJ
ejpam-4931	391	8	√	√	VERB
ejpam-4931	391	9	ξnun	ξnun	VERB
ejpam-4931	391	10	−→	−→	ADJ
ejpam-4931	391	11	√	√	NUM
ejpam-4931	391	12	ξu	ξu	NOUN
ejpam-4931	391	13	,	,	PUNCT
ejpam-4931	391	14	√	√	NUM
ejpam-4931	391	15	ξnũn	ξnũn	PROPN
ejpam-4931	391	16	−→	−→	NOUN
ejpam-4931	391	17	√	√	PROPN
ejpam-4931	391	18	ξũ	ξũ	PRON
ejpam-4931	391	19	and√	and√	PROPN
ejpam-4931	391	20	ξnūn	ξnūn	NOUN
ejpam-4931	391	21	−→	−→	NOUN
ejpam-4931	391	22	√	√	PUNCT
ejpam-4931	391	23	ξū	ξū	NOUN
ejpam-4931	391	24	almost	almost	ADV
ejpam-4931	391	25	everywhere	everywhere	ADV
ejpam-4931	391	26	in	in	ADP
ejpam-4931	391	27	[	[	X
ejpam-4931	391	28	0	0	NUM
ejpam-4931	391	29	,	,	PUNCT
ejpam-4931	391	30	t	t	X
ejpam-4931	391	31	]	]	X
ejpam-4931	391	32	×	×	PROPN
ejpam-4931	391	33	ω	ω	X
ejpam-4931	391	34	.	.	PUNCT
ejpam-4931	392	1	lemma	lemma	PROPN
ejpam-4931	392	2	9	9	NUM
ejpam-4931	392	3	.	.	PUNCT
ejpam-4931	393	1	(	(	PUNCT
ejpam-4931	393	2	convergence	convergence	NOUN
ejpam-4931	393	3	of	of	ADP
ejpam-4931	393	4	(	(	PUNCT
ejpam-4931	393	5	∂y(ξnunvn))n	∂y(ξnunvn))n	PROPN
ejpam-4931	393	6	)	)	PUNCT
ejpam-4931	393	7	.	.	PUNCT
ejpam-4931	394	1	let	let	VERB
ejpam-4931	394	2	φ	φ	PROPN
ejpam-4931	394	3	∈	∈	PROPN
ejpam-4931	394	4	c∞	c∞	PROPN
ejpam-4931	394	5	c	c	NOUN
ejpam-4931	394	6	(	(	PUNCT
ejpam-4931	394	7	[	[	X
ejpam-4931	394	8	0	0	NUM
ejpam-4931	394	9	,	,	PUNCT
ejpam-4931	394	10	t	t	X
ejpam-4931	394	11	]	]	PUNCT
ejpam-4931	394	12	×	×	PROPN
ejpam-4931	394	13	ω	ω	PROPN
ejpam-4931	394	14	)	)	PUNCT
ejpam-4931	394	15	be	be	AUX
ejpam-4931	394	16	a	a	DET
ejpam-4931	394	17	regular	regular	ADJ
ejpam-4931	394	18	test	test	NOUN
ejpam-4931	394	19	function	function	NOUN
ejpam-4931	394	20	,	,	PUNCT
ejpam-4931	394	21	then∫	then∫	NOUN
ejpam-4931	394	22	t	t	PROPN
ejpam-4931	394	23	0	0	NUM
ejpam-4931	395	1	∫	∫	PROPN
ejpam-4931	395	2	ω	ω	NUM
ejpam-4931	395	3	∂y(ξnunvn).φdxdydt	∂y(ξnunvn).φdxdydt	PROPN
ejpam-4931	395	4	−→	−→	PROPN
ejpam-4931	395	5	∫	∫	PROPN
ejpam-4931	395	6	t	t	PROPN
ejpam-4931	395	7	0	0	NUM
ejpam-4931	395	8	∫	∫	PROPN
ejpam-4931	396	1	ω	ω	PROPN
ejpam-4931	396	2	∂y(ξuv).φdxdydt	∂y(ξuv).φdxdydt	PROPN
ejpam-4931	396	3	as	as	ADP
ejpam-4931	396	4	n	n	PRON
ejpam-4931	396	5	−→	−→	NOUN
ejpam-4931	396	6	+	+	ADJ
ejpam-4931	396	7	∞.	∞.	PROPN
ejpam-4931	396	8	proof	proof	NOUN
ejpam-4931	396	9	.	.	PUNCT
ejpam-4931	397	1	let	let	VERB
ejpam-4931	397	2	φ	φ	PROPN
ejpam-4931	397	3	∈	∈	PROPN
ejpam-4931	398	1	c∞	c∞	PROPN
ejpam-4931	398	2	c	c	NOUN
ejpam-4931	398	3	(	(	PUNCT
ejpam-4931	398	4	[	[	X
ejpam-4931	398	5	0	0	NUM
ejpam-4931	398	6	,	,	PUNCT
ejpam-4931	398	7	t	t	X
ejpam-4931	398	8	]	]	X
ejpam-4931	398	9	×	×	PROPN
ejpam-4931	398	10	ω	ω	PROPN
ejpam-4931	398	11	)	)	PUNCT
ejpam-4931	398	12	be	be	AUX
ejpam-4931	398	13	a	a	DET
ejpam-4931	398	14	smooth	smooth	ADJ
ejpam-4931	398	15	function	function	NOUN
ejpam-4931	398	16	.	.	PUNCT
ejpam-4931	399	1	from	from	ADP
ejpam-4931	399	2	(	(	PUNCT
ejpam-4931	399	3	56	56	NUM
ejpam-4931	399	4	)	)	PUNCT
ejpam-4931	399	5	,	,	PUNCT
ejpam-4931	399	6	we	we	PRON
ejpam-4931	399	7	have∫	have∫	VERB
ejpam-4931	399	8	t	t	PROPN
ejpam-4931	399	9	0	0	NUM
ejpam-4931	399	10	∫	∫	PROPN
ejpam-4931	399	11	ω	ω	NUM
ejpam-4931	399	12	∂y(ξnunvn).φdxdydt	∂y(ξnunvn).φdxdydt	PROPN
ejpam-4931	400	1	=	=	PUNCT
ejpam-4931	401	1	−	−	NOUN
ejpam-4931	401	2	∫	∫	PROPN
ejpam-4931	401	3	t	t	PROPN
ejpam-4931	401	4	0	0	NUM
ejpam-4931	401	5	∫	∫	PROPN
ejpam-4931	401	6	ω	ω	PROPN
ejpam-4931	401	7	ξnunvn	ξnunvn	PROPN
ejpam-4931	401	8	·	·	PUNCT
ejpam-4931	401	9	∂yφdxdydt	∂yφdxdydt	PROPN
ejpam-4931	401	10	=	=	SYM
ejpam-4931	402	1	−	−	PROPN
ejpam-4931	402	2	∫	∫	PROPN
ejpam-4931	402	3	t	t	PROPN
ejpam-4931	402	4	0	0	NUM
ejpam-4931	403	1	∫	∫	PROPN
ejpam-4931	403	2	ω	ω	PROPN
ejpam-4931	403	3	un	un	PROPN
ejpam-4931	403	4	(	(	PUNCT
ejpam-4931	403	5	−	−	PROPN
ejpam-4931	403	6	divx(ξnũn	divx(ξnũn	NOUN
ejpam-4931	403	7	)	)	PUNCT
ejpam-4931	404	1	+	+	CCONJ
ejpam-4931	404	2	ydivx(ξnūn	ydivx(ξnūn	NOUN
ejpam-4931	404	3	)	)	PUNCT
ejpam-4931	404	4	)	)	PUNCT
ejpam-4931	405	1	·	·	PUNCT
ejpam-4931	406	1	∂yφdxdydt	∂yφdxdydt	PROPN
ejpam-4931	406	2	=	=	PUNCT
ejpam-4931	407	1	−	−	PROPN
ejpam-4931	407	2	∫	∫	PROPN
ejpam-4931	407	3	t	t	PROPN
ejpam-4931	407	4	0	0	NUM
ejpam-4931	408	1	∫	∫	PROPN
ejpam-4931	409	1	ω	ω	PROPN
ejpam-4931	410	1	(	(	PUNCT
ejpam-4931	410	2	−	−	PROPN
ejpam-4931	410	3	divx(ξnũn	divx(ξnũn	PROPN
ejpam-4931	410	4	⊗	⊗	PROPN
ejpam-4931	410	5	un	un	PROPN
ejpam-4931	410	6	)	)	PUNCT
ejpam-4931	410	7	+	+	CCONJ
ejpam-4931	410	8	ξnũn	ξnũn	NOUN
ejpam-4931	410	9	·	·	PUNCT
ejpam-4931	410	10	∇xun	∇xun	ADJ
ejpam-4931	410	11	+	+	CCONJ
ejpam-4931	410	12	ydivx(ξnūn	ydivx(ξnūn	PROPN
ejpam-4931	411	1	⊗	⊗	PROPN
ejpam-4931	411	2	un)−	un)−	X
ejpam-4931	412	1	yξnūn	yξnūn	PROPN
ejpam-4931	412	2	·	·	PUNCT
ejpam-4931	412	3	∇xun	∇xun	ADJ
ejpam-4931	412	4	)	)	PUNCT
ejpam-4931	412	5	.∂yφdxdydt	.∂yφdxdydt	PROPN
ejpam-4931	412	6	j.	j.	PROPN
ejpam-4931	412	7	ouya	ouya	PROPN
ejpam-4931	412	8	,	,	PUNCT
ejpam-4931	412	9	a.	a.	NOUN
ejpam-4931	412	10	ouédraogo	ouédraogo	PROPN
ejpam-4931	412	11	/	/	SYM
ejpam-4931	412	12	eur	eur	PROPN
ejpam-4931	412	13	.	.	PUNCT
ejpam-4931	413	1	j.	j.	PROPN
ejpam-4931	413	2	pure	pure	PROPN
ejpam-4931	413	3	appl	appl	PROPN
ejpam-4931	413	4	.	.	PROPN
ejpam-4931	413	5	math	math	PROPN
ejpam-4931	413	6	,	,	PUNCT
ejpam-4931	413	7	16	16	NUM
ejpam-4931	413	8	(	(	PUNCT
ejpam-4931	413	9	4	4	NUM
ejpam-4931	413	10	)	)	PUNCT
ejpam-4931	413	11	(	(	PUNCT
ejpam-4931	413	12	2023	2023	NUM
ejpam-4931	413	13	)	)	PUNCT
ejpam-4931	413	14	,	,	PUNCT
ejpam-4931	413	15	2247	2247	NUM
ejpam-4931	413	16	-	-	SYM
ejpam-4931	413	17	2285	2285	NUM
ejpam-4931	413	18	2263	2263	NUM
ejpam-4931	413	19	=	=	SYM
ejpam-4931	414	1	−	−	PROPN
ejpam-4931	414	2	∫	∫	PROPN
ejpam-4931	414	3	t	t	PROPN
ejpam-4931	414	4	0	0	NUM
ejpam-4931	414	5	∫	∫	PROPN
ejpam-4931	415	1	ω	ω	PROPN
ejpam-4931	415	2	ξnũn	ξnũn	PROPN
ejpam-4931	415	3	⊗	⊗	PROPN
ejpam-4931	415	4	un	un	PROPN
ejpam-4931	415	5	:	:	PUNCT
ejpam-4931	416	1	∂y∇xφdxdydt+	∂y∇xφdxdydt+	PROPN
ejpam-4931	416	2	∫	∫	PROPN
ejpam-4931	416	3	t	t	PROPN
ejpam-4931	416	4	0	0	NUM
ejpam-4931	416	5	∫	∫	PROPN
ejpam-4931	416	6	ω	ω	PROPN
ejpam-4931	416	7	ξnūn	ξnūn	PROPN
ejpam-4931	416	8	⊗	⊗	PROPN
ejpam-4931	416	9	un	un	PROPN
ejpam-4931	416	10	:	:	PUNCT
ejpam-4931	417	1	y∂y∇xφdxdydt	y∂y∇xφdxdydt	PROPN
ejpam-4931	417	2	−	−	PROPN
ejpam-4931	418	1	∫	∫	PROPN
ejpam-4931	418	2	t	t	PROPN
ejpam-4931	418	3	0	0	NUM
ejpam-4931	418	4	∫	∫	PROPN
ejpam-4931	418	5	ω	ω	PROPN
ejpam-4931	418	6	ξnũn	ξnũn	PROPN
ejpam-4931	418	7	·	·	PUNCT
ejpam-4931	419	1	∇xun	∇xun	ADJ
ejpam-4931	419	2	·	·	PUNCT
ejpam-4931	419	3	∂yφdxdydt+	∂yφdxdydt+	NOUN
ejpam-4931	419	4	∫	∫	PROPN
ejpam-4931	420	1	t	t	PROPN
ejpam-4931	420	2	0	0	NUM
ejpam-4931	420	3	∫	∫	PROPN
ejpam-4931	420	4	ω	ω	NUM
ejpam-4931	420	5	ξnūn	ξnūn	NOUN
ejpam-4931	420	6	·	·	PUNCT
ejpam-4931	420	7	∇xun	∇xun	ADJ
ejpam-4931	420	8	·	·	PUNCT
ejpam-4931	420	9	y∂yφdxdydt	y∂yφdxdydt	PROPN
ejpam-4931	420	10	.	.	PUNCT
ejpam-4931	421	1	(	(	PUNCT
ejpam-4931	421	2	57	57	NUM
ejpam-4931	421	3	)	)	PUNCT
ejpam-4931	421	4	by	by	ADP
ejpam-4931	421	5	direct	direct	ADJ
ejpam-4931	421	6	computation	computation	NOUN
ejpam-4931	421	7	we	we	PRON
ejpam-4931	421	8	have	have	VERB
ejpam-4931	421	9	∇x	∇x	PROPN
ejpam-4931	421	10	(	(	PUNCT
ejpam-4931	421	11	√	√	NUM
ejpam-4931	421	12	ξnun	ξnun	NOUN
ejpam-4931	421	13	)	)	PUNCT
ejpam-4931	421	14	=	=	SYM
ejpam-4931	422	1	√	√	NUM
ejpam-4931	422	2	ξn∇xun	ξn∇xun	NOUN
ejpam-4931	423	1	+	+	PUNCT
ejpam-4931	423	2	∇x	∇x	NOUN
ejpam-4931	423	3	√	√	VERB
ejpam-4931	423	4	ξn	ξn	PROPN
ejpam-4931	423	5	⊗	⊗	PROPN
ejpam-4931	423	6	un	un	PROPN
ejpam-4931	423	7	,	,	PUNCT
ejpam-4931	423	8	thus∫	thus∫	NOUN
ejpam-4931	423	9	t	t	PROPN
ejpam-4931	423	10	0	0	NUM
ejpam-4931	423	11	∫	∫	PROPN
ejpam-4931	423	12	ω	ω	NUM
ejpam-4931	423	13	√	√	PROPN
ejpam-4931	423	14	ξn∇xun	ξn∇xun	NOUN
ejpam-4931	423	15	:	:	PUNCT
ejpam-4931	423	16	φdxdydt	φdxdydt	ADJ
ejpam-4931	423	17	=	=	SYM
ejpam-4931	423	18	∫	∫	PROPN
ejpam-4931	423	19	t	t	PROPN
ejpam-4931	423	20	0	0	NUM
ejpam-4931	423	21	∫	∫	PROPN
ejpam-4931	423	22	ω	ω	PROPN
ejpam-4931	423	23	(	(	PUNCT
ejpam-4931	423	24	∇x	∇x	PROPN
ejpam-4931	423	25	(	(	PUNCT
ejpam-4931	423	26	√	√	NUM
ejpam-4931	423	27	ξnun)−∇x	ξnun)−∇x	NUM
ejpam-4931	423	28	√	√	PROPN
ejpam-4931	423	29	ξn	ξn	PROPN
ejpam-4931	423	30	⊗	⊗	PROPN
ejpam-4931	423	31	un	un	PROPN
ejpam-4931	423	32	)	)	PUNCT
ejpam-4931	423	33	:	:	PUNCT
ejpam-4931	424	1	φdxdydt	φdxdydt	ADJ
ejpam-4931	424	2	=	=	PUNCT
ejpam-4931	425	1	−	−	NOUN
ejpam-4931	425	2	∫	∫	PROPN
ejpam-4931	425	3	t	t	PROPN
ejpam-4931	425	4	0	0	NUM
ejpam-4931	425	5	∫	∫	PROPN
ejpam-4931	426	1	ω	ω	PROPN
ejpam-4931	426	2	(	(	PUNCT
ejpam-4931	426	3	√	√	NUM
ejpam-4931	426	4	ξnun	ξnun	PROPN
ejpam-4931	426	5	)	)	PUNCT
ejpam-4931	426	6	·	·	PUNCT
ejpam-4931	426	7	divxφdxdydt−	divxφdxdydt−	ADP
ejpam-4931	426	8	∫	∫	PROPN
ejpam-4931	426	9	t	t	PROPN
ejpam-4931	426	10	0	0	NUM
ejpam-4931	426	11	∫	∫	PROPN
ejpam-4931	426	12	ω	ω	NUM
ejpam-4931	426	13	∇x	∇x	PROPN
ejpam-4931	426	14	√	√	ADP
ejpam-4931	426	15	ξn	ξn	PROPN
ejpam-4931	426	16	⊗	⊗	PROPN
ejpam-4931	426	17	un	un	PROPN
ejpam-4931	426	18	:	:	PUNCT
ejpam-4931	426	19	φdxdydt	φdxdydt	ADJ
ejpam-4931	426	20	−→	−→	NOUN
ejpam-4931	426	21	n→+∞	n→+∞	PROPN
ejpam-4931	427	1	−	−	PROPN
ejpam-4931	427	2	∫	∫	PROPN
ejpam-4931	427	3	t	t	PROPN
ejpam-4931	427	4	0	0	NUM
ejpam-4931	428	1	∫	∫	PROPN
ejpam-4931	429	1	ω	ω	PROPN
ejpam-4931	430	1	(	(	PUNCT
ejpam-4931	430	2	√	√	NUM
ejpam-4931	430	3	ξu	ξu	NOUN
ejpam-4931	430	4	)	)	PUNCT
ejpam-4931	430	5	·	·	PUNCT
ejpam-4931	430	6	divxφdxdydt−	divxφdxdydt−	ADP
ejpam-4931	430	7	∫	∫	PROPN
ejpam-4931	430	8	t	t	PROPN
ejpam-4931	430	9	0	0	NUM
ejpam-4931	430	10	∫	∫	PROPN
ejpam-4931	431	1	ω	ω	NUM
ejpam-4931	431	2	∇x	∇x	PROPN
ejpam-4931	431	3	√	√	NUM
ejpam-4931	431	4	ξ	ξ	X
ejpam-4931	431	5	⊗	⊗	PROPN
ejpam-4931	431	6	u	u	NOUN
ejpam-4931	431	7	:	:	PUNCT
ejpam-4931	431	8	φdxdydt	φdxdydt	ADJ
ejpam-4931	431	9	=	=	SYM
ejpam-4931	431	10	∫	∫	PROPN
ejpam-4931	431	11	t	t	PROPN
ejpam-4931	431	12	0	0	NUM
ejpam-4931	431	13	∫	∫	PROPN
ejpam-4931	431	14	ω	ω	NUM
ejpam-4931	431	15	√	√	PROPN
ejpam-4931	431	16	ξ∇xu	ξ∇xu	NUM
ejpam-4931	431	17	:	:	PUNCT
ejpam-4931	431	18	φdxdydt	φdxdydt	ADJ
ejpam-4931	431	19	.	.	PUNCT
ejpam-4931	432	1	hence	hence	ADV
ejpam-4931	432	2	,	,	PUNCT
ejpam-4931	432	3	√	√	NUM
ejpam-4931	432	4	ξn∇xun	ξn∇xun	NOUN
ejpam-4931	433	1	⇀	⇀	NUM
ejpam-4931	433	2	√	√	NUM
ejpam-4931	433	3	ξ∇xu	ξ∇xu	NUM
ejpam-4931	433	4	weakly	weakly	ADV
ejpam-4931	433	5	in	in	ADP
ejpam-4931	433	6	l2	l2	NOUN
ejpam-4931	433	7	(	(	PUNCT
ejpam-4931	433	8	[	[	X
ejpam-4931	433	9	0	0	NUM
ejpam-4931	433	10	,	,	PUNCT
ejpam-4931	433	11	t	t	X
ejpam-4931	433	12	]	]	PUNCT
ejpam-4931	433	13	;	;	PUNCT
ejpam-4931	433	14	l2(ω	l2(ω	NUM
ejpam-4931	433	15	)	)	PUNCT
ejpam-4931	433	16	)	)	PUNCT
ejpam-4931	433	17	.	.	PUNCT
ejpam-4931	434	1	combining	combine	VERB
ejpam-4931	434	2	this	this	DET
ejpam-4931	434	3	last	last	ADJ
ejpam-4931	434	4	weak	weak	ADJ
ejpam-4931	434	5	convergence	convergence	NOUN
ejpam-4931	434	6	with	with	ADP
ejpam-4931	434	7	(	(	PUNCT
ejpam-4931	434	8	57	57	NUM
ejpam-4931	434	9	)	)	PUNCT
ejpam-4931	434	10	,	,	PUNCT
ejpam-4931	434	11	we	we	PRON
ejpam-4931	434	12	get	get	VERB
ejpam-4931	434	13	,	,	PUNCT
ejpam-4931	434	14	after	after	ADP
ejpam-4931	434	15	replacing	replace	VERB
ejpam-4931	434	16	ξn	ξn	NOUN
ejpam-4931	434	17	by	by	ADP
ejpam-4931	434	18	√	√	PROPN
ejpam-4931	434	19	ξn	ξn	PROPN
ejpam-4931	434	20	√	√	PROPN
ejpam-4931	434	21	ξn	ξn	PROPN
ejpam-4931	434	22	and	and	CCONJ
ejpam-4931	434	23	using	use	VERB
ejpam-4931	434	24	the	the	DET
ejpam-4931	434	25	previous	previous	ADJ
ejpam-4931	434	26	lemmas,∫	lemmas,∫	NOUN
ejpam-4931	434	27	t	t	NOUN
ejpam-4931	434	28	0	0	NUM
ejpam-4931	434	29	∫	∫	PROPN
ejpam-4931	434	30	ω	ω	NUM
ejpam-4931	434	31	∂y(ξnunvn).φdxdydt	∂y(ξnunvn).φdxdydt	PROPN
ejpam-4931	435	1	−→	−→	PROPN
ejpam-4931	435	2	∫	∫	PROPN
ejpam-4931	435	3	t	t	PROPN
ejpam-4931	435	4	0	0	NUM
ejpam-4931	435	5	∫	∫	PROPN
ejpam-4931	436	1	ω	ω	PROPN
ejpam-4931	436	2	∂y(ξuv).φdxdydt	∂y(ξuv).φdxdydt	PROPN
ejpam-4931	436	3	as	as	ADP
ejpam-4931	436	4	n	n	CCONJ
ejpam-4931	436	5	−→	−→	NOUN
ejpam-4931	436	6	+	+	NOUN
ejpam-4931	436	7	∞	∞	PROPN
ejpam-4931	436	8	,	,	PUNCT
ejpam-4931	436	9	where	where	SCONJ
ejpam-4931	436	10	ξv	ξv	ADV
ejpam-4931	436	11	=	=	SYM
ejpam-4931	436	12	−divx(ξũ	−divx(ξũ	NOUN
ejpam-4931	436	13	)	)	PUNCT
ejpam-4931	436	14	+	+	NUM
ejpam-4931	436	15	ydivx(ξū	ydivx(ξū	NOUN
ejpam-4931	436	16	)	)	PUNCT
ejpam-4931	436	17	.	.	PUNCT
ejpam-4931	437	1	lemma	lemma	PROPN
ejpam-4931	437	2	10	10	NUM
ejpam-4931	437	3	.	.	PUNCT
ejpam-4931	438	1	(	(	PUNCT
ejpam-4931	438	2	see	see	VERB
ejpam-4931	438	3	subsection	subsection	NOUN
ejpam-4931	438	4	3.3.5	3.3.5	NUM
ejpam-4931	438	5	of	of	ADP
ejpam-4931	438	6	[	[	X
ejpam-4931	438	7	19	19	NUM
ejpam-4931	438	8	]	]	NUM
ejpam-4931	438	9	)	)	PUNCT
ejpam-4931	438	10	(	(	PUNCT
ejpam-4931	438	11	convergence	convergence	NOUN
ejpam-4931	438	12	of	of	ADP
ejpam-4931	438	13	nonlinear	nonlinear	ADJ
ejpam-4931	438	14	diffusion	diffusion	NOUN
ejpam-4931	438	15	terms	term	NOUN
ejpam-4931	438	16	)	)	PUNCT
ejpam-4931	438	17	.	.	PUNCT
ejpam-4931	439	1	for	for	ADP
ejpam-4931	439	2	any	any	DET
ejpam-4931	439	3	smooth	smooth	ADJ
ejpam-4931	439	4	function	function	NOUN
ejpam-4931	439	5	φ	φ	PROPN
ejpam-4931	439	6	∈	∈	PROPN
ejpam-4931	439	7	c∞	c∞	PROPN
ejpam-4931	439	8	c	c	NOUN
ejpam-4931	439	9	(	(	PUNCT
ejpam-4931	439	10	[	[	X
ejpam-4931	439	11	0	0	NUM
ejpam-4931	439	12	,	,	PUNCT
ejpam-4931	439	13	t	t	X
ejpam-4931	439	14	]	]	X
ejpam-4931	439	15	×	×	PROPN
ejpam-4931	439	16	ω	ω	PROPN
ejpam-4931	439	17	)	)	PUNCT
ejpam-4931	439	18	,	,	PUNCT
ejpam-4931	439	19	we	we	PRON
ejpam-4931	439	20	have∫	have∫	VERB
ejpam-4931	439	21	t	t	NOUN
ejpam-4931	439	22	0	0	NUM
ejpam-4931	439	23	∫	∫	PROPN
ejpam-4931	439	24	ω	ω	NUM
ejpam-4931	439	25	divx(ξndx(un	divx(ξndx(un	PROPN
ejpam-4931	439	26	)	)	PUNCT
ejpam-4931	439	27	)	)	PUNCT
ejpam-4931	439	28	·	·	PUNCT
ejpam-4931	440	1	φdxdydt	φdxdydt	ADJ
ejpam-4931	440	2	−→	−→	ADJ
ejpam-4931	440	3	∫	∫	PROPN
ejpam-4931	440	4	t	t	PROPN
ejpam-4931	440	5	0	0	NUM
ejpam-4931	440	6	∫	∫	PROPN
ejpam-4931	440	7	ω	ω	PROPN
ejpam-4931	440	8	divx(ξdx(u	divx(ξdx(u	NOUN
ejpam-4931	440	9	)	)	PUNCT
ejpam-4931	440	10	)	)	PUNCT
ejpam-4931	440	11	·	·	PUNCT
ejpam-4931	441	1	φdxdydt	φdxdydt	ADJ
ejpam-4931	441	2	as	as	ADP
ejpam-4931	441	3	n	n	NUM
ejpam-4931	441	4	−→	−→	NOUN
ejpam-4931	441	5	+	+	NOUN
ejpam-4931	441	6	∞,∫	∞,∫	ADV
ejpam-4931	441	7	t	t	PROPN
ejpam-4931	441	8	0	0	NUM
ejpam-4931	441	9	∫	∫	PROPN
ejpam-4931	442	1	ω	ω	NUM
ejpam-4931	442	2	ξn∇x∆	ξn∇x∆	PROPN
ejpam-4931	442	3	5	5	NUM
ejpam-4931	442	4	xξn	xξn	NOUN
ejpam-4931	442	5	·	·	PUNCT
ejpam-4931	442	6	φdxdydt	φdxdydt	ADJ
ejpam-4931	443	1	−→	−→	ADJ
ejpam-4931	443	2	∫	∫	PROPN
ejpam-4931	443	3	t	t	PROPN
ejpam-4931	443	4	0	0	NUM
ejpam-4931	443	5	∫	∫	PROPN
ejpam-4931	443	6	ω	ω	NUM
ejpam-4931	443	7	ξ∇x∆	ξ∇x∆	PROPN
ejpam-4931	443	8	5	5	NUM
ejpam-4931	443	9	xξ	xξ	NOUN
ejpam-4931	443	10	·	·	PUNCT
ejpam-4931	443	11	φdxdydt	φdxdydt	ADJ
ejpam-4931	443	12	as	as	ADP
ejpam-4931	443	13	n	n	NUM
ejpam-4931	443	14	−→	−→	NOUN
ejpam-4931	443	15	+	+	NOUN
ejpam-4931	443	16	∞,∫	∞,∫	ADV
ejpam-4931	443	17	t	t	PROPN
ejpam-4931	443	18	0	0	NUM
ejpam-4931	443	19	∫	∫	PROPN
ejpam-4931	443	20	ω	ω	PROPN
ejpam-4931	443	21	ξn∇x	ξn∇x	PROPN
ejpam-4931	443	22	(	(	PUNCT
ejpam-4931	443	23	∆x	∆x	PROPN
ejpam-4931	443	24	√	√	NUM
ejpam-4931	443	25	ξn√	ξn√	PROPN
ejpam-4931	443	26	ξn	ξn	NOUN
ejpam-4931	443	27	)	)	PUNCT
ejpam-4931	443	28	φdxdydt	φdxdydt	ADV
ejpam-4931	444	1	−→	−→	ADJ
ejpam-4931	444	2	∫	∫	PROPN
ejpam-4931	444	3	t	t	PROPN
ejpam-4931	444	4	0	0	NUM
ejpam-4931	444	5	∫	∫	PROPN
ejpam-4931	444	6	ω	ω	NUM
ejpam-4931	444	7	ξ∇x	ξ∇x	PROPN
ejpam-4931	444	8	(	(	PUNCT
ejpam-4931	444	9	∆x	∆x	PROPN
ejpam-4931	444	10	√	√	PROPN
ejpam-4931	444	11	ξ√	ξ√	PROPN
ejpam-4931	444	12	ξ	ξ	X
ejpam-4931	444	13	)	)	PUNCT
ejpam-4931	444	14	φdxdydt	φdxdydt	ADJ
ejpam-4931	444	15	as	as	ADP
ejpam-4931	444	16	n	n	PRON
ejpam-4931	444	17	−→	−→	NOUN
ejpam-4931	444	18	+	+	PROPN
ejpam-4931	444	19	∞.	∞.	PROPN
ejpam-4931	444	20	due	due	ADP
ejpam-4931	444	21	to	to	ADP
ejpam-4931	444	22	the	the	DET
ejpam-4931	444	23	compactness	compactness	NOUN
ejpam-4931	444	24	above	above	ADV
ejpam-4931	444	25	,	,	PUNCT
ejpam-4931	444	26	taking	take	VERB
ejpam-4931	444	27	the	the	DET
ejpam-4931	444	28	limits	limit	NOUN
ejpam-4931	444	29	in	in	ADP
ejpam-4931	444	30	the	the	DET
ejpam-4931	444	31	approximate	approximate	ADJ
ejpam-4931	444	32	system	system	NOUN
ejpam-4931	444	33	of	of	ADP
ejpam-4931	444	34	(	(	PUNCT
ejpam-4931	444	35	19	19	NUM
ejpam-4931	444	36	)	)	PUNCT
ejpam-4931	444	37	and	and	CCONJ
ejpam-4931	444	38	(	(	PUNCT
ejpam-4931	444	39	24	24	NUM
ejpam-4931	444	40	)	)	PUNCT
ejpam-4931	444	41	,	,	PUNCT
ejpam-4931	444	42	then	then	ADV
ejpam-4931	444	43	(	(	PUNCT
ejpam-4931	444	44	ξ	ξ	X
ejpam-4931	444	45	,	,	PUNCT
ejpam-4931	444	46	u	u	NOUN
ejpam-4931	444	47	,	,	PUNCT
ejpam-4931	444	48	v	v	NOUN
ejpam-4931	444	49	)	)	PUNCT
ejpam-4931	444	50	satisfies	satisfie	NOUN
ejpam-4931	444	51	∂tξ	∂tξ	VERB
ejpam-4931	444	52	+	+	CCONJ
ejpam-4931	444	53	divx(ξu	divx(ξu	NOUN
ejpam-4931	444	54	)	)	PUNCT
ejpam-4931	444	55	+	+	SYM
ejpam-4931	444	56	∂y(ξv	∂y(ξv	NOUN
ejpam-4931	444	57	)	)	PUNCT
ejpam-4931	444	58	=	=	SYM
ejpam-4931	445	1	ϵ∆xξ	ϵ∆xξ	NOUN
ejpam-4931	445	2	on	on	ADP
ejpam-4931	445	3	[	[	X
ejpam-4931	445	4	0	0	NUM
ejpam-4931	445	5	,	,	PUNCT
ejpam-4931	445	6	t	t	X
ejpam-4931	445	7	]	]	X
ejpam-4931	445	8	×	×	PROPN
ejpam-4931	445	9	ω	ω	NOUN
ejpam-4931	445	10	and	and	CCONJ
ejpam-4931	445	11	the	the	DET
ejpam-4931	445	12	following	follow	VERB
ejpam-4931	445	13	identity	identity	NOUN
ejpam-4931	445	14	holds:∫	holds:∫	PROPN
ejpam-4931	445	15	ω	ω	PROPN
ejpam-4931	445	16	ξu(t	ξu(t	PUNCT
ejpam-4931	445	17	)	)	PUNCT
ejpam-4931	445	18	φdx	φdx	NOUN
ejpam-4931	445	19	−	−	PROPN
ejpam-4931	445	20	∫	∫	PROPN
ejpam-4931	445	21	ω	ω	NUM
ejpam-4931	446	1	m0φdxdt−	m0φdxdt−	PROPN
ejpam-4931	446	2	∫	∫	PROPN
ejpam-4931	446	3	t	t	PROPN
ejpam-4931	446	4	0	0	NUM
ejpam-4931	447	1	∫	∫	PROPN
ejpam-4931	448	1	ω	ω	PROPN
ejpam-4931	449	1	(	(	PUNCT
ejpam-4931	450	1	ξu⊗	ξu⊗	PROPN
ejpam-4931	450	2	u	u	PROPN
ejpam-4931	450	3	)	)	PUNCT
ejpam-4931	450	4	:	:	PUNCT
ejpam-4931	451	1	∇xφdx	∇xφdx	NOUN
ejpam-4931	451	2	+	+	CCONJ
ejpam-4931	451	3	∫	∫	PROPN
ejpam-4931	451	4	t	t	PROPN
ejpam-4931	451	5	0	0	NUM
ejpam-4931	451	6	∫	∫	PROPN
ejpam-4931	451	7	ω	ω	NUM
ejpam-4931	451	8	ξ∂yu∂yφdxdt	ξ∂yu∂yφdxdt	PROPN
ejpam-4931	451	9	j.	j.	PROPN
ejpam-4931	451	10	ouya	ouya	PROPN
ejpam-4931	451	11	,	,	PUNCT
ejpam-4931	451	12	a.	a.	NOUN
ejpam-4931	451	13	ouédraogo	ouédraogo	PROPN
ejpam-4931	451	14	/	/	SYM
ejpam-4931	451	15	eur	eur	PROPN
ejpam-4931	451	16	.	.	PUNCT
ejpam-4931	452	1	j.	j.	PROPN
ejpam-4931	452	2	pure	pure	PROPN
ejpam-4931	452	3	appl	appl	PROPN
ejpam-4931	452	4	.	.	PROPN
ejpam-4931	452	5	math	math	PROPN
ejpam-4931	452	6	,	,	PUNCT
ejpam-4931	452	7	16	16	NUM
ejpam-4931	452	8	(	(	PUNCT
ejpam-4931	452	9	4	4	NUM
ejpam-4931	452	10	)	)	PUNCT
ejpam-4931	452	11	(	(	PUNCT
ejpam-4931	452	12	2023	2023	NUM
ejpam-4931	452	13	)	)	PUNCT
ejpam-4931	452	14	,	,	PUNCT
ejpam-4931	452	15	2247	2247	NUM
ejpam-4931	452	16	-	-	SYM
ejpam-4931	452	17	2285	2285	NUM
ejpam-4931	452	18	2264	2264	NUM
ejpam-4931	452	19	−	−	PROPN
ejpam-4931	453	1	∫	∫	PROPN
ejpam-4931	453	2	t	t	PROPN
ejpam-4931	453	3	0	0	NUM
ejpam-4931	454	1	∫	∫	PROPN
ejpam-4931	455	1	ω	ω	NUM
ejpam-4931	455	2	ξuv∂yφdxdt+	ξuv∂yφdxdt+	NOUN
ejpam-4931	456	1	∫	∫	PROPN
ejpam-4931	456	2	t	t	PROPN
ejpam-4931	456	3	0	0	NUM
ejpam-4931	457	1	∫	∫	PROPN
ejpam-4931	457	2	ω	ω	PROPN
ejpam-4931	457	3	∇xξ	∇xξ	PROPN
ejpam-4931	457	4	2	2	NUM
ejpam-4931	457	5	·	·	PUNCT
ejpam-4931	457	6	φdxdt+	φdxdt+	SYM
ejpam-4931	457	7	r	r	NOUN
ejpam-4931	457	8	∫	∫	PROPN
ejpam-4931	457	9	t	t	PROPN
ejpam-4931	457	10	0	0	NUM
ejpam-4931	457	11	∫	∫	PROPN
ejpam-4931	457	12	ω	ω	NUM
ejpam-4931	457	13	ξ|u|uφdxdt	ξ|u|uφdxdt	PROPN
ejpam-4931	457	14	+	+	CCONJ
ejpam-4931	457	15	r1	r1	PROPN
ejpam-4931	457	16	∫	∫	PROPN
ejpam-4931	457	17	t	t	PROPN
ejpam-4931	457	18	0	0	NUM
ejpam-4931	457	19	∫	∫	PROPN
ejpam-4931	457	20	ω	ω	PROPN
ejpam-4931	457	21	uφdxdt+	uφdxdt+	X
ejpam-4931	458	1	α	α	DET
ejpam-4931	458	2	∫	∫	PROPN
ejpam-4931	458	3	t	t	PROPN
ejpam-4931	458	4	0	0	NUM
ejpam-4931	458	5	∫	∫	PROPN
ejpam-4931	458	6	ω	ω	NUM
ejpam-4931	458	7	∆xu	∆xu	X
ejpam-4931	458	8	·	·	SYM
ejpam-4931	458	9	∆xφdxdt	∆xφdxdt	NOUN
ejpam-4931	458	10	=	=	SYM
ejpam-4931	458	11	−	−	PROPN
ejpam-4931	458	12	∫	∫	PROPN
ejpam-4931	458	13	t	t	PROPN
ejpam-4931	458	14	0	0	NUM
ejpam-4931	458	15	∫	∫	PROPN
ejpam-4931	458	16	ω	ω	NUM
ejpam-4931	458	17	2ξdx(u	2ξdx(u	NUM
ejpam-4931	458	18	)	)	PUNCT
ejpam-4931	458	19	:	:	PUNCT
ejpam-4931	459	1	∇xφdxdt+	∇xφdxdt+	X
ejpam-4931	460	1	ϵ	ϵ	X
ejpam-4931	460	2	∫	∫	PROPN
ejpam-4931	460	3	t	t	PROPN
ejpam-4931	460	4	0	0	NUM
ejpam-4931	461	1	∫	∫	PROPN
ejpam-4931	461	2	ω	ω	PROPN
ejpam-4931	461	3	(	(	PUNCT
ejpam-4931	461	4	∇xξ	∇xξ	PROPN
ejpam-4931	461	5	·	·	PUNCT
ejpam-4931	461	6	∇xu	∇xu	ADJ
ejpam-4931	461	7	)	)	PUNCT
ejpam-4931	461	8	φdx	φdx	NOUN
ejpam-4931	461	9	−	−	PROPN
ejpam-4931	461	10	r2	r2	PROPN
ejpam-4931	461	11	∫	∫	PROPN
ejpam-4931	462	1	t	t	PROPN
ejpam-4931	462	2	0	0	NUM
ejpam-4931	462	3	∫	∫	PROPN
ejpam-4931	462	4	ω	ω	PROPN
ejpam-4931	462	5	ξ−βdivxφdxdt	ξ−βdivxφdxdt	PROPN
ejpam-4931	462	6	−	−	PROPN
ejpam-4931	462	7	2k1	2k1	NUM
ejpam-4931	463	1	∫	∫	PROPN
ejpam-4931	463	2	t	t	PROPN
ejpam-4931	463	3	0	0	NUM
ejpam-4931	463	4	∫	∫	PROPN
ejpam-4931	463	5	ω	ω	PROPN
ejpam-4931	463	6	φ∆x	φ∆x	VERB
ejpam-4931	463	7	√	√	PROPN
ejpam-4931	463	8	ξ∇x	ξ∇x	PROPN
ejpam-4931	463	9	√	√	NUM
ejpam-4931	463	10	ξdxdt−	ξdxdt−	PROPN
ejpam-4931	463	11	k1	k1	PROPN
ejpam-4931	463	12	∫	∫	PROPN
ejpam-4931	463	13	t	t	PROPN
ejpam-4931	463	14	0	0	NUM
ejpam-4931	464	1	∫	∫	PROPN
ejpam-4931	465	1	ω	ω	PROPN
ejpam-4931	465	2	divxφ	divxφ	VERB
ejpam-4931	465	3	(	(	PUNCT
ejpam-4931	465	4	∆x	∆x	PROPN
ejpam-4931	465	5	√	√	PROPN
ejpam-4931	465	6	ξ	ξ	X
ejpam-4931	465	7	)	)	PUNCT
ejpam-4931	465	8	√	√	PROPN
ejpam-4931	465	9	ξdxdt+	ξdxdt+	ADP
ejpam-4931	465	10	δ	δ	PROPN
ejpam-4931	465	11	∫	∫	PROPN
ejpam-4931	465	12	t	t	PROPN
ejpam-4931	465	13	0	0	NUM
ejpam-4931	465	14	∫	∫	PROPN
ejpam-4931	465	15	ω	ω	NUM
ejpam-4931	465	16	φξ∇x∆	φξ∇x∆	PROPN
ejpam-4931	465	17	5	5	NUM
ejpam-4931	465	18	xξdxdt	xξdxdt	NOUN
ejpam-4931	465	19	,	,	PUNCT
ejpam-4931	465	20	(	(	PUNCT
ejpam-4931	465	21	58	58	NUM
ejpam-4931	465	22	)	)	PUNCT
ejpam-4931	465	23	for	for	ADP
ejpam-4931	465	24	any	any	DET
ejpam-4931	465	25	smooth	smooth	ADJ
ejpam-4931	465	26	function	function	NOUN
ejpam-4931	465	27	φ	φ	PROPN
ejpam-4931	465	28	∈	∈	PROPN
ejpam-4931	465	29	c∞	c∞	PROPN
ejpam-4931	466	1	c	c	NOUN
ejpam-4931	467	1	(	(	PUNCT
ejpam-4931	467	2	[	[	X
ejpam-4931	467	3	0	0	NUM
ejpam-4931	467	4	,	,	PUNCT
ejpam-4931	467	5	t	t	X
ejpam-4931	467	6	]	]	PUNCT
ejpam-4931	467	7	×	×	PROPN
ejpam-4931	467	8	ω	ω	PROPN
ejpam-4931	467	9	)	)	PUNCT
ejpam-4931	467	10	,	,	PUNCT
ejpam-4931	467	11	where	where	SCONJ
ejpam-4931	467	12	m0	m0	NOUN
ejpam-4931	467	13	=	=	SYM
ejpam-4931	467	14	ξ(0	ξ(0	PROPN
ejpam-4931	467	15	,	,	PUNCT
ejpam-4931	467	16	x	x	NOUN
ejpam-4931	467	17	,	,	PUNCT
ejpam-4931	467	18	y)u(0	y)u(0	PROPN
ejpam-4931	467	19	,	,	PUNCT
ejpam-4931	467	20	x	x	NOUN
ejpam-4931	467	21	,	,	PUNCT
ejpam-4931	467	22	y	y	PROPN
ejpam-4931	467	23	)	)	PUNCT
ejpam-4931	467	24	and	and	CCONJ
ejpam-4931	467	25	dx	dx	PROPN
ejpam-4931	467	26	=	=	PROPN
ejpam-4931	467	27	dxdy	dxdy	PROPN
ejpam-4931	467	28	.	.	PUNCT
ejpam-4931	468	1	using	use	VERB
ejpam-4931	468	2	the	the	DET
ejpam-4931	468	3	lower	low	ADJ
ejpam-4931	468	4	semi	semi	NOUN
ejpam-4931	468	5	-	-	NOUN
ejpam-4931	468	6	continuity	continuity	NOUN
ejpam-4931	468	7	of	of	ADP
ejpam-4931	468	8	convex	convex	NOUN
ejpam-4931	468	9	functions	function	NOUN
ejpam-4931	468	10	,	,	PUNCT
ejpam-4931	468	11	we	we	PRON
ejpam-4931	468	12	take	take	VERB
ejpam-4931	468	13	the	the	DET
ejpam-4931	468	14	limits	limit	NOUN
ejpam-4931	468	15	in	in	ADP
ejpam-4931	468	16	the	the	DET
ejpam-4931	468	17	energy	energy	NOUN
ejpam-4931	468	18	estimate	estimate	NOUN
ejpam-4931	468	19	(	(	PUNCT
ejpam-4931	468	20	47	47	NUM
ejpam-4931	468	21	)	)	PUNCT
ejpam-4931	468	22	to	to	PART
ejpam-4931	468	23	obtain	obtain	VERB
ejpam-4931	468	24	the	the	DET
ejpam-4931	468	25	following	follow	VERB
ejpam-4931	468	26	energy	energy	NOUN
ejpam-4931	468	27	inequality	inequality	NOUN
ejpam-4931	468	28	:	:	PUNCT
ejpam-4931	468	29	sup	sup	NOUN
ejpam-4931	468	30	t∈[0,t	t∈[0,t	NOUN
ejpam-4931	468	31	]	]	PUNCT
ejpam-4931	468	32	e(ξ	e(ξ	PROPN
ejpam-4931	468	33	,	,	PUNCT
ejpam-4931	468	34	u	u	NOUN
ejpam-4931	468	35	)	)	PUNCT
ejpam-4931	469	1	+	+	NUM
ejpam-4931	469	2	2ϵ	2ϵ	NUM
ejpam-4931	469	3	∫	∫	PROPN
ejpam-4931	469	4	t	t	NOUN
ejpam-4931	469	5	0	0	NUM
ejpam-4931	469	6	∫	∫	PROPN
ejpam-4931	469	7	ω	ω	PROPN
ejpam-4931	469	8	|∇xξ|2dxdt+	|∇xξ|2dxdt+	PROPN
ejpam-4931	469	9	r1	r1	PROPN
ejpam-4931	469	10	∫	∫	PROPN
ejpam-4931	470	1	t	t	PROPN
ejpam-4931	470	2	0	0	NUM
ejpam-4931	471	1	∫	∫	PROPN
ejpam-4931	472	1	ω	ω	NUM
ejpam-4931	472	2	u2dxdt+	u2dxdt+	PROPN
ejpam-4931	472	3	r	r	NOUN
ejpam-4931	472	4	∫	∫	PROPN
ejpam-4931	472	5	t	t	PROPN
ejpam-4931	472	6	0	0	NUM
ejpam-4931	472	7	∫	∫	PROPN
ejpam-4931	472	8	ω	ω	NUM
ejpam-4931	472	9	ξ|u|3dxdt	ξ|u|3dxdt	PROPN
ejpam-4931	472	10	+	+	CCONJ
ejpam-4931	472	11	∫	∫	PROPN
ejpam-4931	472	12	t	t	PROPN
ejpam-4931	472	13	0	0	NUM
ejpam-4931	472	14	∫	∫	PROPN
ejpam-4931	473	1	ω	ω	NUM
ejpam-4931	473	2	2ξ|dx(u)|2dxdt+	2ξ|dx(u)|2dxdt+	NUM
ejpam-4931	473	3	α	α	NOUN
ejpam-4931	473	4	∫	∫	PROPN
ejpam-4931	473	5	t	t	PROPN
ejpam-4931	473	6	0	0	NUM
ejpam-4931	473	7	∫	∫	PROPN
ejpam-4931	473	8	ω	ω	PROPN
ejpam-4931	473	9	|∆xu|2dxdt+	|∆xu|2dxdt+	PROPN
ejpam-4931	473	10	4ϵr2	4ϵr2	PUNCT
ejpam-4931	474	1	β	β	PROPN
ejpam-4931	474	2	∫	∫	PROPN
ejpam-4931	474	3	t	t	PROPN
ejpam-4931	474	4	0	0	NUM
ejpam-4931	474	5	∫	∫	PROPN
ejpam-4931	474	6	ω	ω	PROPN
ejpam-4931	474	7	|∇xξ	|∇xξ	PROPN
ejpam-4931	474	8	−β	−β	ADJ
ejpam-4931	474	9	2	2	NUM
ejpam-4931	474	10	|2dxdt	|2dxdt	NOUN
ejpam-4931	474	11	+	+	CCONJ
ejpam-4931	474	12	ϵk1	ϵk1	PROPN
ejpam-4931	474	13	2	2	NUM
ejpam-4931	474	14	∫	∫	NOUN
ejpam-4931	474	15	t	t	PROPN
ejpam-4931	474	16	0	0	NUM
ejpam-4931	474	17	∫	∫	PROPN
ejpam-4931	474	18	ω	ω	NUM
ejpam-4931	474	19	ξ|∇2	ξ|∇2	PROPN
ejpam-4931	474	20	x	x	SYM
ejpam-4931	474	21	ln	ln	NOUN
ejpam-4931	475	1	ξ|2dxdt+	ξ|2dxdt+	NUM
ejpam-4931	475	2	δϵ	δϵ	ADP
ejpam-4931	475	3	∫	∫	PROPN
ejpam-4931	475	4	t	t	PROPN
ejpam-4931	475	5	0	0	NUM
ejpam-4931	475	6	∫	∫	PROPN
ejpam-4931	475	7	ω	ω	PROPN
ejpam-4931	475	8	|∆3	|∆3	PROPN
ejpam-4931	475	9	xξ|2dxdt+	xξ|2dxdt+	PROPN
ejpam-4931	476	1	∫	∫	PROPN
ejpam-4931	476	2	t	t	PROPN
ejpam-4931	476	3	0	0	NUM
ejpam-4931	476	4	∫	∫	PROPN
ejpam-4931	476	5	ω	ω	NUM
ejpam-4931	476	6	ξ|∂yu|2dxdt	ξ|∂yu|2dxdt	PROPN
ejpam-4931	476	7	≤	≤	PROPN
ejpam-4931	476	8	e(ξ0	e(ξ0	PROPN
ejpam-4931	476	9	,	,	PUNCT
ejpam-4931	476	10	u0	u0	ADJ
ejpam-4931	476	11	)	)	PUNCT
ejpam-4931	476	12	,	,	PUNCT
ejpam-4931	476	13	(	(	PUNCT
ejpam-4931	476	14	59	59	NUM
ejpam-4931	476	15	)	)	PUNCT
ejpam-4931	476	16	with	with	ADP
ejpam-4931	476	17	e(ξ	e(ξ	PROPN
ejpam-4931	476	18	,	,	PUNCT
ejpam-4931	476	19	u	u	NOUN
ejpam-4931	476	20	)	)	PUNCT
ejpam-4931	476	21	=	=	SYM
ejpam-4931	477	1	∫	∫	PROPN
ejpam-4931	477	2	ω	ω	PROPN
ejpam-4931	477	3	(	(	PUNCT
ejpam-4931	477	4	1	1	NUM
ejpam-4931	477	5	2	2	NUM
ejpam-4931	477	6	ξu2	ξu2	NOUN
ejpam-4931	477	7	+	+	CCONJ
ejpam-4931	477	8	ξ2	ξ2	NOUN
ejpam-4931	477	9	+	+	CCONJ
ejpam-4931	477	10	r2	r2	PROPN
ejpam-4931	477	11	β	β	X
ejpam-4931	477	12	+	+	CCONJ
ejpam-4931	477	13	1	1	NUM
ejpam-4931	477	14	ξ−β	ξ−β	VERB
ejpam-4931	477	15	+	+	CCONJ
ejpam-4931	477	16	k|∇x	k|∇x	NOUN
ejpam-4931	477	17	√	√	PROPN
ejpam-4931	478	1	ξ|2	ξ|2	PROPN
ejpam-4931	478	2	+	+	CCONJ
ejpam-4931	478	3	δ	δ	PROPN
ejpam-4931	478	4	2	2	NUM
ejpam-4931	478	5	|∇x∆	|∇x∆	NOUN
ejpam-4931	478	6	2	2	NUM
ejpam-4931	478	7	xξ|2	xξ|2	PROPN
ejpam-4931	478	8	)	)	PUNCT
ejpam-4931	478	9	dx	dx	PROPN
ejpam-4931	478	10	.	.	PUNCT
ejpam-4931	479	1	consequently	consequently	ADV
ejpam-4931	479	2	,	,	PUNCT
ejpam-4931	479	3	we	we	PRON
ejpam-4931	479	4	obtain	obtain	VERB
ejpam-4931	479	5	the	the	DET
ejpam-4931	479	6	existence	existence	NOUN
ejpam-4931	479	7	of	of	ADP
ejpam-4931	479	8	weak	weak	ADJ
ejpam-4931	479	9	solutions	solution	NOUN
ejpam-4931	479	10	of	of	ADP
ejpam-4931	479	11	the	the	DET
ejpam-4931	479	12	approximated	approximate	VERB
ejpam-4931	479	13	system	system	NOUN
ejpam-4931	479	14	(	(	PUNCT
ejpam-4931	479	15	17	17	NUM
ejpam-4931	479	16	)	)	PUNCT
ejpam-4931	479	17	,	,	PUNCT
ejpam-4931	479	18	through	through	ADP
ejpam-4931	479	19	the	the	DET
ejpam-4931	479	20	following	following	NOUN
ejpam-4931	479	21	.	.	PUNCT
ejpam-4931	480	1	proposition	proposition	NOUN
ejpam-4931	480	2	3.2	3.2	NUM
ejpam-4931	480	3	.	.	PUNCT
ejpam-4931	481	1	for	for	ADP
ejpam-4931	481	2	any	any	DET
ejpam-4931	481	3	t	t	PROPN
ejpam-4931	481	4	>	>	X
ejpam-4931	481	5	0	0	PROPN
ejpam-4931	481	6	,	,	PUNCT
ejpam-4931	481	7	the	the	DET
ejpam-4931	481	8	following	follow	VERB
ejpam-4931	481	9	system	system	PROPN
ejpam-4931	481	10	∂tξ	∂tξ	NOUN
ejpam-4931	481	11	+	+	CCONJ
ejpam-4931	481	12	divx(ξu	divx(ξu	NOUN
ejpam-4931	481	13	)	)	PUNCT
ejpam-4931	482	1	+	+	CCONJ
ejpam-4931	482	2	∂y	∂y	SYM
ejpam-4931	482	3	(	(	PUNCT
ejpam-4931	482	4	ξv	ξv	NOUN
ejpam-4931	482	5	)	)	PUNCT
ejpam-4931	482	6	=	=	SYM
ejpam-4931	482	7	ϵ∆xξ	ϵ∆xξ	NOUN
ejpam-4931	482	8	,	,	PUNCT
ejpam-4931	482	9	∂t(ξu	∂t(ξu	X
ejpam-4931	482	10	)	)	PUNCT
ejpam-4931	482	11	+	+	CCONJ
ejpam-4931	482	12	divx(ξu⊗	divx(ξu⊗	NOUN
ejpam-4931	482	13	u	u	NOUN
ejpam-4931	482	14	)	)	PUNCT
ejpam-4931	482	15	+	+	CCONJ
ejpam-4931	482	16	∂y(ξuv	∂y(ξuv	X
ejpam-4931	482	17	)	)	PUNCT
ejpam-4931	483	1	+	+	X
ejpam-4931	483	2	∇xξ	∇xξ	PROPN
ejpam-4931	483	3	2	2	NUM
ejpam-4931	483	4	+	+	CCONJ
ejpam-4931	483	5	rξ|u|u	rξ|u|u	NOUN
ejpam-4931	483	6	+	+	NOUN
ejpam-4931	483	7	r1u+	r1u+	NOUN
ejpam-4931	483	8	α∆2	α∆2	INTJ
ejpam-4931	483	9	xu	xu	NOUN
ejpam-4931	483	10	=	=	SYM
ejpam-4931	483	11	2divx	2divx	NUM
ejpam-4931	483	12	(	(	PUNCT
ejpam-4931	483	13	ξd(u	ξd(u	NUM
ejpam-4931	483	14	)	)	PUNCT
ejpam-4931	483	15	)	)	PUNCT
ejpam-4931	484	1	+	+	CCONJ
ejpam-4931	484	2	∂y	∂y	SYM
ejpam-4931	484	3	(	(	PUNCT
ejpam-4931	484	4	ξ∂yu	ξ∂yu	PROPN
ejpam-4931	484	5	)	)	PUNCT
ejpam-4931	484	6	+	+	CCONJ
ejpam-4931	484	7	ϵ∇xξ	ϵ∇xξ	PROPN
ejpam-4931	484	8	·	·	PUNCT
ejpam-4931	484	9	∇xu	∇xu	PROPN
ejpam-4931	485	1	+	+	ADJ
ejpam-4931	485	2	r2∇xξ	r2∇xξ	NOUN
ejpam-4931	485	3	−β	−β	NOUN
ejpam-4931	485	4	+	+	CCONJ
ejpam-4931	485	5	k1ξ∇x	k1ξ∇x	PROPN
ejpam-4931	485	6	(	(	PUNCT
ejpam-4931	485	7	∆x	∆x	PROPN
ejpam-4931	485	8	√	√	PROPN
ejpam-4931	485	9	ξ√	ξ√	PROPN
ejpam-4931	485	10	ξ	ξ	PROPN
ejpam-4931	485	11	)	)	PUNCT
ejpam-4931	486	1	+	+	CCONJ
ejpam-4931	486	2	δξ∇x∆	δξ∇x∆	PROPN
ejpam-4931	486	3	5	5	NUM
ejpam-4931	486	4	xξ	xξ	NOUN
ejpam-4931	486	5	,	,	PUNCT
ejpam-4931	486	6	∂yξ	∂yξ	PROPN
ejpam-4931	486	7	=	=	SYM
ejpam-4931	486	8	0	0	NUM
ejpam-4931	486	9	,	,	PUNCT
ejpam-4931	486	10	(	(	PUNCT
ejpam-4931	486	11	60	60	NUM
ejpam-4931	486	12	)	)	PUNCT
ejpam-4931	486	13	admits	admit	VERB
ejpam-4931	486	14	a	a	DET
ejpam-4931	486	15	weak	weak	ADJ
ejpam-4931	486	16	solution	solution	NOUN
ejpam-4931	486	17	(	(	PUNCT
ejpam-4931	486	18	ξ	ξ	X
ejpam-4931	486	19	,	,	PUNCT
ejpam-4931	486	20	u	u	NOUN
ejpam-4931	486	21	,	,	PUNCT
ejpam-4931	486	22	v	v	NOUN
ejpam-4931	486	23	)	)	PUNCT
ejpam-4931	486	24	with	with	ADP
ejpam-4931	486	25	continuous	continuous	ADJ
ejpam-4931	486	26	initial	initial	ADJ
ejpam-4931	486	27	data	datum	NOUN
ejpam-4931	486	28	.	.	PUNCT
ejpam-4931	487	1	in	in	ADP
ejpam-4931	487	2	particular	particular	ADJ
ejpam-4931	487	3	,	,	PUNCT
ejpam-4931	487	4	the	the	DET
ejpam-4931	487	5	weak	weak	ADJ
ejpam-4931	487	6	solution	solution	NOUN
ejpam-4931	487	7	satisfies	satisfy	VERB
ejpam-4931	487	8	the	the	DET
ejpam-4931	487	9	energy	energy	NOUN
ejpam-4931	487	10	inequality	inequality	NOUN
ejpam-4931	487	11	(	(	PUNCT
ejpam-4931	487	12	59	59	NUM
ejpam-4931	487	13	)	)	PUNCT
ejpam-4931	487	14	.	.	PUNCT
ejpam-4931	488	1	j.	j.	PROPN
ejpam-4931	488	2	ouya	ouya	PROPN
ejpam-4931	488	3	,	,	PUNCT
ejpam-4931	488	4	a.	a.	NOUN
ejpam-4931	488	5	ouédraogo	ouédraogo	PROPN
ejpam-4931	488	6	/	/	SYM
ejpam-4931	488	7	eur	eur	PROPN
ejpam-4931	488	8	.	.	PUNCT
ejpam-4931	489	1	j.	j.	PROPN
ejpam-4931	489	2	pure	pure	PROPN
ejpam-4931	489	3	appl	appl	PROPN
ejpam-4931	489	4	.	.	PROPN
ejpam-4931	489	5	math	math	PROPN
ejpam-4931	489	6	,	,	PUNCT
ejpam-4931	489	7	16	16	NUM
ejpam-4931	489	8	(	(	PUNCT
ejpam-4931	489	9	4	4	NUM
ejpam-4931	489	10	)	)	PUNCT
ejpam-4931	489	11	(	(	PUNCT
ejpam-4931	489	12	2023	2023	NUM
ejpam-4931	489	13	)	)	PUNCT
ejpam-4931	489	14	,	,	PUNCT
ejpam-4931	489	15	2247	2247	NUM
ejpam-4931	489	16	-	-	SYM
ejpam-4931	489	17	2285	2285	NUM
ejpam-4931	489	18	2265	2265	NUM
ejpam-4931	489	19	4	4	NUM
ejpam-4931	489	20	.	.	PUNCT
ejpam-4931	490	1	bresch	bresch	NOUN
ejpam-4931	490	2	-	-	PUNCT
ejpam-4931	490	3	desjardins	desjardin	NOUN
ejpam-4931	490	4	entropy	entropy	NOUN
ejpam-4931	490	5	in	in	ADP
ejpam-4931	490	6	this	this	DET
ejpam-4931	490	7	section	section	NOUN
ejpam-4931	490	8	,	,	PUNCT
ejpam-4931	490	9	we	we	PRON
ejpam-4931	490	10	deal	deal	VERB
ejpam-4931	490	11	with	with	ADP
ejpam-4931	490	12	the	the	DET
ejpam-4931	490	13	bresch	bresch	NOUN
ejpam-4931	490	14	-	-	PUNCT
ejpam-4931	490	15	desjardins	desjardins	PROPN
ejpam-4931	490	16	(	(	PUNCT
ejpam-4931	490	17	b	b	X
ejpam-4931	490	18	-	-	PUNCT
ejpam-4931	490	19	d	d	NOUN
ejpam-4931	490	20	)	)	PUNCT
ejpam-4931	490	21	estimate	estimate	NOUN
ejpam-4931	490	22	for	for	ADP
ejpam-4931	490	23	the	the	DET
ejpam-4931	490	24	approximate	approximate	ADJ
ejpam-4931	490	25	system	system	NOUN
ejpam-4931	490	26	of	of	ADP
ejpam-4931	490	27	the	the	DET
ejpam-4931	490	28	proposition	proposition	NOUN
ejpam-4931	490	29	3.2	3.2	NUM
ejpam-4931	490	30	,	,	PUNCT
ejpam-4931	490	31	which	which	PRON
ejpam-4931	490	32	was	be	AUX
ejpam-4931	490	33	first	first	ADV
ejpam-4931	490	34	introduced	introduce	VERB
ejpam-4931	490	35	by	by	ADP
ejpam-4931	490	36	d.	d.	PROPN
ejpam-4931	490	37	bresch	bresch	PROPN
ejpam-4931	490	38	and	and	CCONJ
ejpam-4931	490	39	b.	b.	PROPN
ejpam-4931	490	40	desjardins	desjardins	PROPN
ejpam-4931	490	41	in	in	ADP
ejpam-4931	490	42	[	[	X
ejpam-4931	490	43	2	2	NUM
ejpam-4931	490	44	]	]	PUNCT
ejpam-4931	490	45	.	.	PUNCT
ejpam-4931	491	1	by	by	ADP
ejpam-4931	491	2	(	(	PUNCT
ejpam-4931	491	3	48	48	NUM
ejpam-4931	491	4	)	)	PUNCT
ejpam-4931	491	5	and	and	CCONJ
ejpam-4931	491	6	(	(	PUNCT
ejpam-4931	491	7	53	53	NUM
ejpam-4931	491	8	)	)	PUNCT
ejpam-4931	491	9	,	,	PUNCT
ejpam-4931	491	10	we	we	PRON
ejpam-4931	491	11	have	have	NUM
ejpam-4931	491	12	ξ(t	ξ(t	NOUN
ejpam-4931	491	13	,	,	PUNCT
ejpam-4931	491	14	x	x	SYM
ejpam-4931	491	15	)	)	PUNCT
ejpam-4931	491	16	≥	≥	PROPN
ejpam-4931	491	17	c(δ	c(δ	PROPN
ejpam-4931	491	18	,	,	PUNCT
ejpam-4931	491	19	r2	r2	PROPN
ejpam-4931	491	20	)	)	PUNCT
ejpam-4931	491	21	>	>	PUNCT
ejpam-4931	491	22	0	0	PUNCT
ejpam-4931	491	23	ξ	ξ	X
ejpam-4931	491	24	∈	∈	PROPN
ejpam-4931	491	25	l∞	l∞	NOUN
ejpam-4931	491	26	(	(	PUNCT
ejpam-4931	491	27	[	[	X
ejpam-4931	491	28	0	0	NUM
ejpam-4931	491	29	,	,	PUNCT
ejpam-4931	491	30	t	t	X
ejpam-4931	491	31	]	]	PUNCT
ejpam-4931	491	32	;	;	PUNCT
ejpam-4931	491	33	h5(ω	h5(ω	NUM
ejpam-4931	491	34	)	)	PUNCT
ejpam-4931	491	35	)	)	PUNCT
ejpam-4931	491	36	∩	∩	ADJ
ejpam-4931	491	37	l2	l2	NOUN
ejpam-4931	491	38	(	(	PUNCT
ejpam-4931	491	39	[	[	X
ejpam-4931	491	40	0	0	NUM
ejpam-4931	491	41	,	,	PUNCT
ejpam-4931	491	42	t	t	X
ejpam-4931	491	43	]	]	PUNCT
ejpam-4931	491	44	;	;	PUNCT
ejpam-4931	491	45	h6(ω	h6(ω	X
ejpam-4931	491	46	)	)	PUNCT
ejpam-4931	491	47	)	)	PUNCT
ejpam-4931	491	48	.	.	PUNCT
ejpam-4931	492	1	(	(	PUNCT
ejpam-4931	492	2	61	61	NUM
ejpam-4931	492	3	)	)	PUNCT
ejpam-4931	492	4	as	as	SCONJ
ejpam-4931	492	5	many	many	ADJ
ejpam-4931	492	6	authors	author	NOUN
ejpam-4931	492	7	have	have	AUX
ejpam-4931	492	8	pointed	point	VERB
ejpam-4931	492	9	out	out	ADP
ejpam-4931	492	10	,	,	PUNCT
ejpam-4931	492	11	a	a	DET
ejpam-4931	492	12	main	main	ADJ
ejpam-4931	492	13	difficulty	difficulty	NOUN
ejpam-4931	492	14	in	in	ADP
ejpam-4931	492	15	the	the	DET
ejpam-4931	492	16	proof	proof	NOUN
ejpam-4931	492	17	in	in	ADP
ejpam-4931	492	18	this	this	DET
ejpam-4931	492	19	type	type	NOUN
ejpam-4931	492	20	of	of	ADP
ejpam-4931	492	21	model	model	NOUN
ejpam-4931	492	22	is	be	AUX
ejpam-4931	492	23	to	to	PART
ejpam-4931	492	24	pass	pass	VERB
ejpam-4931	492	25	to	to	ADP
ejpam-4931	492	26	the	the	DET
ejpam-4931	492	27	limit	limit	NOUN
ejpam-4931	492	28	in	in	ADP
ejpam-4931	492	29	the	the	DET
ejpam-4931	492	30	nonlinear	nonlinear	ADJ
ejpam-4931	492	31	term	term	NOUN
ejpam-4931	492	32	ξu	ξu	ADP
ejpam-4931	492	33	⊗	⊗	PROPN
ejpam-4931	492	34	u	u	NOUN
ejpam-4931	492	35	which	which	PRON
ejpam-4931	492	36	requires	require	VERB
ejpam-4931	492	37	a	a	DET
ejpam-4931	492	38	strong	strong	ADJ
ejpam-4931	492	39	convergence	convergence	NOUN
ejpam-4931	492	40	of	of	ADP
ejpam-4931	492	41	√	√	NUM
ejpam-4931	492	42	ξu	ξu	NOUN
ejpam-4931	492	43	.	.	PUNCT
ejpam-4931	493	1	it	it	PRON
ejpam-4931	493	2	seems	seem	VERB
ejpam-4931	493	3	necessary	necessary	ADJ
ejpam-4931	493	4	to	to	PART
ejpam-4931	493	5	obtain	obtain	VERB
ejpam-4931	493	6	additional	additional	ADJ
ejpam-4931	493	7	information	information	NOUN
ejpam-4931	493	8	on	on	ADP
ejpam-4931	493	9	the	the	DET
ejpam-4931	493	10	density	density	NOUN
ejpam-4931	493	11	ξ	ξ	PROPN
ejpam-4931	493	12	.	.	PUNCT
ejpam-4931	494	1	in	in	ADP
ejpam-4931	494	2	this	this	DET
ejpam-4931	494	3	perspective	perspective	NOUN
ejpam-4931	494	4	,	,	PUNCT
ejpam-4931	494	5	we	we	PRON
ejpam-4931	494	6	use	use	VERB
ejpam-4931	494	7	a	a	DET
ejpam-4931	494	8	mathematical	mathematical	ADJ
ejpam-4931	494	9	entropy	entropy	NOUN
ejpam-4931	494	10	,	,	PUNCT
ejpam-4931	494	11	called	call	VERB
ejpam-4931	494	12	b	b	X
ejpam-4931	494	13	-	-	PUNCT
ejpam-4931	494	14	d	d	NOUN
ejpam-4931	494	15	entropy	entropy	NOUN
ejpam-4931	494	16	.	.	PUNCT
ejpam-4931	495	1	thanks	thank	NOUN
ejpam-4931	495	2	to	to	ADP
ejpam-4931	495	3	(	(	PUNCT
ejpam-4931	495	4	61	61	NUM
ejpam-4931	495	5	)	)	PUNCT
ejpam-4931	495	6	,	,	PUNCT
ejpam-4931	495	7	we	we	PRON
ejpam-4931	495	8	can	can	AUX
ejpam-4931	495	9	take	take	VERB
ejpam-4931	495	10	∇ξ	∇ξ	PROPN
ejpam-4931	495	11	ξ	ξ	X
ejpam-4931	495	12	=	=	SYM
ejpam-4931	495	13	∇	∇	X
ejpam-4931	495	14	ln	ln	X
ejpam-4931	495	15	ξ	ξ	PROPN
ejpam-4931	495	16	as	as	ADP
ejpam-4931	495	17	a	a	DET
ejpam-4931	495	18	test	test	NOUN
ejpam-4931	495	19	function	function	NOUN
ejpam-4931	495	20	to	to	PART
ejpam-4931	495	21	derive	derive	VERB
ejpam-4931	495	22	the	the	DET
ejpam-4931	495	23	b	b	PROPN
ejpam-4931	495	24	-	-	PUNCT
ejpam-4931	495	25	d	d	ADJ
ejpam-4931	495	26	entropy	entropy	NOUN
ejpam-4931	495	27	from	from	ADP
ejpam-4931	495	28	the	the	DET
ejpam-4931	495	29	momentum	momentum	NOUN
ejpam-4931	495	30	equation	equation	NOUN
ejpam-4931	495	31	.	.	PUNCT
ejpam-4931	496	1	to	to	ADP
ejpam-4931	496	2	this	this	DET
ejpam-4931	496	3	end	end	NOUN
ejpam-4931	496	4	,	,	PUNCT
ejpam-4931	496	5	we	we	PRON
ejpam-4931	496	6	first	first	ADV
ejpam-4931	496	7	take	take	VERB
ejpam-4931	496	8	the	the	DET
ejpam-4931	496	9	gradient	gradient	NOUN
ejpam-4931	496	10	of	of	ADP
ejpam-4931	496	11	the	the	DET
ejpam-4931	496	12	mass	mass	ADJ
ejpam-4931	496	13	equation	equation	NOUN
ejpam-4931	496	14	with	with	ADP
ejpam-4931	496	15	respect	respect	NOUN
ejpam-4931	496	16	to	to	ADP
ejpam-4931	496	17	x	x	PRON
ejpam-4931	496	18	,	,	PUNCT
ejpam-4931	496	19	we	we	PRON
ejpam-4931	496	20	obtain	obtain	VERB
ejpam-4931	496	21	∂t∇xξ	∂t∇xξ	NOUN
ejpam-4931	496	22	+	+	ADJ
ejpam-4931	496	23	∇x	∇x	NOUN
ejpam-4931	496	24	(	(	PUNCT
ejpam-4931	496	25	ξdivx(u	ξdivx(u	PROPN
ejpam-4931	496	26	)	)	PUNCT
ejpam-4931	496	27	)	)	PUNCT
ejpam-4931	497	1	+	+	VERB
ejpam-4931	497	2	∇x(u	∇x(u	X
ejpam-4931	497	3	·	·	PUNCT
ejpam-4931	497	4	∇xξ	∇xξ	X
ejpam-4931	497	5	)	)	PUNCT
ejpam-4931	497	6	+	+	CCONJ
ejpam-4931	497	7	∂y∇x(ξv	∂y∇x(ξv	NOUN
ejpam-4931	497	8	)	)	PUNCT
ejpam-4931	497	9	=	=	SYM
ejpam-4931	498	1	ϵ∇x∆xξ	ϵ∇x∆xξ	X
ejpam-4931	498	2	.	.	PUNCT
ejpam-4931	499	1	(	(	PUNCT
ejpam-4931	499	2	62	62	NUM
ejpam-4931	499	3	)	)	PUNCT
ejpam-4931	499	4	multiplying	multiplying	NOUN
ejpam-4931	499	5	(	(	PUNCT
ejpam-4931	499	6	62	62	NUM
ejpam-4931	499	7	)	)	PUNCT
ejpam-4931	499	8	by	by	ADP
ejpam-4931	499	9	2	2	NUM
ejpam-4931	499	10	and	and	CCONJ
ejpam-4931	499	11	writing	write	VERB
ejpam-4931	499	12	the	the	DET
ejpam-4931	499	13	∇xξ	∇xξ	PROPN
ejpam-4931	499	14	terms	term	NOUN
ejpam-4931	499	15	as	as	ADP
ejpam-4931	499	16	ξ∇x	ξ∇x	PROPN
ejpam-4931	499	17	ln	ln	PROPN
ejpam-4931	499	18	ξ	ξ	PROPN
ejpam-4931	499	19	,	,	PUNCT
ejpam-4931	499	20	we	we	PRON
ejpam-4931	499	21	get	get	VERB
ejpam-4931	499	22	∂t	∂t	PROPN
ejpam-4931	499	23	(	(	PUNCT
ejpam-4931	499	24	2ξ∇x	2ξ∇x	NUM
ejpam-4931	499	25	ln	ln	PROPN
ejpam-4931	499	26	ξ	ξ	PROPN
ejpam-4931	499	27	)	)	PUNCT
ejpam-4931	500	1	+	+	NUM
ejpam-4931	500	2	divx	divx	PROPN
ejpam-4931	500	3	(	(	PUNCT
ejpam-4931	500	4	2ξ∇t	2ξ∇t	NUM
ejpam-4931	500	5	xu	xu	INTJ
ejpam-4931	500	6	)	)	PUNCT
ejpam-4931	501	1	+	+	CCONJ
ejpam-4931	501	2	divx	divx	PROPN
ejpam-4931	501	3	(	(	PUNCT
ejpam-4931	501	4	2ξ∇x	2ξ∇x	NUM
ejpam-4931	501	5	ln	ln	PROPN
ejpam-4931	501	6	ξ	ξ	PROPN
ejpam-4931	501	7	⊗	⊗	PROPN
ejpam-4931	501	8	u	u	NOUN
ejpam-4931	501	9	)	)	PUNCT
ejpam-4931	501	10	+	+	NUM
ejpam-4931	501	11	2∂y∇x(ξv	2∂y∇x(ξv	NUM
ejpam-4931	501	12	)	)	PUNCT
ejpam-4931	501	13	=	=	SYM
ejpam-4931	502	1	2ϵ∇x∆xξ	2ϵ∇x∆xξ	NUM
ejpam-4931	502	2	.	.	PUNCT
ejpam-4931	503	1	(	(	PUNCT
ejpam-4931	503	2	63	63	NUM
ejpam-4931	503	3	)	)	PUNCT
ejpam-4931	503	4	then	then	ADV
ejpam-4931	503	5	,	,	PUNCT
ejpam-4931	503	6	we	we	PRON
ejpam-4931	503	7	add	add	VERB
ejpam-4931	503	8	(	(	PUNCT
ejpam-4931	503	9	63	63	NUM
ejpam-4931	503	10	)	)	PUNCT
ejpam-4931	503	11	with	with	ADP
ejpam-4931	503	12	that	that	PRON
ejpam-4931	503	13	of	of	ADP
ejpam-4931	503	14	the	the	DET
ejpam-4931	503	15	conservation	conservation	NOUN
ejpam-4931	503	16	of	of	ADP
ejpam-4931	503	17	moments	moment	NOUN
ejpam-4931	503	18	to	to	PART
ejpam-4931	503	19	obtain	obtain	VERB
ejpam-4931	503	20	∂t	∂t	PROPN
ejpam-4931	503	21	(	(	PUNCT
ejpam-4931	503	22	ξ(u+	ξ(u+	PROPN
ejpam-4931	503	23	2∇x	2∇x	NUM
ejpam-4931	503	24	ln	ln	ADJ
ejpam-4931	503	25	ξ	ξ	NOUN
ejpam-4931	503	26	)	)	PUNCT
ejpam-4931	503	27	)	)	PUNCT
ejpam-4931	504	1	+	+	CCONJ
ejpam-4931	504	2	divx	divx	PROPN
ejpam-4931	504	3	(	(	PUNCT
ejpam-4931	504	4	ξ(u+	ξ(u+	PROPN
ejpam-4931	504	5	2∇x	2∇x	NUM
ejpam-4931	504	6	ln	ln	NOUN
ejpam-4931	504	7	ξ)⊗	ξ)⊗	NUM
ejpam-4931	504	8	u	u	NOUN
ejpam-4931	504	9	)	)	PUNCT
ejpam-4931	504	10	+	+	CCONJ
ejpam-4931	504	11	∂y	∂y	SYM
ejpam-4931	504	12	(	(	PUNCT
ejpam-4931	504	13	2∇x(ξv	2∇x(ξv	NUM
ejpam-4931	504	14	)	)	PUNCT
ejpam-4931	504	15	)	)	PUNCT
ejpam-4931	505	1	+	+	CCONJ
ejpam-4931	506	1	∂y(ξuv	∂y(ξuv	X
ejpam-4931	506	2	)	)	PUNCT
ejpam-4931	507	1	+	+	X
ejpam-4931	507	2	∇xξ	∇xξ	PROPN
ejpam-4931	507	3	2	2	NUM
ejpam-4931	507	4	+	+	NUM
ejpam-4931	507	5	r1u+	r1u+	NOUN
ejpam-4931	507	6	rξ|u|u+	rξ|u|u+	VERB
ejpam-4931	507	7	α∆2	α∆2	PRON
ejpam-4931	507	8	xu	xu	PROPN
ejpam-4931	508	1	=	=	SYM
ejpam-4931	508	2	divx	divx	PROPN
ejpam-4931	508	3	(	(	PUNCT
ejpam-4931	508	4	2ξax(u	2ξax(u	NUM
ejpam-4931	508	5	)	)	PUNCT
ejpam-4931	508	6	)	)	PUNCT
ejpam-4931	509	1	+	+	CCONJ
ejpam-4931	509	2	∂y(ξ∂yu	∂y(ξ∂yu	NOUN
ejpam-4931	509	3	)	)	PUNCT
ejpam-4931	510	1	+	+	CCONJ
ejpam-4931	511	1	r2∇xξ	r2∇xξ	NOUN
ejpam-4931	511	2	−β	−β	NOUN
ejpam-4931	511	3	−	−	PROPN
ejpam-4931	511	4	ϵ∇xξ	ϵ∇xξ	PROPN
ejpam-4931	511	5	·	·	PUNCT
ejpam-4931	511	6	∇xu+	∇xu+	X
ejpam-4931	511	7	2ϵ∇x∆xξ	2ϵ∇x∆xξ	NUM
ejpam-4931	512	1	+	+	CCONJ
ejpam-4931	512	2	k1ξ∇x	k1ξ∇x	PROPN
ejpam-4931	512	3	(	(	PUNCT
ejpam-4931	512	4	∆x	∆x	PROPN
ejpam-4931	512	5	√	√	PROPN
ejpam-4931	512	6	ξ√	ξ√	PROPN
ejpam-4931	512	7	ξ	ξ	PROPN
ejpam-4931	512	8	)	)	PUNCT
ejpam-4931	513	1	+	+	CCONJ
ejpam-4931	514	1	δξ∇x∆	δξ∇x∆	PROPN
ejpam-4931	514	2	5	5	NUM
ejpam-4931	514	3	xξ	xξ	NOUN
ejpam-4931	514	4	,	,	PUNCT
ejpam-4931	514	5	(	(	PUNCT
ejpam-4931	514	6	64	64	NUM
ejpam-4931	514	7	)	)	PUNCT
ejpam-4931	514	8	where	where	SCONJ
ejpam-4931	514	9	ax(u	ax(u	NOUN
ejpam-4931	514	10	)	)	PUNCT
ejpam-4931	514	11	=	=	PUNCT
ejpam-4931	514	12	∇xu−∇t	∇xu−∇t	NOUN
ejpam-4931	514	13	xu	xu	PROPN
ejpam-4931	514	14	2	2	NUM
ejpam-4931	515	1	=	=	SYM
ejpam-4931	515	2	(	(	PUNCT
ejpam-4931	515	3	∂xiuj	∂xiuj	ADJ
ejpam-4931	515	4	−	−	PROPN
ejpam-4931	515	5	∂xjui	∂xjui	PROPN
ejpam-4931	515	6	2	2	NUM
ejpam-4931	515	7	)	)	PUNCT
ejpam-4931	515	8	1≤i	1≤i	NUM
ejpam-4931	515	9	,	,	PUNCT
ejpam-4931	515	10	j≤2	j≤2	PROPN
ejpam-4931	515	11	is	be	AUX
ejpam-4931	515	12	the	the	DET
ejpam-4931	515	13	vorticity	vorticity	NOUN
ejpam-4931	515	14	rate	rate	NOUN
ejpam-4931	515	15	tensor	tensor	NOUN
ejpam-4931	515	16	.	.	PUNCT
ejpam-4931	516	1	lemma	lemma	PROPN
ejpam-4931	516	2	11	11	NUM
ejpam-4931	516	3	.	.	PUNCT
ejpam-4931	517	1	:	:	PUNCT
ejpam-4931	517	2	under	under	ADP
ejpam-4931	517	3	the	the	DET
ejpam-4931	517	4	assumption	assumption	NOUN
ejpam-4931	517	5	(	(	PUNCT
ejpam-4931	517	6	61	61	NUM
ejpam-4931	517	7	)	)	PUNCT
ejpam-4931	517	8	,	,	PUNCT
ejpam-4931	517	9	we	we	PRON
ejpam-4931	517	10	have	have	VERB
ejpam-4931	517	11	the	the	DET
ejpam-4931	517	12	following	follow	VERB
ejpam-4931	517	13	b	b	X
ejpam-4931	517	14	-	-	PUNCT
ejpam-4931	517	15	d	d	NOUN
ejpam-4931	517	16	entropy:∫	entropy:∫	NOUN
ejpam-4931	517	17	ω	ω	NOUN
ejpam-4931	517	18	(	(	PUNCT
ejpam-4931	517	19	1	1	NUM
ejpam-4931	517	20	2	2	NUM
ejpam-4931	517	21	ξ|u+	ξ|u+	NOUN
ejpam-4931	517	22	2∇x	2∇x	NUM
ejpam-4931	517	23	ln	ln	PROPN
ejpam-4931	517	24	ξ|2	ξ|2	PROPN
ejpam-4931	517	25	−	−	PROPN
ejpam-4931	517	26	2r1	2r1	NUM
ejpam-4931	517	27	ln	ln	PROPN
ejpam-4931	517	28	ξ	ξ	PROPN
ejpam-4931	517	29	)	)	PUNCT
ejpam-4931	517	30	dxdy	dxdy	NOUN
ejpam-4931	517	31	+	+	CCONJ
ejpam-4931	517	32	2	2	NUM
ejpam-4931	517	33	∫	∫	NOUN
ejpam-4931	517	34	t	t	PROPN
ejpam-4931	517	35	0	0	NUM
ejpam-4931	517	36	∫	∫	PROPN
ejpam-4931	518	1	ω	ω	NUM
ejpam-4931	518	2	ξ|∂yv|2dxdydt+	ξ|∂yv|2dxdydt+	PROPN
ejpam-4931	519	1	r	r	NOUN
ejpam-4931	519	2	∫	∫	PROPN
ejpam-4931	519	3	t	t	PROPN
ejpam-4931	519	4	0	0	NUM
ejpam-4931	519	5	∫	∫	PROPN
ejpam-4931	519	6	ω	ω	NUM
ejpam-4931	519	7	ξ|u|3dxdydt	ξ|u|3dxdydt	PROPN
ejpam-4931	519	8	+	+	CCONJ
ejpam-4931	519	9	16r2	16r2	NUM
ejpam-4931	519	10	β	β	NOUN
ejpam-4931	519	11	∫	∫	PROPN
ejpam-4931	519	12	t	t	PROPN
ejpam-4931	519	13	0	0	NUM
ejpam-4931	519	14	∫	∫	PROPN
ejpam-4931	520	1	ω	ω	PROPN
ejpam-4931	520	2	|∇xξ	|∇xξ	PROPN
ejpam-4931	520	3	−β/2|2dxdydt+	−β/2|2dxdydt+	PROPN
ejpam-4931	520	4	α	α	NUM
ejpam-4931	520	5	∫	∫	PROPN
ejpam-4931	521	1	t	t	PROPN
ejpam-4931	521	2	0	0	NUM
ejpam-4931	521	3	∫	∫	PROPN
ejpam-4931	521	4	ω	ω	PROPN
ejpam-4931	521	5	|∆xu|2dxdydt+	|∆xu|2dxdydt+	PUNCT
ejpam-4931	522	1	r1	r1	PROPN
ejpam-4931	522	2	∫	∫	PROPN
ejpam-4931	522	3	t	t	PROPN
ejpam-4931	522	4	0	0	NUM
ejpam-4931	522	5	∫	∫	PROPN
ejpam-4931	522	6	ω	ω	PROPN
ejpam-4931	522	7	u2dxdydt	u2dxdydt	PROPN
ejpam-4931	522	8	+	+	PROPN
ejpam-4931	522	9	k1	k1	PROPN
ejpam-4931	522	10	∫	∫	PROPN
ejpam-4931	522	11	t	t	PROPN
ejpam-4931	522	12	0	0	NUM
ejpam-4931	522	13	∫	∫	PROPN
ejpam-4931	522	14	ω	ω	NUM
ejpam-4931	522	15	ξ|∇2	ξ|∇2	PROPN
ejpam-4931	523	1	x	x	SYM
ejpam-4931	523	2	ln	ln	NOUN
ejpam-4931	523	3	ξ|2dxdydt+	ξ|2dxdydt+	NUM
ejpam-4931	523	4	2δ	2δ	NUM
ejpam-4931	524	1	∫	∫	PROPN
ejpam-4931	524	2	t	t	PROPN
ejpam-4931	524	3	0	0	NUM
ejpam-4931	524	4	∫	∫	PROPN
ejpam-4931	524	5	ω	ω	PROPN
ejpam-4931	524	6	|∆3	|∆3	NOUN
ejpam-4931	524	7	xξ|2dxdydt+	xξ|2dxdydt+	PROPN
ejpam-4931	524	8	2	2	NUM
ejpam-4931	524	9	∫	∫	NOUN
ejpam-4931	524	10	t	t	PROPN
ejpam-4931	524	11	0	0	NUM
ejpam-4931	524	12	∫	∫	PROPN
ejpam-4931	524	13	ω	ω	PROPN
ejpam-4931	525	1	ξ|ax(u)|2dxdydt	ξ|ax(u)|2dxdydt	PROPN
ejpam-4931	525	2	+	+	NUM
ejpam-4931	525	3	8	8	NUM
ejpam-4931	525	4	∫	∫	NOUN
ejpam-4931	525	5	t	t	PROPN
ejpam-4931	525	6	0	0	NUM
ejpam-4931	525	7	∫	∫	PROPN
ejpam-4931	525	8	ω	ω	NUM
ejpam-4931	525	9	ξ|∇x	ξ|∇x	PROPN
ejpam-4931	526	1	√	√	PROPN
ejpam-4931	526	2	ξ|2dxdydt+	ξ|2dxdydt+	NUM
ejpam-4931	527	1	2r1ϵ	2r1ϵ	NUM
ejpam-4931	527	2	∫	∫	PROPN
ejpam-4931	527	3	t	t	PROPN
ejpam-4931	527	4	0	0	NUM
ejpam-4931	528	1	∫	∫	PROPN
ejpam-4931	529	1	ω	ω	PROPN
ejpam-4931	529	2	|∇xξ|2	|∇xξ|2	NOUN
ejpam-4931	529	3	ξ2	ξ2	PROPN
ejpam-4931	529	4	dxdydt+	dxdydt+	ADP
ejpam-4931	529	5	∫	∫	PROPN
ejpam-4931	529	6	t	t	PROPN
ejpam-4931	529	7	0	0	NUM
ejpam-4931	530	1	∫	∫	PROPN
ejpam-4931	530	2	ω	ω	PROPN
ejpam-4931	530	3	ξ|∂yu|2dxdy	ξ|∂yu|2dxdy	PROPN
ejpam-4931	530	4	j.	j.	PROPN
ejpam-4931	530	5	ouya	ouya	PROPN
ejpam-4931	530	6	,	,	PUNCT
ejpam-4931	530	7	a.	a.	NOUN
ejpam-4931	530	8	ouédraogo	ouédraogo	PROPN
ejpam-4931	530	9	/	/	SYM
ejpam-4931	530	10	eur	eur	PROPN
ejpam-4931	530	11	.	.	PUNCT
ejpam-4931	531	1	j.	j.	PROPN
ejpam-4931	531	2	pure	pure	PROPN
ejpam-4931	531	3	appl	appl	PROPN
ejpam-4931	531	4	.	.	PROPN
ejpam-4931	531	5	math	math	PROPN
ejpam-4931	531	6	,	,	PUNCT
ejpam-4931	531	7	16	16	NUM
ejpam-4931	531	8	(	(	PUNCT
ejpam-4931	531	9	4	4	NUM
ejpam-4931	531	10	)	)	PUNCT
ejpam-4931	531	11	(	(	PUNCT
ejpam-4931	531	12	2023	2023	NUM
ejpam-4931	531	13	)	)	PUNCT
ejpam-4931	531	14	,	,	PUNCT
ejpam-4931	531	15	2247	2247	NUM
ejpam-4931	531	16	-	-	SYM
ejpam-4931	531	17	2285	2285	NUM
ejpam-4931	531	18	2266	2266	NUM
ejpam-4931	531	19	≤	≤	NUM
ejpam-4931	531	20	∫	∫	PROPN
ejpam-4931	531	21	ω	ω	PROPN
ejpam-4931	531	22	(	(	PUNCT
ejpam-4931	531	23	ξ0u	ξ0u	NOUN
ejpam-4931	531	24	2	2	NUM
ejpam-4931	531	25	0	0	NUM
ejpam-4931	532	1	+	+	CCONJ
ejpam-4931	532	2	10(∇x	10(∇x	NUM
ejpam-4931	532	3	√	√	ADJ
ejpam-4931	532	4	ξ0	ξ0	PROPN
ejpam-4931	532	5	)	)	PUNCT
ejpam-4931	532	6	2	2	NUM
ejpam-4931	532	7	−	−	PROPN
ejpam-4931	532	8	2r1	2r1	NUM
ejpam-4931	532	9	ln	ln	PROPN
ejpam-4931	532	10	ξ0	ξ0	PROPN
ejpam-4931	532	11	)	)	PUNCT
ejpam-4931	532	12	dxdy	dxdy	PROPN
ejpam-4931	532	13	+	+	CCONJ
ejpam-4931	532	14	e0	e0	PROPN
ejpam-4931	533	1	+	+	CCONJ
ejpam-4931	533	2	c	c	PROPN
ejpam-4931	533	3	+	+	SYM
ejpam-4931	533	4	ϵc(δ	ϵc(δ	NUM
ejpam-4931	533	5	,	,	PUNCT
ejpam-4931	533	6	r2	r2	PROPN
ejpam-4931	533	7	)	)	PUNCT
ejpam-4931	534	1	+	+	CCONJ
ejpam-4931	534	2	√	√	NUM
ejpam-4931	534	3	αc(δ	αc(δ	NOUN
ejpam-4931	534	4	,	,	PUNCT
ejpam-4931	534	5	r2	r2	PROPN
ejpam-4931	534	6	)	)	PUNCT
ejpam-4931	534	7	,	,	PUNCT
ejpam-4931	534	8	(	(	PUNCT
ejpam-4931	534	9	65	65	NUM
ejpam-4931	534	10	)	)	PUNCT
ejpam-4931	534	11	where	where	SCONJ
ejpam-4931	534	12	c	c	NOUN
ejpam-4931	534	13	is	be	AUX
ejpam-4931	534	14	a	a	DET
ejpam-4931	534	15	generic	generic	ADJ
ejpam-4931	534	16	positive	positive	ADJ
ejpam-4931	534	17	constant	constant	ADJ
ejpam-4931	534	18	depending	depend	VERB
ejpam-4931	534	19	on	on	ADP
ejpam-4931	534	20	the	the	DET
ejpam-4931	534	21	initial	initial	ADJ
ejpam-4931	534	22	data	datum	NOUN
ejpam-4931	534	23	and	and	CCONJ
ejpam-4931	534	24	other	other	ADJ
ejpam-4931	534	25	constants	constant	NOUN
ejpam-4931	534	26	but	but	CCONJ
ejpam-4931	534	27	independent	independent	ADJ
ejpam-4931	534	28	of	of	ADP
ejpam-4931	534	29	ϵ	ϵ	PROPN
ejpam-4931	534	30	,	,	PUNCT
ejpam-4931	534	31	δ	δ	PROPN
ejpam-4931	534	32	,	,	PUNCT
ejpam-4931	534	33	r1	r1	NOUN
ejpam-4931	534	34	,	,	PUNCT
ejpam-4931	534	35	r2	r2	PROPN
ejpam-4931	534	36	,	,	PUNCT
ejpam-4931	534	37	α	α	X
ejpam-4931	534	38	,	,	PUNCT
ejpam-4931	534	39	and	and	CCONJ
ejpam-4931	534	40	c(δ	c(δ	PROPN
ejpam-4931	534	41	,	,	PUNCT
ejpam-4931	534	42	r2	r2	PROPN
ejpam-4931	534	43	)	)	PUNCT
ejpam-4931	534	44	is	be	AUX
ejpam-4931	534	45	a	a	DET
ejpam-4931	534	46	generic	generic	ADJ
ejpam-4931	534	47	positive	positive	ADJ
ejpam-4931	534	48	constant	constant	NOUN
ejpam-4931	534	49	only	only	ADV
ejpam-4931	534	50	depending	depend	VERB
ejpam-4931	534	51	on	on	ADP
ejpam-4931	534	52	δ	δ	PROPN
ejpam-4931	534	53	and	and	CCONJ
ejpam-4931	534	54	r2	r2	PROPN
ejpam-4931	534	55	.	.	PUNCT
ejpam-4931	535	1	proof	proof	NOUN
ejpam-4931	535	2	.	.	PUNCT
ejpam-4931	536	1	multiplying	multiply	VERB
ejpam-4931	536	2	(	(	PUNCT
ejpam-4931	536	3	64	64	NUM
ejpam-4931	536	4	)	)	PUNCT
ejpam-4931	536	5	by	by	ADP
ejpam-4931	536	6	u+	u+	NUM
ejpam-4931	536	7	2∇x	2∇x	NUM
ejpam-4931	536	8	ln	ln	PROPN
ejpam-4931	536	9	ξ	ξ	PROPN
ejpam-4931	536	10	=	=	SYM
ejpam-4931	536	11	ψ	ψ	NOUN
ejpam-4931	536	12	and	and	CCONJ
ejpam-4931	536	13	integrating	integrate	VERB
ejpam-4931	536	14	over	over	ADP
ejpam-4931	536	15	ω	ω	PROPN
ejpam-4931	536	16	,	,	PUNCT
ejpam-4931	536	17	we	we	PRON
ejpam-4931	536	18	obtain:∫	obtain:∫	VERB
ejpam-4931	536	19	ω	ω	NUM
ejpam-4931	536	20	∂t(ξψ)ψdxdy	∂t(ξψ)ψdxdy	X
ejpam-4931	537	1	+	+	CCONJ
ejpam-4931	537	2	∫	∫	PROPN
ejpam-4931	537	3	ω	ω	PROPN
ejpam-4931	537	4	divx(ξψ	divx(ξψ	PROPN
ejpam-4931	537	5	⊗	⊗	PROPN
ejpam-4931	537	6	u)ψdxdy	u)ψdxdy	PROPN
ejpam-4931	538	1	+	+	CCONJ
ejpam-4931	538	2	∫	∫	PROPN
ejpam-4931	538	3	ω	ω	NUM
ejpam-4931	538	4	∂y(ξuv)ψdxdy	∂y(ξuv)ψdxdy	X
ejpam-4931	538	5	+	+	CCONJ
ejpam-4931	538	6	2	2	NUM
ejpam-4931	538	7	∫	∫	NOUN
ejpam-4931	538	8	ω	ω	PROPN
ejpam-4931	538	9	∂y∇x(ξv)ψdxdy	∂y∇x(ξv)ψdxdy	PROPN
ejpam-4931	538	10	+	+	CCONJ
ejpam-4931	538	11	∫	∫	PROPN
ejpam-4931	538	12	ω	ω	PROPN
ejpam-4931	538	13	∇xξ	∇xξ	PROPN
ejpam-4931	538	14	2ψdxdy	2ψdxdy	NUM
ejpam-4931	539	1	+	+	NUM
ejpam-4931	540	1	∫	∫	PROPN
ejpam-4931	540	2	ω	ω	PROPN
ejpam-4931	540	3	(	(	PUNCT
ejpam-4931	540	4	r1u+	r1u+	PROPN
ejpam-4931	540	5	rξ|u|u+	rξ|u|u+	VERB
ejpam-4931	540	6	α∆2u	α∆2u	PROPN
ejpam-4931	540	7	)	)	PUNCT
ejpam-4931	540	8	ψdxdy	ψdxdy	NOUN
ejpam-4931	540	9	−	−	PROPN
ejpam-4931	540	10	2	2	NUM
ejpam-4931	540	11	∫	∫	PROPN
ejpam-4931	540	12	ω	ω	PROPN
ejpam-4931	540	13	divx(ξax(u))ψdxdy	divx(ξax(u))ψdxdy	PROPN
ejpam-4931	540	14	−	−	PROPN
ejpam-4931	540	15	∫	∫	PROPN
ejpam-4931	540	16	ω	ω	X
ejpam-4931	540	17	∂y(ξ∂yu)ψdxdy	∂y(ξ∂yu)ψdxdy	X
ejpam-4931	540	18	−	−	PROPN
ejpam-4931	540	19	r2	r2	PROPN
ejpam-4931	540	20	∫	∫	PROPN
ejpam-4931	541	1	ω	ω	PROPN
ejpam-4931	541	2	∇xξ	∇xξ	PROPN
ejpam-4931	541	3	−βψdxdy	−βψdxdy	PROPN
ejpam-4931	542	1	+	+	CCONJ
ejpam-4931	542	2	ϵ	ϵ	X
ejpam-4931	542	3	∫	∫	PROPN
ejpam-4931	542	4	ω	ω	PROPN
ejpam-4931	542	5	(	(	PUNCT
ejpam-4931	542	6	∇xξ	∇xξ	PROPN
ejpam-4931	542	7	·	·	PUNCT
ejpam-4931	542	8	∇xu)ψdxdy	∇xu)ψdxdy	PROPN
ejpam-4931	543	1	−	−	PROPN
ejpam-4931	543	2	2ϵ	2ϵ	NUM
ejpam-4931	543	3	∫	∫	PROPN
ejpam-4931	544	1	ω	ω	INTJ
ejpam-4931	544	2	(	(	PUNCT
ejpam-4931	544	3	∇x∆xξ	∇x∆xξ	PROPN
ejpam-4931	544	4	)	)	PUNCT
ejpam-4931	544	5	ψdxdy	ψdxdy	NOUN
ejpam-4931	544	6	−	−	PROPN
ejpam-4931	544	7	k1	k1	PROPN
ejpam-4931	544	8	∫	∫	PROPN
ejpam-4931	544	9	ω	ω	PROPN
ejpam-4931	544	10	ξ∇x	ξ∇x	PROPN
ejpam-4931	545	1	(	(	PUNCT
ejpam-4931	545	2	∆x	∆x	PROPN
ejpam-4931	545	3	√	√	PROPN
ejpam-4931	545	4	ξ√	ξ√	PROPN
ejpam-4931	545	5	ξ	ξ	PROPN
ejpam-4931	545	6	)	)	PUNCT
ejpam-4931	546	1	ψdxdy	ψdxdy	NOUN
ejpam-4931	546	2	−	−	PROPN
ejpam-4931	546	3	δ	δ	PROPN
ejpam-4931	546	4	∫	∫	PROPN
ejpam-4931	546	5	ω	ω	PROPN
ejpam-4931	546	6	(	(	PUNCT
ejpam-4931	546	7	ξ∇x∆	ξ∇x∆	PROPN
ejpam-4931	546	8	5	5	NUM
ejpam-4931	546	9	xξ)ψdxdy	xξ)ψdxdy	X
ejpam-4931	546	10	=	=	PUNCT
ejpam-4931	547	1	0	0	X
ejpam-4931	547	2	.	.	PUNCT
ejpam-4931	548	1	(	(	PUNCT
ejpam-4931	548	2	66	66	NUM
ejpam-4931	548	3	)	)	PUNCT
ejpam-4931	548	4	the	the	DET
ejpam-4931	548	5	two	two	NUM
ejpam-4931	548	6	first	first	ADJ
ejpam-4931	548	7	terms	term	NOUN
ejpam-4931	548	8	of	of	ADP
ejpam-4931	548	9	(	(	PUNCT
ejpam-4931	548	10	66	66	NUM
ejpam-4931	548	11	)	)	PUNCT
ejpam-4931	548	12	give	give	NOUN
ejpam-4931	548	13	:	:	PUNCT
ejpam-4931	548	14	•	•	NUM
ejpam-4931	548	15	∫	∫	PROPN
ejpam-4931	548	16	ω	ω	X
ejpam-4931	548	17	∂t(ξψ)ψdxdy	∂t(ξψ)ψdxdy	PROPN
ejpam-4931	549	1	+	+	CCONJ
ejpam-4931	549	2	∫	∫	PROPN
ejpam-4931	549	3	ω	ω	PROPN
ejpam-4931	549	4	divx(ξψ	divx(ξψ	PROPN
ejpam-4931	549	5	⊗	⊗	PROPN
ejpam-4931	549	6	u)ψdxdy	u)ψdxdy	PROPN
ejpam-4931	550	1	=	=	SYM
ejpam-4931	550	2	∫	∫	PROPN
ejpam-4931	550	3	ω	ω	NUM
ejpam-4931	550	4	ψ2∂tξdxdy	ψ2∂tξdxdy	PUNCT
ejpam-4931	550	5	+	+	CCONJ
ejpam-4931	550	6	∫	∫	PROPN
ejpam-4931	550	7	ω	ω	NUM
ejpam-4931	550	8	ξ∂t	ξ∂t	NOUN
ejpam-4931	550	9	ψ2	ψ2	NOUN
ejpam-4931	550	10	2	2	NUM
ejpam-4931	550	11	dxdy	dxdy	NOUN
ejpam-4931	550	12	+	+	CCONJ
ejpam-4931	550	13	∫	∫	PROPN
ejpam-4931	550	14	ω	ω	PROPN
ejpam-4931	550	15	(	(	PUNCT
ejpam-4931	550	16	ξψ	ξψ	PROPN
ejpam-4931	550	17	divx(u	divx(u	PROPN
ejpam-4931	550	18	)	)	PUNCT
ejpam-4931	550	19	+	+	NUM
ejpam-4931	550	20	u	u	NOUN
ejpam-4931	550	21	·	·	PUNCT
ejpam-4931	550	22	∇x(ξψ	∇x(ξψ	NUM
ejpam-4931	550	23	)	)	PUNCT
ejpam-4931	550	24	)	)	PUNCT
ejpam-4931	551	1	ψdxdy	ψdxdy	X
ejpam-4931	551	2	=	=	SYM
ejpam-4931	551	3	∫	∫	PROPN
ejpam-4931	551	4	ω	ω	NUM
ejpam-4931	551	5	ψ2∂tξdxdy	ψ2∂tξdxdy	PUNCT
ejpam-4931	551	6	+	+	CCONJ
ejpam-4931	551	7	∫	∫	PROPN
ejpam-4931	551	8	ω	ω	NUM
ejpam-4931	551	9	ξ∂t	ξ∂t	NOUN
ejpam-4931	551	10	ψ2	ψ2	NOUN
ejpam-4931	551	11	2	2	NUM
ejpam-4931	551	12	dxdy	dxdy	NOUN
ejpam-4931	551	13	+	+	CCONJ
ejpam-4931	551	14	∫	∫	PROPN
ejpam-4931	551	15	ω	ω	PROPN
ejpam-4931	551	16	(	(	PUNCT
ejpam-4931	551	17	ξψ2divx(u	ξψ2divx(u	PROPN
ejpam-4931	551	18	)	)	PUNCT
ejpam-4931	551	19	+	+	CCONJ
ejpam-4931	551	20	1	1	NUM
ejpam-4931	551	21	2	2	NUM
ejpam-4931	551	22	ξu∇xψ	ξu∇xψ	NUM
ejpam-4931	551	23	2	2	NUM
ejpam-4931	551	24	+	+	CCONJ
ejpam-4931	551	25	uψ2∇xξ	uψ2∇xξ	ADJ
ejpam-4931	551	26	)	)	PUNCT
ejpam-4931	551	27	dxdy	dxdy	PROPN
ejpam-4931	551	28	=	=	SYM
ejpam-4931	551	29	∫	∫	PROPN
ejpam-4931	551	30	ω	ω	NUM
ejpam-4931	551	31	ψ2∂tξdxdy	ψ2∂tξdxdy	PUNCT
ejpam-4931	551	32	+	+	CCONJ
ejpam-4931	551	33	∫	∫	PROPN
ejpam-4931	551	34	ω	ω	NUM
ejpam-4931	551	35	ξ∂t	ξ∂t	NOUN
ejpam-4931	551	36	ψ2	ψ2	NOUN
ejpam-4931	551	37	2	2	NUM
ejpam-4931	551	38	dxdy	dxdy	NOUN
ejpam-4931	551	39	+	+	CCONJ
ejpam-4931	551	40	∫	∫	PROPN
ejpam-4931	551	41	ω	ω	X
ejpam-4931	551	42	[	[	PUNCT
ejpam-4931	551	43	ψ2	ψ2	NOUN
ejpam-4931	551	44	(	(	PUNCT
ejpam-4931	551	45	ξdivx(u	ξdivx(u	PROPN
ejpam-4931	551	46	)	)	PUNCT
ejpam-4931	551	47	+	+	NUM
ejpam-4931	551	48	u∇xξ	u∇xξ	PROPN
ejpam-4931	551	49	)	)	PUNCT
ejpam-4931	551	50	−	−	PROPN
ejpam-4931	551	51	1	1	NUM
ejpam-4931	551	52	2	2	NUM
ejpam-4931	551	53	divx(ξu)ψ	divx(ξu)ψ	NOUN
ejpam-4931	551	54	2	2	NUM
ejpam-4931	551	55	]	]	PUNCT
ejpam-4931	551	56	dxdy	dxdy	PROPN
ejpam-4931	551	57	=	=	SYM
ejpam-4931	551	58	∫	∫	PROPN
ejpam-4931	551	59	ω	ω	NUM
ejpam-4931	551	60	ψ2∂tξdxdy	ψ2∂tξdxdy	X
ejpam-4931	551	61	+	+	CCONJ
ejpam-4931	551	62	1	1	NUM
ejpam-4931	551	63	2	2	NUM
ejpam-4931	551	64	∫	∫	NOUN
ejpam-4931	551	65	ω	ω	NUM
ejpam-4931	551	66	ξ∂tψ	ξ∂tψ	PROPN
ejpam-4931	551	67	2dxdy	2dxdy	NUM
ejpam-4931	552	1	+	+	CCONJ
ejpam-4931	552	2	1	1	NUM
ejpam-4931	552	3	2	2	NUM
ejpam-4931	552	4	∫	∫	PROPN
ejpam-4931	552	5	ω	ω	X
ejpam-4931	552	6	ψ2divx(ξu)dxdy	ψ2divx(ξu)dxdy	PROPN
ejpam-4931	552	7	.	.	PUNCT
ejpam-4931	553	1	(	(	PUNCT
ejpam-4931	553	2	67	67	NUM
ejpam-4931	553	3	)	)	PUNCT
ejpam-4931	553	4	remark	remark	NOUN
ejpam-4931	553	5	that	that	SCONJ
ejpam-4931	553	6	∂y(ξuv	∂y(ξuv	ADV
ejpam-4931	553	7	)	)	PUNCT
ejpam-4931	554	1	=	=	SYM
ejpam-4931	554	2	∂y(ξvψ)−	∂y(ξvψ)−	PROPN
ejpam-4931	554	3	2∂y(v∇xξ	2∂y(v∇xξ	NUM
ejpam-4931	554	4	)	)	PUNCT
ejpam-4931	554	5	,	,	PUNCT
ejpam-4931	554	6	then	then	ADV
ejpam-4931	554	7	the	the	DET
ejpam-4931	554	8	third	third	ADJ
ejpam-4931	554	9	term	term	NOUN
ejpam-4931	554	10	of	of	ADP
ejpam-4931	554	11	(	(	PUNCT
ejpam-4931	554	12	66	66	NUM
ejpam-4931	554	13	)	)	PUNCT
ejpam-4931	554	14	becomes	become	VERB
ejpam-4931	554	15	•	•	NUM
ejpam-4931	554	16	∫	∫	PROPN
ejpam-4931	554	17	ω	ω	PROPN
ejpam-4931	554	18	∂y(ξuv)ψdxdy	∂y(ξuv)ψdxdy	PROPN
ejpam-4931	554	19	=	=	SYM
ejpam-4931	554	20	∫	∫	PROPN
ejpam-4931	554	21	ω	ω	PROPN
ejpam-4931	554	22	∂y(ξvψ)ψdxdy	∂y(ξvψ)ψdxdy	PROPN
ejpam-4931	555	1	−	−	PROPN
ejpam-4931	555	2	2	2	NUM
ejpam-4931	555	3	∫	∫	PROPN
ejpam-4931	555	4	ω	ω	NUM
ejpam-4931	555	5	∂y(v∇xξ)ψdxdy	∂y(v∇xξ)ψdxdy	PROPN
ejpam-4931	555	6	=	=	SYM
ejpam-4931	555	7	∫	∫	PROPN
ejpam-4931	555	8	ω	ω	NUM
ejpam-4931	555	9	ψ2∂y(ξv)dxdy	ψ2∂y(ξv)dxdy	X
ejpam-4931	556	1	+	+	CCONJ
ejpam-4931	556	2	∫	∫	PROPN
ejpam-4931	556	3	ω	ω	NUM
ejpam-4931	556	4	ξv∂y	ξv∂y	PROPN
ejpam-4931	556	5	ψ2	ψ2	VERB
ejpam-4931	556	6	2	2	NUM
ejpam-4931	556	7	dxdy	dxdy	NOUN
ejpam-4931	556	8	−	−	PROPN
ejpam-4931	556	9	2	2	NUM
ejpam-4931	556	10	∫	∫	PROPN
ejpam-4931	556	11	ω	ω	PROPN
ejpam-4931	556	12	ψ∇xξ∂y(v)dxdy	ψ∇xξ∂y(v)dxdy	PROPN
ejpam-4931	556	13	=	=	SYM
ejpam-4931	556	14	∫	∫	PROPN
ejpam-4931	556	15	ω	ω	PROPN
ejpam-4931	556	16	ψ2∂y(ξv)dxdy	ψ2∂y(ξv)dxdy	X
ejpam-4931	557	1	−	−	NOUN
ejpam-4931	557	2	1	1	NUM
ejpam-4931	557	3	2	2	NUM
ejpam-4931	557	4	∫	∫	PROPN
ejpam-4931	557	5	ω	ω	NUM
ejpam-4931	557	6	ψ2∂y(ξv)dxdy	ψ2∂y(ξv)dxdy	X
ejpam-4931	558	1	+	+	CCONJ
ejpam-4931	558	2	2	2	NUM
ejpam-4931	558	3	∫	∫	PROPN
ejpam-4931	558	4	ω	ω	NOUN
ejpam-4931	558	5	v∇xξ∂y(ψ)dxdy	v∇xξ∂y(ψ)dxdy	PROPN
ejpam-4931	558	6	=	=	SYM
ejpam-4931	558	7	1	1	NUM
ejpam-4931	558	8	2	2	NUM
ejpam-4931	558	9	∫	∫	NOUN
ejpam-4931	558	10	ω	ω	NUM
ejpam-4931	558	11	ψ2∂y(ξv)dxdy	ψ2∂y(ξv)dxdy	X
ejpam-4931	559	1	+	+	CCONJ
ejpam-4931	559	2	2	2	NUM
ejpam-4931	559	3	∫	∫	PROPN
ejpam-4931	559	4	ω	ω	NUM
ejpam-4931	559	5	v∇xξ∂yudxdy	v∇xξ∂yudxdy	X
ejpam-4931	559	6	.	.	PUNCT
ejpam-4931	560	1	(	(	PUNCT
ejpam-4931	560	2	68	68	NUM
ejpam-4931	560	3	)	)	PUNCT
ejpam-4931	560	4	adding	add	VERB
ejpam-4931	560	5	the	the	DET
ejpam-4931	560	6	last	last	ADJ
ejpam-4931	560	7	term	term	NOUN
ejpam-4931	560	8	of	of	ADP
ejpam-4931	560	9	(	(	PUNCT
ejpam-4931	560	10	67	67	NUM
ejpam-4931	560	11	)	)	PUNCT
ejpam-4931	560	12	and	and	CCONJ
ejpam-4931	560	13	the	the	DET
ejpam-4931	560	14	first	first	ADJ
ejpam-4931	560	15	term	term	NOUN
ejpam-4931	560	16	in	in	ADP
ejpam-4931	560	17	the	the	DET
ejpam-4931	560	18	right	right	ADJ
ejpam-4931	560	19	hand	hand	NOUN
ejpam-4931	560	20	side	side	NOUN
ejpam-4931	560	21	of	of	ADP
ejpam-4931	560	22	(	(	PUNCT
ejpam-4931	560	23	68	68	NUM
ejpam-4931	560	24	)	)	PUNCT
ejpam-4931	560	25	,	,	PUNCT
ejpam-4931	560	26	we	we	PRON
ejpam-4931	560	27	obtain	obtain	VERB
ejpam-4931	560	28	1	1	NUM
ejpam-4931	560	29	2	2	NUM
ejpam-4931	560	30	∫	∫	PROPN
ejpam-4931	560	31	ω	ω	NUM
ejpam-4931	560	32	ψ2divx(ξu)dxdy	ψ2divx(ξu)dxdy	PROPN
ejpam-4931	560	33	+	+	CCONJ
ejpam-4931	560	34	1	1	NUM
ejpam-4931	560	35	2	2	NUM
ejpam-4931	560	36	∫	∫	NOUN
ejpam-4931	560	37	ω	ω	NOUN
ejpam-4931	560	38	ψ2∂y(ξv)dxdy	ψ2∂y(ξv)dxdy	X
ejpam-4931	561	1	=	=	NOUN
ejpam-4931	561	2	1	1	NUM
ejpam-4931	561	3	2	2	NUM
ejpam-4931	561	4	ϵ	ϵ	ADP
ejpam-4931	561	5	∫	∫	PROPN
ejpam-4931	561	6	ω	ω	X
ejpam-4931	561	7	ψ2∆xξdxdy	ψ2∆xξdxdy	X
ejpam-4931	562	1	−	−	NOUN
ejpam-4931	562	2	1	1	NUM
ejpam-4931	562	3	2	2	NUM
ejpam-4931	562	4	∫	∫	PROPN
ejpam-4931	562	5	ω	ω	NUM
ejpam-4931	562	6	ψ2∂tξdxdy	ψ2∂tξdxdy	PROPN
ejpam-4931	562	7	.	.	PUNCT
ejpam-4931	563	1	(	(	PUNCT
ejpam-4931	563	2	69	69	NUM
ejpam-4931	563	3	)	)	PUNCT
ejpam-4931	563	4	j.	j.	PROPN
ejpam-4931	563	5	ouya	ouya	PROPN
ejpam-4931	563	6	,	,	PUNCT
ejpam-4931	563	7	a.	a.	NOUN
ejpam-4931	563	8	ouédraogo	ouédraogo	PROPN
ejpam-4931	563	9	/	/	SYM
ejpam-4931	563	10	eur	eur	PROPN
ejpam-4931	563	11	.	.	PUNCT
ejpam-4931	564	1	j.	j.	PROPN
ejpam-4931	564	2	pure	pure	PROPN
ejpam-4931	564	3	appl	appl	PROPN
ejpam-4931	564	4	.	.	PROPN
ejpam-4931	564	5	math	math	PROPN
ejpam-4931	564	6	,	,	PUNCT
ejpam-4931	564	7	16	16	NUM
ejpam-4931	564	8	(	(	PUNCT
ejpam-4931	564	9	4	4	NUM
ejpam-4931	564	10	)	)	PUNCT
ejpam-4931	564	11	(	(	PUNCT
ejpam-4931	564	12	2023	2023	NUM
ejpam-4931	564	13	)	)	PUNCT
ejpam-4931	564	14	,	,	PUNCT
ejpam-4931	564	15	2247	2247	NUM
ejpam-4931	564	16	-	-	SYM
ejpam-4931	564	17	2285	2285	NUM
ejpam-4931	564	18	2267	2267	NUM
ejpam-4931	564	19	thus	thus	ADV
ejpam-4931	564	20	,	,	PUNCT
ejpam-4931	564	21	the	the	DET
ejpam-4931	564	22	first	first	ADJ
ejpam-4931	564	23	three	three	NUM
ejpam-4931	564	24	terms	term	NOUN
ejpam-4931	564	25	of	of	ADP
ejpam-4931	564	26	(	(	PUNCT
ejpam-4931	564	27	66	66	NUM
ejpam-4931	564	28	)	)	PUNCT
ejpam-4931	564	29	give∫	give∫	NOUN
ejpam-4931	564	30	ω	ω	PROPN
ejpam-4931	564	31	(	(	PUNCT
ejpam-4931	564	32	∂t(ξψ	∂t(ξψ	NOUN
ejpam-4931	564	33	)	)	PUNCT
ejpam-4931	564	34	+	+	CCONJ
ejpam-4931	564	35	divx(ξψ	divx(ξψ	ADJ
ejpam-4931	564	36	⊗	⊗	PROPN
ejpam-4931	564	37	u	u	NOUN
ejpam-4931	564	38	)	)	PUNCT
ejpam-4931	564	39	+	+	CCONJ
ejpam-4931	564	40	∂z(ξuv))ψdxdy	∂z(ξuv))ψdxdy	X
ejpam-4931	564	41	=	=	SYM
ejpam-4931	564	42	1	1	NUM
ejpam-4931	564	43	2	2	NUM
ejpam-4931	564	44	d	d	NOUN
ejpam-4931	564	45	dt	dt	X
ejpam-4931	564	46	∫	∫	PROPN
ejpam-4931	564	47	ω	ω	X
ejpam-4931	564	48	ξψ2dxdy	ξψ2dxdy	X
ejpam-4931	565	1	+	+	CCONJ
ejpam-4931	565	2	2	2	NUM
ejpam-4931	565	3	∫	∫	NOUN
ejpam-4931	565	4	ω	ω	NUM
ejpam-4931	565	5	v∇xξ∂yudxdy	v∇xξ∂yudxdy	X
ejpam-4931	566	1	+	+	X
ejpam-4931	566	2	1	1	NUM
ejpam-4931	566	3	2	2	NUM
ejpam-4931	566	4	ϵ	ϵ	ADP
ejpam-4931	566	5	∫	∫	PROPN
ejpam-4931	566	6	ω	ω	NUM
ejpam-4931	566	7	ψ2∆xξdxdy	ψ2∆xξdxdy	PROPN
ejpam-4931	566	8	.	.	PUNCT
ejpam-4931	567	1	(	(	PUNCT
ejpam-4931	567	2	70	70	NUM
ejpam-4931	567	3	)	)	PUNCT
ejpam-4931	567	4	the	the	DET
ejpam-4931	567	5	fourth	fourth	ADJ
ejpam-4931	567	6	term	term	NOUN
ejpam-4931	567	7	of	of	ADP
ejpam-4931	567	8	(	(	PUNCT
ejpam-4931	567	9	66	66	NUM
ejpam-4931	567	10	)	)	PUNCT
ejpam-4931	567	11	gives	give	VERB
ejpam-4931	567	12	•	•	NOUN
ejpam-4931	567	13	2	2	NUM
ejpam-4931	567	14	∫	∫	PROPN
ejpam-4931	567	15	ω	ω	PROPN
ejpam-4931	567	16	∂y∇x(ξv)ψdxdy	∂y∇x(ξv)ψdxdy	PROPN
ejpam-4931	567	17	=	=	PUNCT
ejpam-4931	567	18	−	−	PROPN
ejpam-4931	567	19	∫	∫	PROPN
ejpam-4931	567	20	ω	ω	X
ejpam-4931	567	21	2∇x(ξv)∂yudxdy	2∇x(ξv)∂yudxdy	PROPN
ejpam-4931	568	1	−	−	PROPN
ejpam-4931	568	2	∫	∫	PROPN
ejpam-4931	569	1	ω	ω	NUM
ejpam-4931	570	1	4∇x(ξv)∂y(∇x	4∇x(ξv)∂y(∇x	PROPN
ejpam-4931	570	2	ln	ln	ADJ
ejpam-4931	570	3	ξ)dxdy	ξ)dxdy	X
ejpam-4931	571	1	=	=	SYM
ejpam-4931	571	2	∫	∫	PROPN
ejpam-4931	571	3	ω	ω	NUM
ejpam-4931	571	4	2ξv∂ydivx(u)dxdy	2ξv∂ydivx(u)dxdy	NUM
ejpam-4931	571	5	=	=	SYM
ejpam-4931	571	6	∫	∫	PROPN
ejpam-4931	571	7	ω	ω	NUM
ejpam-4931	571	8	2	2	NUM
ejpam-4931	571	9	(	(	PUNCT
ejpam-4931	571	10	v∂ydivx(ξu)−	v∂ydivx(ξu)−	NOUN
ejpam-4931	571	11	v∇xξ∂yu	v∇xξ∂yu	PROPN
ejpam-4931	571	12	)	)	PUNCT
ejpam-4931	571	13	dxdy	dxdy	PROPN
ejpam-4931	571	14	=	=	SYM
ejpam-4931	571	15	∫	∫	PROPN
ejpam-4931	571	16	ω	ω	NUM
ejpam-4931	571	17	2	2	NUM
ejpam-4931	571	18	(	(	PUNCT
ejpam-4931	571	19	−	−	PROPN
ejpam-4931	571	20	ξv∂2yv	ξv∂2yv	PROPN
ejpam-4931	571	21	−	−	PROPN
ejpam-4931	571	22	v∇xξ∂yu	v∇xξ∂yu	PROPN
ejpam-4931	571	23	)	)	PUNCT
ejpam-4931	571	24	dxdy	dxdy	PROPN
ejpam-4931	571	25	=	=	SYM
ejpam-4931	571	26	∫	∫	PROPN
ejpam-4931	571	27	ω	ω	NUM
ejpam-4931	571	28	2	2	NUM
ejpam-4931	571	29	(	(	PUNCT
ejpam-4931	571	30	ξ|∂yv|2	ξ|∂yv|2	PROPN
ejpam-4931	571	31	−	−	PROPN
ejpam-4931	571	32	v∇xξ∂yu	v∇xξ∂yu	PROPN
ejpam-4931	571	33	)	)	PUNCT
ejpam-4931	571	34	dxdy	dxdy	PROPN
ejpam-4931	571	35	.	.	PUNCT
ejpam-4931	572	1	(	(	PUNCT
ejpam-4931	572	2	71	71	NUM
ejpam-4931	572	3	)	)	PUNCT
ejpam-4931	572	4	thus	thus	ADV
ejpam-4931	572	5	,	,	PUNCT
ejpam-4931	572	6	the	the	DET
ejpam-4931	572	7	first	first	ADJ
ejpam-4931	572	8	four	four	NUM
ejpam-4931	572	9	terms	term	NOUN
ejpam-4931	572	10	of	of	ADP
ejpam-4931	572	11	(	(	PUNCT
ejpam-4931	572	12	66	66	NUM
ejpam-4931	572	13	)	)	PUNCT
ejpam-4931	572	14	are	be	AUX
ejpam-4931	572	15	exactly	exactly	ADV
ejpam-4931	572	16	1	1	NUM
ejpam-4931	572	17	2	2	NUM
ejpam-4931	572	18	d	d	NOUN
ejpam-4931	572	19	dt	dt	X
ejpam-4931	572	20	∫	∫	PROPN
ejpam-4931	572	21	ω	ω	X
ejpam-4931	572	22	ξψ2dxdy	ξψ2dxdy	X
ejpam-4931	573	1	+	+	CCONJ
ejpam-4931	573	2	1	1	NUM
ejpam-4931	573	3	2	2	NUM
ejpam-4931	573	4	ϵ	ϵ	ADP
ejpam-4931	573	5	∫	∫	PROPN
ejpam-4931	573	6	ω	ω	NUM
ejpam-4931	573	7	ψ2∆xξdxdy	ψ2∆xξdxdy	PUNCT
ejpam-4931	574	1	+	+	CCONJ
ejpam-4931	574	2	∫	∫	PROPN
ejpam-4931	574	3	ω	ω	NUM
ejpam-4931	574	4	2ξ|∂yv|2dxdy	2ξ|∂yv|2dxdy	PROPN
ejpam-4931	574	5	.	.	PUNCT
ejpam-4931	575	1	(	(	PUNCT
ejpam-4931	575	2	72	72	NUM
ejpam-4931	575	3	)	)	PUNCT
ejpam-4931	575	4	moreover	moreover	ADV
ejpam-4931	575	5	,	,	PUNCT
ejpam-4931	575	6	by	by	ADP
ejpam-4931	575	7	summing	sum	VERB
ejpam-4931	575	8	the	the	DET
ejpam-4931	575	9	second	second	ADJ
ejpam-4931	575	10	term	term	NOUN
ejpam-4931	575	11	of	of	ADP
ejpam-4931	575	12	(	(	PUNCT
ejpam-4931	575	13	72	72	NUM
ejpam-4931	575	14	)	)	PUNCT
ejpam-4931	575	15	with	with	ADP
ejpam-4931	575	16	ϵ	ϵ	PROPN
ejpam-4931	575	17	∫	∫	PROPN
ejpam-4931	575	18	ω(∇xξ	ω(∇xξ	NUM
ejpam-4931	575	19	·	·	PUNCT
ejpam-4931	575	20	∇xu)ψdxdz	∇xu)ψdxdz	NUM
ejpam-4931	575	21	,	,	PUNCT
ejpam-4931	575	22	we	we	PRON
ejpam-4931	575	23	obtain	obtain	VERB
ejpam-4931	575	24	,	,	PUNCT
ejpam-4931	575	25	by	by	ADP
ejpam-4931	575	26	replacing	replace	VERB
ejpam-4931	575	27	ψ	ψ	PRON
ejpam-4931	575	28	by	by	ADP
ejpam-4931	575	29	u+	u+	NUM
ejpam-4931	575	30	2∇x	2∇x	NUM
ejpam-4931	575	31	ln	ln	PROPN
ejpam-4931	575	32	ξ	ξ	PROPN
ejpam-4931	575	33	,	,	PUNCT
ejpam-4931	575	34	ϵ	ϵ	PROPN
ejpam-4931	575	35	∫	∫	PROPN
ejpam-4931	575	36	ω	ω	PROPN
ejpam-4931	575	37	(	(	PUNCT
ejpam-4931	575	38	∇xξ	∇xξ	PROPN
ejpam-4931	575	39	·	·	PUNCT
ejpam-4931	575	40	∇xu)ψdxdy	∇xu)ψdxdy	X
ejpam-4931	576	1	+	+	CCONJ
ejpam-4931	576	2	1	1	NUM
ejpam-4931	576	3	2	2	NUM
ejpam-4931	576	4	ϵ	ϵ	ADP
ejpam-4931	576	5	∫	∫	PROPN
ejpam-4931	576	6	ω	ω	NOUN
ejpam-4931	576	7	ψ2∆xξdxdy	ψ2∆xξdxdy	X
ejpam-4931	576	8	=	=	PUNCT
ejpam-4931	577	1	−2ϵ	−2ϵ	PROPN
ejpam-4931	577	2	∫	∫	PROPN
ejpam-4931	577	3	ω	ω	PROPN
ejpam-4931	577	4	∇xξ	∇xξ	PROPN
ejpam-4931	577	5	·	·	PUNCT
ejpam-4931	577	6	∇2	∇2	PROPN
ejpam-4931	577	7	x	x	SYM
ejpam-4931	577	8	ln	ln	PROPN
ejpam-4931	577	9	ξ	ξ	PROPN
ejpam-4931	577	10	·	·	PUNCT
ejpam-4931	577	11	udxdy	udxdy	PROPN
ejpam-4931	577	12	−	−	PROPN
ejpam-4931	577	13	4ϵ	4ϵ	PROPN
ejpam-4931	577	14	∫	∫	PROPN
ejpam-4931	577	15	ω	ω	PROPN
ejpam-4931	577	16	∇xξ	∇xξ	PROPN
ejpam-4931	577	17	·	·	PUNCT
ejpam-4931	577	18	∇2	∇2	PROPN
ejpam-4931	577	19	x	x	SYM
ejpam-4931	577	20	ln	ln	PROPN
ejpam-4931	577	21	ξ	ξ	PROPN
ejpam-4931	577	22	·	·	PUNCT
ejpam-4931	577	23	∇x	∇x	PROPN
ejpam-4931	577	24	ln	ln	ADJ
ejpam-4931	577	25	ξdxdy	ξdxdy	NOUN
ejpam-4931	577	26	.	.	PUNCT
ejpam-4931	578	1	(	(	PUNCT
ejpam-4931	578	2	73	73	NUM
ejpam-4931	578	3	)	)	PUNCT
ejpam-4931	578	4	the	the	DET
ejpam-4931	578	5	term	term	NOUN
ejpam-4931	579	1	−2	−2	PROPN
ejpam-4931	580	1	∫	∫	PROPN
ejpam-4931	580	2	ω	ω	X
ejpam-4931	580	3	divx(ξax(u))ψdxdy	divx(ξax(u))ψdxdy	X
ejpam-4931	580	4	in	in	ADP
ejpam-4931	580	5	(	(	PUNCT
ejpam-4931	580	6	66	66	NUM
ejpam-4931	580	7	)	)	PUNCT
ejpam-4931	580	8	can	can	AUX
ejpam-4931	580	9	be	be	AUX
ejpam-4931	580	10	written	write	VERB
ejpam-4931	580	11	:	:	PUNCT
ejpam-4931	580	12	•	•	NUM
ejpam-4931	580	13	−	−	PROPN
ejpam-4931	580	14	2	2	NUM
ejpam-4931	580	15	∫	∫	NOUN
ejpam-4931	580	16	ω	ω	NOUN
ejpam-4931	581	1	divx(ξax(u))ψdxdy	divx(ξax(u))ψdxdy	PROPN
ejpam-4931	581	2	=	=	SYM
ejpam-4931	581	3	−2	−2	PROPN
ejpam-4931	581	4	∫	∫	PROPN
ejpam-4931	581	5	ω	ω	X
ejpam-4931	581	6	divx(ξax(u))udxdy	divx(ξax(u))udxdy	PUNCT
ejpam-4931	581	7	−	−	PROPN
ejpam-4931	581	8	2	2	NUM
ejpam-4931	581	9	∫	∫	NOUN
ejpam-4931	581	10	ω	ω	NOUN
ejpam-4931	582	1	divx(2ξax(u))∇x	divx(2ξax(u))∇x	PROPN
ejpam-4931	582	2	ln	ln	NOUN
ejpam-4931	582	3	ξdxdy	ξdxdy	NOUN
ejpam-4931	582	4	=	=	SYM
ejpam-4931	582	5	2	2	NUM
ejpam-4931	582	6	∫	∫	PROPN
ejpam-4931	582	7	ω	ω	NUM
ejpam-4931	582	8	ξ|ax(u)|2dxdy	ξ|ax(u)|2dxdy	PROPN
ejpam-4931	582	9	−	−	PROPN
ejpam-4931	582	10	2	2	NUM
ejpam-4931	582	11	∫	∫	NOUN
ejpam-4931	582	12	ω	ω	NUM
ejpam-4931	583	1	divx(2ξax(u))∇x	divx(2ξax(u))∇x	PROPN
ejpam-4931	583	2	ln	ln	NOUN
ejpam-4931	583	3	ξdxdy	ξdxdy	PROPN
ejpam-4931	583	4	.	.	PUNCT
ejpam-4931	584	1	(	(	PUNCT
ejpam-4931	584	2	74	74	NUM
ejpam-4931	584	3	)	)	PUNCT
ejpam-4931	584	4	the	the	DET
ejpam-4931	584	5	other	other	ADJ
ejpam-4931	584	6	terms	term	NOUN
ejpam-4931	584	7	in	in	ADP
ejpam-4931	584	8	(	(	PUNCT
ejpam-4931	584	9	66	66	NUM
ejpam-4931	584	10	)	)	PUNCT
ejpam-4931	584	11	yield	yield	NOUN
ejpam-4931	584	12	:	:	PUNCT
ejpam-4931	584	13	•	•	NUM
ejpam-4931	584	14	∫	∫	PROPN
ejpam-4931	584	15	ω	ω	NUM
ejpam-4931	584	16	rξ|u|uψdxdy	rξ|u|uψdxdy	X
ejpam-4931	584	17	=	=	PUNCT
ejpam-4931	584	18	∫	∫	PROPN
ejpam-4931	584	19	ω	ω	PROPN
ejpam-4931	584	20	rξ|u|3dxdy	rξ|u|3dxdy	PROPN
ejpam-4931	585	1	+	+	CCONJ
ejpam-4931	585	2	2r	2r	NUM
ejpam-4931	585	3	∫	∫	PROPN
ejpam-4931	585	4	ω	ω	NUM
ejpam-4931	585	5	|u|u∇xξdxdy	|u|u∇xξdxdy	PROPN
ejpam-4931	585	6	.	.	PUNCT
ejpam-4931	586	1	(	(	PUNCT
ejpam-4931	586	2	75	75	NUM
ejpam-4931	586	3	)	)	PUNCT
ejpam-4931	586	4	j.	j.	PROPN
ejpam-4931	586	5	ouya	ouya	PROPN
ejpam-4931	586	6	,	,	PUNCT
ejpam-4931	586	7	a.	a.	NOUN
ejpam-4931	586	8	ouédraogo	ouédraogo	PROPN
ejpam-4931	586	9	/	/	SYM
ejpam-4931	586	10	eur	eur	PROPN
ejpam-4931	586	11	.	.	PUNCT
ejpam-4931	587	1	j.	j.	PROPN
ejpam-4931	587	2	pure	pure	PROPN
ejpam-4931	587	3	appl	appl	PROPN
ejpam-4931	587	4	.	.	PROPN
ejpam-4931	587	5	math	math	PROPN
ejpam-4931	587	6	,	,	PUNCT
ejpam-4931	587	7	16	16	NUM
ejpam-4931	587	8	(	(	PUNCT
ejpam-4931	587	9	4	4	NUM
ejpam-4931	587	10	)	)	PUNCT
ejpam-4931	587	11	(	(	PUNCT
ejpam-4931	587	12	2023	2023	NUM
ejpam-4931	587	13	)	)	PUNCT
ejpam-4931	587	14	,	,	PUNCT
ejpam-4931	587	15	2247	2247	NUM
ejpam-4931	587	16	-	-	SYM
ejpam-4931	587	17	2285	2285	NUM
ejpam-4931	587	18	2268	2268	NUM
ejpam-4931	587	19	•	•	NOUN
ejpam-4931	587	20	−	−	PROPN
ejpam-4931	588	1	∫	∫	PROPN
ejpam-4931	588	2	ω	ω	X
ejpam-4931	588	3	∂y(ξ∂yu)ψdxdy	∂y(ξ∂yu)ψdxdy	X
ejpam-4931	589	1	=	=	PUNCT
ejpam-4931	589	2	−	−	PROPN
ejpam-4931	589	3	∫	∫	PROPN
ejpam-4931	589	4	ω	ω	NUM
ejpam-4931	589	5	∂y(ξ∂yu)udxdy	∂y(ξ∂yu)udxdy	NUM
ejpam-4931	589	6	=	=	SYM
ejpam-4931	589	7	∫	∫	PROPN
ejpam-4931	589	8	ω	ω	PROPN
ejpam-4931	589	9	ξ|∂yu|2dxdy	ξ|∂yu|2dxdy	PROPN
ejpam-4931	589	10	,	,	PUNCT
ejpam-4931	589	11	(	(	PUNCT
ejpam-4931	589	12	76	76	NUM
ejpam-4931	589	13	)	)	PUNCT
ejpam-4931	589	14	since	since	SCONJ
ejpam-4931	589	15	∫	∫	PROPN
ejpam-4931	589	16	ω	ω	PROPN
ejpam-4931	589	17	∂y(ξ∂yu)∇x	∂y(ξ∂yu)∇x	NOUN
ejpam-4931	589	18	ln	ln	PROPN
ejpam-4931	589	19	ξdxdy	ξdxdy	NOUN
ejpam-4931	589	20	=	=	SYM
ejpam-4931	589	21	0	0	X
ejpam-4931	589	22	.	.	PUNCT
ejpam-4931	590	1	using	use	VERB
ejpam-4931	590	2	(	(	PUNCT
ejpam-4931	590	3	26	26	NUM
ejpam-4931	590	4	)	)	PUNCT
ejpam-4931	590	5	,	,	PUNCT
ejpam-4931	590	6	we	we	PRON
ejpam-4931	590	7	get	get	VERB
ejpam-4931	590	8	•	•	NUM
ejpam-4931	590	9	∫	∫	PROPN
ejpam-4931	590	10	ω	ω	PROPN
ejpam-4931	590	11	∇xξ	∇xξ	PROPN
ejpam-4931	590	12	2ψdxdy	2ψdxdy	NUM
ejpam-4931	591	1	=	=	SYM
ejpam-4931	591	2	∫	∫	PROPN
ejpam-4931	591	3	ω	ω	PROPN
ejpam-4931	591	4	∇xξ	∇xξ	PROPN
ejpam-4931	591	5	2udxdy	2udxdy	NUM
ejpam-4931	591	6	+	+	CCONJ
ejpam-4931	591	7	2	2	NUM
ejpam-4931	591	8	∫	∫	PROPN
ejpam-4931	591	9	ω	ω	PROPN
ejpam-4931	591	10	∇xξ	∇xξ	PROPN
ejpam-4931	591	11	2∇x	2∇x	NUM
ejpam-4931	591	12	ln	ln	NOUN
ejpam-4931	591	13	ξdxdy	ξdxdy	NOUN
ejpam-4931	592	1	=	=	SYM
ejpam-4931	592	2	d	d	NOUN
ejpam-4931	592	3	dt	dt	X
ejpam-4931	593	1	∫	∫	PROPN
ejpam-4931	593	2	ω	ω	PROPN
ejpam-4931	593	3	ξ2dxdy	ξ2dxdy	PROPN
ejpam-4931	593	4	+	+	CCONJ
ejpam-4931	593	5	2ϵ	2ϵ	NUM
ejpam-4931	593	6	∫	∫	PROPN
ejpam-4931	593	7	ω	ω	NUM
ejpam-4931	593	8	|∇xξ|2	|∇xξ|2	PROPN
ejpam-4931	593	9	dxdy	dxdy	PROPN
ejpam-4931	593	10	+	+	CCONJ
ejpam-4931	593	11	2	2	NUM
ejpam-4931	593	12	∫	∫	NOUN
ejpam-4931	593	13	ω	ω	NUM
ejpam-4931	593	14	2ξ	2ξ	NUM
ejpam-4931	593	15	√	√	PROPN
ejpam-4931	593	16	ξ∇x	ξ∇x	PROPN
ejpam-4931	593	17	√	√	NUM
ejpam-4931	593	18	ξ	ξ	SYM
ejpam-4931	593	19	.	.	NOUN
ejpam-4931	593	20	2	2	NUM
ejpam-4931	593	21	√	√	NUM
ejpam-4931	593	22	ξ∇x	ξ∇x	PROPN
ejpam-4931	593	23	√	√	NUM
ejpam-4931	593	24	ξ	ξ	SYM
ejpam-4931	593	25	ξ	ξ	X
ejpam-4931	593	26	dxdy	dxdy	NOUN
ejpam-4931	593	27	=	=	PUNCT
ejpam-4931	594	1	d	d	PROPN
ejpam-4931	594	2	dt	dt	X
ejpam-4931	595	1	∫	∫	PROPN
ejpam-4931	595	2	ω	ω	PROPN
ejpam-4931	595	3	ξ2dxdy	ξ2dxdy	PROPN
ejpam-4931	595	4	+	+	CCONJ
ejpam-4931	595	5	2ϵ	2ϵ	NUM
ejpam-4931	595	6	∫	∫	PROPN
ejpam-4931	595	7	ω	ω	NUM
ejpam-4931	595	8	|∇xξ|2	|∇xξ|2	PROPN
ejpam-4931	595	9	dxdy	dxdy	PROPN
ejpam-4931	595	10	+	+	CCONJ
ejpam-4931	595	11	8	8	NUM
ejpam-4931	595	12	∫	∫	NOUN
ejpam-4931	595	13	ω	ω	NUM
ejpam-4931	595	14	ξ|∇x	ξ|∇x	ADJ
ejpam-4931	595	15	√	√	PROPN
ejpam-4931	595	16	ξ|2dxdy	ξ|2dxdy	PROPN
ejpam-4931	595	17	(	(	PUNCT
ejpam-4931	595	18	77	77	NUM
ejpam-4931	595	19	)	)	PUNCT
ejpam-4931	595	20	on	on	ADP
ejpam-4931	595	21	another	another	DET
ejpam-4931	595	22	note	note	NOUN
ejpam-4931	595	23	,	,	PUNCT
ejpam-4931	595	24	•	•	NUM
ejpam-4931	595	25	∫	∫	PROPN
ejpam-4931	595	26	ω	ω	PROPN
ejpam-4931	595	27	r1uψdxdy	r1uψdxdy	PROPN
ejpam-4931	595	28	=	=	PROPN
ejpam-4931	595	29	r1	r1	PROPN
ejpam-4931	595	30	∫	∫	PROPN
ejpam-4931	595	31	ω	ω	PROPN
ejpam-4931	595	32	u2dxdy	u2dxdy	PROPN
ejpam-4931	595	33	+	+	NOUN
ejpam-4931	595	34	2r1	2r1	NUM
ejpam-4931	595	35	∫	∫	PROPN
ejpam-4931	595	36	ω	ω	X
ejpam-4931	595	37	u∇x	u∇x	NUM
ejpam-4931	595	38	ln	ln	PROPN
ejpam-4931	595	39	ξdxdy	ξdxdy	NOUN
ejpam-4931	595	40	=	=	SYM
ejpam-4931	595	41	r1	r1	PROPN
ejpam-4931	595	42	∫	∫	PROPN
ejpam-4931	595	43	ω	ω	PROPN
ejpam-4931	595	44	u2dxdy	u2dxdy	PROPN
ejpam-4931	595	45	+	+	NOUN
ejpam-4931	595	46	2r1	2r1	NUM
ejpam-4931	595	47	∫	∫	PROPN
ejpam-4931	595	48	ω	ω	NUM
ejpam-4931	595	49	u	u	PROPN
ejpam-4931	595	50	∇xξ	∇xξ	PROPN
ejpam-4931	595	51	ξ	ξ	PROPN
ejpam-4931	595	52	dxdy	dxdy	PROPN
ejpam-4931	595	53	(	(	PUNCT
ejpam-4931	595	54	78	78	NUM
ejpam-4931	595	55	)	)	PUNCT
ejpam-4931	595	56	and	and	CCONJ
ejpam-4931	595	57	•	•	NUM
ejpam-4931	595	58	∫	∫	PROPN
ejpam-4931	595	59	ω	ω	NUM
ejpam-4931	596	1	α∆2uψdxdz	α∆2uψdxdz	PROPN
ejpam-4931	596	2	=	=	SYM
ejpam-4931	596	3	α	α	PROPN
ejpam-4931	596	4	∫	∫	PROPN
ejpam-4931	596	5	ω	ω	PROPN
ejpam-4931	596	6	∆2	∆2	PROPN
ejpam-4931	596	7	xu.udxdy	xu.udxdy	PUNCT
ejpam-4931	597	1	+	+	CCONJ
ejpam-4931	597	2	2α	2α	NOUN
ejpam-4931	597	3	∫	∫	PROPN
ejpam-4931	597	4	ω	ω	PROPN
ejpam-4931	597	5	∆2	∆2	PROPN
ejpam-4931	597	6	xu∇x	xu∇x	PROPN
ejpam-4931	597	7	ln	ln	PROPN
ejpam-4931	597	8	ξdxdy	ξdxdy	NOUN
ejpam-4931	597	9	=	=	SYM
ejpam-4931	598	1	α	α	PROPN
ejpam-4931	598	2	∫	∫	PROPN
ejpam-4931	598	3	ω	ω	NUM
ejpam-4931	598	4	|∆xu|2dxdy	|∆xu|2dxdy	PROPN
ejpam-4931	598	5	+	+	CCONJ
ejpam-4931	598	6	2α	2α	NUM
ejpam-4931	598	7	∫	∫	PROPN
ejpam-4931	598	8	ω	ω	NOUN
ejpam-4931	598	9	∆xu∇x∆x	∆xu∇x∆x	NUM
ejpam-4931	598	10	ln	ln	ADJ
ejpam-4931	598	11	ξdxdy	ξdxdy	NOUN
ejpam-4931	598	12	.	.	PUNCT
ejpam-4931	599	1	(	(	PUNCT
ejpam-4931	599	2	79	79	NUM
ejpam-4931	599	3	)	)	PUNCT
ejpam-4931	599	4	referring	refer	VERB
ejpam-4931	599	5	to	to	ADP
ejpam-4931	599	6	(	(	PUNCT
ejpam-4931	599	7	27	27	NUM
ejpam-4931	599	8	)	)	PUNCT
ejpam-4931	599	9	,	,	PUNCT
ejpam-4931	599	10	we	we	PRON
ejpam-4931	599	11	obtain	obtain	VERB
ejpam-4931	599	12	•	•	NUM
ejpam-4931	599	13	−	−	PROPN
ejpam-4931	600	1	r2	r2	PROPN
ejpam-4931	600	2	∫	∫	PROPN
ejpam-4931	600	3	ω	ω	PROPN
ejpam-4931	600	4	∇xξ	∇xξ	PROPN
ejpam-4931	600	5	−βψdxdy	−βψdxdy	PUNCT
ejpam-4931	601	1	=	=	PUNCT
ejpam-4931	602	1	−r2	−r2	PROPN
ejpam-4931	602	2	∫	∫	PROPN
ejpam-4931	602	3	ω	ω	PROPN
ejpam-4931	602	4	∇xξ	∇xξ	PROPN
ejpam-4931	602	5	−βudxdy	−βudxdy	PROPN
ejpam-4931	603	1	−	−	X
ejpam-4931	604	1	2r2	2r2	NUM
ejpam-4931	604	2	∫	∫	PROPN
ejpam-4931	604	3	ω	ω	PROPN
ejpam-4931	604	4	∇xξ	∇xξ	PROPN
ejpam-4931	604	5	−β∇x	−β∇x	PROPN
ejpam-4931	604	6	ln	ln	PROPN
ejpam-4931	604	7	ξdxdy	ξdxdy	NOUN
ejpam-4931	604	8	=	=	SYM
ejpam-4931	604	9	r2	r2	PROPN
ejpam-4931	604	10	β	β	X
ejpam-4931	604	11	+	+	NOUN
ejpam-4931	604	12	1	1	NUM
ejpam-4931	604	13	d	d	NOUN
ejpam-4931	604	14	dt	dt	X
ejpam-4931	604	15	∫	∫	PROPN
ejpam-4931	604	16	ω	ω	PROPN
ejpam-4931	604	17	ξ−β	ξ−β	PROPN
ejpam-4931	604	18	n	n	PRON
ejpam-4931	604	19	dxdy	dxdy	PROPN
ejpam-4931	604	20	+	+	CCONJ
ejpam-4931	604	21	4r2	4r2	NUM
ejpam-4931	604	22	β	β	X
ejpam-4931	604	23	(	(	PUNCT
ejpam-4931	604	24	ϵ+	ϵ+	X
ejpam-4931	604	25	4	4	X
ejpam-4931	604	26	)	)	PUNCT
ejpam-4931	604	27	∫	∫	PROPN
ejpam-4931	605	1	ω	ω	NUM
ejpam-4931	605	2	|∇xξ	|∇xξ	PROPN
ejpam-4931	605	3	−β	−β	ADJ
ejpam-4931	605	4	2	2	NUM
ejpam-4931	605	5	n	n	NUM
ejpam-4931	605	6	|2dxdy	|2dxdy	NOUN
ejpam-4931	605	7	.	.	PUNCT
ejpam-4931	606	1	(	(	PUNCT
ejpam-4931	606	2	80	80	NUM
ejpam-4931	606	3	)	)	PUNCT
ejpam-4931	606	4	as	as	ADP
ejpam-4931	606	5	in	in	ADP
ejpam-4931	606	6	(	(	PUNCT
ejpam-4931	606	7	28	28	NUM
ejpam-4931	606	8	)	)	PUNCT
ejpam-4931	606	9	,	,	PUNCT
ejpam-4931	606	10	we	we	PRON
ejpam-4931	606	11	get	get	VERB
ejpam-4931	606	12	•	•	NOUN
ejpam-4931	606	13	−	−	NOUN
ejpam-4931	607	1	δ	δ	X
ejpam-4931	607	2	∫	∫	PROPN
ejpam-4931	607	3	ω	ω	PROPN
ejpam-4931	607	4	(	(	PUNCT
ejpam-4931	607	5	ξ∇x∆	ξ∇x∆	PROPN
ejpam-4931	607	6	5	5	NUM
ejpam-4931	607	7	xξ)ψdxdy	xξ)ψdxdy	NOUN
ejpam-4931	607	8	=	=	SYM
ejpam-4931	607	9	δ	δ	PROPN
ejpam-4931	607	10	∫	∫	PROPN
ejpam-4931	607	11	ω	ω	PROPN
ejpam-4931	607	12	divx(ξu)∆	divx(ξu)∆	NUM
ejpam-4931	607	13	5	5	NUM
ejpam-4931	607	14	xξdxdy	xξdxdy	NOUN
ejpam-4931	607	15	+	+	X
ejpam-4931	607	16	2δ	2δ	NUM
ejpam-4931	607	17	∫	∫	PROPN
ejpam-4931	607	18	ω	ω	PROPN
ejpam-4931	607	19	∆xξ∆	∆xξ∆	PROPN
ejpam-4931	607	20	5	5	NUM
ejpam-4931	607	21	xξdxdy	xξdxdy	X
ejpam-4931	607	22	=	=	SYM
ejpam-4931	607	23	δ	δ	PROPN
ejpam-4931	607	24	2	2	NUM
ejpam-4931	607	25	d	d	NOUN
ejpam-4931	607	26	dt	dt	X
ejpam-4931	607	27	∫	∫	PROPN
ejpam-4931	607	28	ω	ω	PROPN
ejpam-4931	607	29	|∇x∆	|∇x∆	NOUN
ejpam-4931	607	30	2	2	NUM
ejpam-4931	607	31	xξ|2dxdy	xξ|2dxdy	PUNCT
ejpam-4931	608	1	+	+	CCONJ
ejpam-4931	608	2	δϵ	δϵ	PROPN
ejpam-4931	608	3	∫	∫	PROPN
ejpam-4931	608	4	ω	ω	PROPN
ejpam-4931	608	5	|∆3	|∆3	PROPN
ejpam-4931	608	6	xξ|2dxdy	xξ|2dxdy	PROPN
ejpam-4931	609	1	+	+	CCONJ
ejpam-4931	609	2	2δ	2δ	NUM
ejpam-4931	609	3	∫	∫	PROPN
ejpam-4931	609	4	ω	ω	PROPN
ejpam-4931	609	5	|∆3	|∆3	PROPN
ejpam-4931	609	6	xξ|2dxdy	xξ|2dxdy	PROPN
ejpam-4931	609	7	.	.	PUNCT
ejpam-4931	610	1	(	(	PUNCT
ejpam-4931	610	2	81	81	NUM
ejpam-4931	610	3	)	)	PUNCT
ejpam-4931	610	4	similarly	similarly	ADV
ejpam-4931	610	5	,	,	PUNCT
ejpam-4931	610	6	by	by	ADP
ejpam-4931	610	7	exploiting	exploit	VERB
ejpam-4931	610	8	(	(	PUNCT
ejpam-4931	610	9	29	29	NUM
ejpam-4931	610	10	)	)	PUNCT
ejpam-4931	610	11	,	,	PUNCT
ejpam-4931	610	12	we	we	PRON
ejpam-4931	610	13	finally	finally	ADV
ejpam-4931	610	14	obtain	obtain	VERB
ejpam-4931	610	15	•	•	NOUN
ejpam-4931	610	16	−	−	PROPN
ejpam-4931	611	1	k1	k1	PROPN
ejpam-4931	611	2	∫	∫	PROPN
ejpam-4931	611	3	ω	ω	PROPN
ejpam-4931	611	4	ξ∇x	ξ∇x	PROPN
ejpam-4931	611	5	(	(	PUNCT
ejpam-4931	611	6	∆x	∆x	PROPN
ejpam-4931	611	7	√	√	PROPN
ejpam-4931	611	8	ξ√	ξ√	PROPN
ejpam-4931	611	9	ξ	ξ	PROPN
ejpam-4931	611	10	)	)	PUNCT
ejpam-4931	611	11	ψdxdy	ψdxdy	NOUN
ejpam-4931	611	12	=	=	PROPN
ejpam-4931	611	13	k1	k1	PROPN
ejpam-4931	611	14	∫	∫	PROPN
ejpam-4931	611	15	ω	ω	PROPN
ejpam-4931	611	16	divx(ξu	divx(ξu	PROPN
ejpam-4931	611	17	)	)	PUNCT
ejpam-4931	611	18	(	(	PUNCT
ejpam-4931	611	19	∆x	∆x	PROPN
ejpam-4931	611	20	√	√	PROPN
ejpam-4931	611	21	ξ√	ξ√	PROPN
ejpam-4931	611	22	ξ	ξ	PROPN
ejpam-4931	611	23	)	)	PUNCT
ejpam-4931	611	24	dxdy	dxdy	NOUN
ejpam-4931	611	25	+	+	CCONJ
ejpam-4931	611	26	2k1	2k1	NUM
ejpam-4931	611	27	∫	∫	PROPN
ejpam-4931	611	28	ω	ω	PROPN
ejpam-4931	611	29	(	(	PUNCT
ejpam-4931	611	30	∆x	∆x	PROPN
ejpam-4931	611	31	√	√	PROPN
ejpam-4931	611	32	ξ√	ξ√	PROPN
ejpam-4931	611	33	ξ	ξ	PROPN
ejpam-4931	611	34	)	)	PUNCT
ejpam-4931	611	35	∆xξdxdy	∆xξdxdy	PROPN
ejpam-4931	611	36	j.	j.	PROPN
ejpam-4931	611	37	ouya	ouya	PROPN
ejpam-4931	611	38	,	,	PUNCT
ejpam-4931	611	39	a.	a.	NOUN
ejpam-4931	611	40	ouédraogo	ouédraogo	PROPN
ejpam-4931	611	41	/	/	SYM
ejpam-4931	611	42	eur	eur	PROPN
ejpam-4931	611	43	.	.	PUNCT
ejpam-4931	612	1	j.	j.	PROPN
ejpam-4931	612	2	pure	pure	PROPN
ejpam-4931	612	3	appl	appl	PROPN
ejpam-4931	612	4	.	.	PROPN
ejpam-4931	612	5	math	math	PROPN
ejpam-4931	612	6	,	,	PUNCT
ejpam-4931	612	7	16	16	NUM
ejpam-4931	612	8	(	(	PUNCT
ejpam-4931	612	9	4	4	NUM
ejpam-4931	612	10	)	)	PUNCT
ejpam-4931	612	11	(	(	PUNCT
ejpam-4931	612	12	2023	2023	NUM
ejpam-4931	612	13	)	)	PUNCT
ejpam-4931	612	14	,	,	PUNCT
ejpam-4931	613	1	2247	2247	NUM
ejpam-4931	613	2	-	-	SYM
ejpam-4931	613	3	2285	2285	NUM
ejpam-4931	613	4	2269	2269	NUM
ejpam-4931	613	5	=	=	SYM
ejpam-4931	613	6	k1	k1	PROPN
ejpam-4931	613	7	d	d	NOUN
ejpam-4931	613	8	dt	dt	X
ejpam-4931	614	1	∫	∫	PROPN
ejpam-4931	614	2	ω	ω	PROPN
ejpam-4931	614	3	|∇x	|∇x	VERB
ejpam-4931	614	4	√	√	PROPN
ejpam-4931	615	1	ξ|2	ξ|2	PROPN
ejpam-4931	615	2	+	+	CCONJ
ejpam-4931	615	3	k1ϵ	k1ϵ	PROPN
ejpam-4931	615	4	2	2	NUM
ejpam-4931	615	5	∫	∫	PROPN
ejpam-4931	615	6	ω	ω	NUM
ejpam-4931	615	7	ξ|∇2	ξ|∇2	PROPN
ejpam-4931	615	8	x	x	SYM
ejpam-4931	615	9	ln	ln	ADJ
ejpam-4931	615	10	ξ|2dxdy	ξ|2dxdy	NOUN
ejpam-4931	615	11	+	+	CCONJ
ejpam-4931	615	12	k1	k1	PROPN
ejpam-4931	615	13	∫	∫	PROPN
ejpam-4931	615	14	ω	ω	PROPN
ejpam-4931	615	15	ξ|∇2	ξ|∇2	PROPN
ejpam-4931	615	16	x	x	SYM
ejpam-4931	615	17	ln	ln	ADJ
ejpam-4931	615	18	ξ|2dxdy	ξ|2dxdy	NOUN
ejpam-4931	615	19	.	.	PUNCT
ejpam-4931	616	1	(	(	PUNCT
ejpam-4931	616	2	82	82	NUM
ejpam-4931	616	3	)	)	PUNCT
ejpam-4931	616	4	finally	finally	ADV
ejpam-4931	616	5	,	,	PUNCT
ejpam-4931	616	6	putting	put	VERB
ejpam-4931	616	7	the	the	DET
ejpam-4931	616	8	above	above	ADJ
ejpam-4931	616	9	results	result	NOUN
ejpam-4931	616	10	together	together	ADV
ejpam-4931	616	11	,	,	PUNCT
ejpam-4931	616	12	the	the	DET
ejpam-4931	616	13	equation	equation	NOUN
ejpam-4931	616	14	(	(	PUNCT
ejpam-4931	616	15	66	66	NUM
ejpam-4931	616	16	)	)	PUNCT
ejpam-4931	616	17	is	be	AUX
ejpam-4931	616	18	written	write	VERB
ejpam-4931	616	19	:	:	PUNCT
ejpam-4931	617	1	d	d	X
ejpam-4931	617	2	dt	dt	X
ejpam-4931	617	3	∫	∫	PROPN
ejpam-4931	617	4	ω	ω	PROPN
ejpam-4931	617	5	(	(	PUNCT
ejpam-4931	617	6	1	1	NUM
ejpam-4931	617	7	2	2	NUM
ejpam-4931	617	8	ξψ2	ξψ2	NOUN
ejpam-4931	617	9	+	+	CCONJ
ejpam-4931	617	10	ξ2	ξ2	NOUN
ejpam-4931	617	11	+	+	CCONJ
ejpam-4931	617	12	r2	r2	PROPN
ejpam-4931	617	13	β	β	X
ejpam-4931	617	14	+	+	CCONJ
ejpam-4931	617	15	1	1	NUM
ejpam-4931	617	16	ξ−β	ξ−β	VERB
ejpam-4931	617	17	+	+	NOUN
ejpam-4931	617	18	k1|∇x	k1|∇x	PROPN
ejpam-4931	617	19	√	√	PROPN
ejpam-4931	618	1	ξ|2	ξ|2	PROPN
ejpam-4931	618	2	+	+	CCONJ
ejpam-4931	618	3	δ	δ	PROPN
ejpam-4931	618	4	2	2	NUM
ejpam-4931	618	5	|∇x∆	|∇x∆	NOUN
ejpam-4931	618	6	2	2	NUM
ejpam-4931	618	7	xξ|2	xξ|2	PROPN
ejpam-4931	618	8	)	)	PUNCT
ejpam-4931	618	9	dxdy	dxdy	NOUN
ejpam-4931	618	10	+	+	CCONJ
ejpam-4931	618	11	2	2	NUM
ejpam-4931	618	12	∫	∫	PROPN
ejpam-4931	618	13	ω	ω	NUM
ejpam-4931	618	14	ξ|∂yv|2dxdy	ξ|∂yv|2dxdy	PROPN
ejpam-4931	619	1	+	+	CCONJ
ejpam-4931	619	2	r	r	NOUN
ejpam-4931	619	3	∫	∫	PROPN
ejpam-4931	619	4	ω	ω	NUM
ejpam-4931	619	5	ξ|u|3dxdy	ξ|u|3dxdy	NOUN
ejpam-4931	619	6	+	+	CCONJ
ejpam-4931	619	7	∫	∫	PROPN
ejpam-4931	619	8	ω	ω	NUM
ejpam-4931	619	9	ξ|∂yu|2dxdy	ξ|∂yu|2dxdy	X
ejpam-4931	620	1	+	+	CCONJ
ejpam-4931	620	2	r1	r1	PROPN
ejpam-4931	620	3	∫	∫	PROPN
ejpam-4931	620	4	ω	ω	PROPN
ejpam-4931	620	5	u2dxdy	u2dxdy	PROPN
ejpam-4931	620	6	+	+	NUM
ejpam-4931	620	7	4r2	4r2	NUM
ejpam-4931	620	8	β	β	X
ejpam-4931	620	9	(	(	PUNCT
ejpam-4931	620	10	ϵ+	ϵ+	X
ejpam-4931	620	11	4	4	X
ejpam-4931	620	12	)	)	PUNCT
ejpam-4931	620	13	∫	∫	PROPN
ejpam-4931	620	14	ω	ω	NUM
ejpam-4931	620	15	|∇xξ	|∇xξ	PROPN
ejpam-4931	620	16	−β/2|2dxdy	−β/2|2dxdy	NUM
ejpam-4931	620	17	+	+	CCONJ
ejpam-4931	620	18	α	α	PROPN
ejpam-4931	620	19	∫	∫	PROPN
ejpam-4931	620	20	ω	ω	NUM
ejpam-4931	620	21	|∆xu|2dxdy	|∆xu|2dxdy	PROPN
ejpam-4931	620	22	+	+	CCONJ
ejpam-4931	620	23	∫	∫	PROPN
ejpam-4931	620	24	ω	ω	NUM
ejpam-4931	620	25	2ξ|ax(u)|2dxdy	2ξ|ax(u)|2dxdy	NUM
ejpam-4931	621	1	+	+	X
ejpam-4931	621	2	k1(ϵ+	k1(ϵ+	PROPN
ejpam-4931	621	3	2	2	NUM
ejpam-4931	621	4	)	)	PUNCT
ejpam-4931	621	5	2	2	NUM
ejpam-4931	621	6	∫	∫	NOUN
ejpam-4931	621	7	ω	ω	NUM
ejpam-4931	621	8	ξ|∇2	ξ|∇2	PROPN
ejpam-4931	621	9	x	x	SYM
ejpam-4931	621	10	ln	ln	PROPN
ejpam-4931	621	11	ξ|2	ξ|2	NOUN
ejpam-4931	621	12	+	+	CCONJ
ejpam-4931	621	13	δ(ϵ+	δ(ϵ+	ADP
ejpam-4931	621	14	2	2	NUM
ejpam-4931	621	15	)	)	PUNCT
ejpam-4931	621	16	∫	∫	PROPN
ejpam-4931	621	17	ω	ω	PROPN
ejpam-4931	621	18	|∆3	|∆3	PROPN
ejpam-4931	621	19	xξ|2dxdy	xξ|2dxdy	PROPN
ejpam-4931	621	20	+	+	CCONJ
ejpam-4931	621	21	∫	∫	PROPN
ejpam-4931	621	22	ω	ω	NUM
ejpam-4931	621	23	2ϵ|∇xξ|2dxdy	2ϵ|∇xξ|2dxdy	NUM
ejpam-4931	622	1	+	+	CCONJ
ejpam-4931	622	2	8	8	NUM
ejpam-4931	622	3	∫	∫	NOUN
ejpam-4931	622	4	ω	ω	NUM
ejpam-4931	622	5	ξ|∇x	ξ|∇x	ADJ
ejpam-4931	622	6	√	√	VERB
ejpam-4931	623	1	ξ|2dxdy	ξ|2dxdy	NOUN
ejpam-4931	623	2	=	=	SYM
ejpam-4931	623	3	2	2	NUM
ejpam-4931	623	4	∫	∫	NOUN
ejpam-4931	623	5	ω	ω	NUM
ejpam-4931	623	6	divx(2ξax(u))∇x	divx(2ξax(u))∇x	PROPN
ejpam-4931	623	7	ln	ln	NOUN
ejpam-4931	623	8	ξdxdy	ξdxdy	NOUN
ejpam-4931	624	1	−	−	PROPN
ejpam-4931	624	2	2α	2α	PROPN
ejpam-4931	624	3	∫	∫	PROPN
ejpam-4931	624	4	ω	ω	NOUN
ejpam-4931	624	5	∆xu∇x∆x	∆xu∇x∆x	NUM
ejpam-4931	624	6	ln	ln	ADJ
ejpam-4931	624	7	ξdxdy	ξdxdy	NOUN
ejpam-4931	624	8	+	+	CCONJ
ejpam-4931	624	9	2ϵ	2ϵ	NUM
ejpam-4931	624	10	∫	∫	PROPN
ejpam-4931	624	11	ω	ω	X
ejpam-4931	624	12	∇xξ	∇xξ	PROPN
ejpam-4931	624	13	·	·	PUNCT
ejpam-4931	624	14	∇2	∇2	PROPN
ejpam-4931	624	15	x	x	SYM
ejpam-4931	624	16	ln	ln	PROPN
ejpam-4931	624	17	ξ	ξ	PROPN
ejpam-4931	624	18	·	·	PUNCT
ejpam-4931	624	19	udxdy	udxdy	PROPN
ejpam-4931	624	20	+	+	X
ejpam-4931	624	21	4ϵ	4ϵ	PROPN
ejpam-4931	624	22	∫	∫	PROPN
ejpam-4931	624	23	ω	ω	PROPN
ejpam-4931	624	24	∇xξ	∇xξ	PROPN
ejpam-4931	624	25	·	·	PUNCT
ejpam-4931	624	26	∇2	∇2	PROPN
ejpam-4931	624	27	x	x	SYM
ejpam-4931	624	28	ln	ln	PROPN
ejpam-4931	624	29	ξ	ξ	PROPN
ejpam-4931	624	30	·	·	PUNCT
ejpam-4931	624	31	∇x	∇x	PROPN
ejpam-4931	624	32	ln	ln	ADJ
ejpam-4931	624	33	ξdxdy	ξdxdy	NOUN
ejpam-4931	624	34	+	+	CCONJ
ejpam-4931	624	35	2ϵ	2ϵ	NUM
ejpam-4931	624	36	∫	∫	PROPN
ejpam-4931	625	1	ω	ω	PROPN
ejpam-4931	625	2	∇x∆xξψdxdy	∇x∆xξψdxdy	PROPN
ejpam-4931	625	3	−	−	PROPN
ejpam-4931	625	4	2r	2r	NUM
ejpam-4931	625	5	∫	∫	PROPN
ejpam-4931	625	6	ω	ω	PROPN
ejpam-4931	625	7	|u|u∇xξdxdy	|u|u∇xξdxdy	X
ejpam-4931	625	8	−	−	PROPN
ejpam-4931	625	9	2r1	2r1	NUM
ejpam-4931	625	10	∫	∫	PROPN
ejpam-4931	625	11	ω	ω	NUM
ejpam-4931	625	12	u	u	PROPN
ejpam-4931	625	13	∇xξ	∇xξ	PROPN
ejpam-4931	625	14	ξ	ξ	PROPN
ejpam-4931	625	15	dxdy	dxdy	NOUN
ejpam-4931	625	16	=	=	NOUN
ejpam-4931	625	17	7∑	7∑	NUM
ejpam-4931	625	18	i=1	i=1	PROPN
ejpam-4931	625	19	ii	ii	PROPN
ejpam-4931	625	20	.	.	PUNCT
ejpam-4931	626	1	(	(	PUNCT
ejpam-4931	626	2	83	83	NUM
ejpam-4931	626	3	)	)	PUNCT
ejpam-4931	626	4	we	we	PRON
ejpam-4931	626	5	have	have	VERB
ejpam-4931	626	6	i1	i1	PROPN
ejpam-4931	626	7	=	=	PUNCT
ejpam-4931	626	8	0	0	PUNCT
ejpam-4931	627	1	due	due	ADP
ejpam-4931	627	2	to	to	ADP
ejpam-4931	627	3	the	the	DET
ejpam-4931	627	4	periodic	periodic	ADJ
ejpam-4931	627	5	conditions	condition	NOUN
ejpam-4931	627	6	on	on	ADP
ejpam-4931	627	7	ωx	ωx	PRON
ejpam-4931	627	8	,	,	PUNCT
ejpam-4931	627	9	that	that	ADV
ejpam-4931	627	10	is	is	ADV
ejpam-4931	627	11	,	,	PUNCT
ejpam-4931	627	12	2	2	NUM
ejpam-4931	627	13	∫	∫	NOUN
ejpam-4931	627	14	ω	ω	PROPN
ejpam-4931	627	15	divx(2ξax(u))∇x	divx(2ξax(u))∇x	PROPN
ejpam-4931	627	16	ln	ln	NOUN
ejpam-4931	627	17	ξdxdy	ξdxdy	NOUN
ejpam-4931	627	18	=	=	SYM
ejpam-4931	627	19	∫	∫	PROPN
ejpam-4931	627	20	ω	ω	PROPN
ejpam-4931	627	21	∂i	∂i	PROPN
ejpam-4931	627	22	(	(	PUNCT
ejpam-4931	627	23	ξ(∂iuj	ξ(∂iuj	NOUN
ejpam-4931	627	24	−	−	NOUN
ejpam-4931	627	25	∂jui	∂jui	NUM
ejpam-4931	627	26	)	)	PUNCT
ejpam-4931	627	27	)	)	PUNCT
ejpam-4931	627	28	∂jξ	∂jξ	VERB
ejpam-4931	627	29	ξ	ξ	PRON
ejpam-4931	627	30	dxdy	dxdy	NOUN
ejpam-4931	627	31	=	=	SYM
ejpam-4931	627	32	∫	∫	PROPN
ejpam-4931	627	33	ω	ω	PROPN
ejpam-4931	627	34	(	(	PUNCT
ejpam-4931	627	35	∂iξ∂jξ	∂iξ∂jξ	PROPN
ejpam-4931	627	36	ξ	ξ	PROPN
ejpam-4931	627	37	(	(	PUNCT
ejpam-4931	627	38	∂iuj	∂iuj	NOUN
ejpam-4931	627	39	−	−	PROPN
ejpam-4931	627	40	∂j	∂j	PROPN
ejpam-4931	627	41	)	)	PUNCT
ejpam-4931	628	1	+	+	CCONJ
ejpam-4931	628	2	(	(	PUNCT
ejpam-4931	628	3	∂i∂iuj	∂i∂iuj	INTJ
ejpam-4931	628	4	−	−	PROPN
ejpam-4931	628	5	∂i∂jui)∂jξ	∂i∂jui)∂jξ	NOUN
ejpam-4931	628	6	)	)	PUNCT
ejpam-4931	628	7	dxdy	dxdy	PROPN
ejpam-4931	628	8	=	=	SYM
ejpam-4931	628	9	∫	∫	PROPN
ejpam-4931	628	10	ω	ω	PROPN
ejpam-4931	628	11	(	(	PUNCT
ejpam-4931	628	12	∂i∂iuj∂jξ	∂i∂iuj∂jξ	PROPN
ejpam-4931	628	13	−	−	PROPN
ejpam-4931	628	14	∂i∂jui∂jξ)dxdy	∂i∂jui∂jξ)dxdy	NOUN
ejpam-4931	628	15	=	=	SYM
ejpam-4931	628	16	∫	∫	PROPN
ejpam-4931	628	17	ω	ω	PROPN
ejpam-4931	628	18	(	(	PUNCT
ejpam-4931	628	19	∂i∂iuj∂jξ	∂i∂iuj∂jξ	PROPN
ejpam-4931	628	20	−	−	NOUN
ejpam-4931	628	21	∂j∂jui∂iξ)dxdy	∂j∂jui∂iξ)dxdy	NOUN
ejpam-4931	628	22	=	=	NOUN
ejpam-4931	628	23	0	0	PROPN
ejpam-4931	628	24	.	.	PUNCT
ejpam-4931	628	25	(	(	PUNCT
ejpam-4931	628	26	84	84	NUM
ejpam-4931	628	27	)	)	PUNCT
ejpam-4931	628	28	for	for	ADP
ejpam-4931	628	29	i7	i7	NOUN
ejpam-4931	628	30	,	,	PUNCT
ejpam-4931	628	31	we	we	PRON
ejpam-4931	628	32	have	have	VERB
ejpam-4931	628	33	,	,	PUNCT
ejpam-4931	628	34	i7	i7	NOUN
ejpam-4931	628	35	=	=	SYM
ejpam-4931	628	36	−2r1	−2r1	NUM
ejpam-4931	628	37	∫	∫	PROPN
ejpam-4931	628	38	ω	ω	NUM
ejpam-4931	628	39	u	u	PROPN
ejpam-4931	628	40	∇xξ	∇xξ	PROPN
ejpam-4931	628	41	ξ	ξ	PROPN
ejpam-4931	628	42	dxdy	dxdy	NOUN
ejpam-4931	628	43	=	=	PUNCT
ejpam-4931	628	44	−2r1	−2r1	NUM
ejpam-4931	628	45	∫	∫	PROPN
ejpam-4931	628	46	ω	ω	PROPN
ejpam-4931	628	47	divx(ξu	divx(ξu	PROPN
ejpam-4931	628	48	)	)	PUNCT
ejpam-4931	628	49	ξ	ξ	PROPN
ejpam-4931	628	50	dxdy	dxdy	NOUN
ejpam-4931	628	51	=	=	SYM
ejpam-4931	628	52	2r1	2r1	NUM
ejpam-4931	628	53	∫	∫	PROPN
ejpam-4931	628	54	ω	ω	PROPN
ejpam-4931	628	55	∂tξ	∂tξ	PROPN
ejpam-4931	628	56	+	+	CCONJ
ejpam-4931	628	57	∂y(ξv)−	∂y(ξv)−	ADJ
ejpam-4931	628	58	ε∆xξ	ε∆xξ	NOUN
ejpam-4931	628	59	ξ	ξ	X
ejpam-4931	628	60	dxdy	dxdy	NOUN
ejpam-4931	628	61	=	=	SYM
ejpam-4931	628	62	2r1	2r1	NUM
ejpam-4931	628	63	∫	∫	PROPN
ejpam-4931	628	64	ω	ω	PROPN
ejpam-4931	628	65	∂t	∂t	PROPN
ejpam-4931	628	66	ln	ln	PROPN
ejpam-4931	628	67	ξdxdy	ξdxdy	NOUN
ejpam-4931	629	1	−	−	PROPN
ejpam-4931	630	1	2r1ϵ	2r1ϵ	NUM
ejpam-4931	630	2	∫	∫	PROPN
ejpam-4931	630	3	ω	ω	NUM
ejpam-4931	630	4	∆xξ	∆xξ	PROPN
ejpam-4931	630	5	ξ	ξ	X
ejpam-4931	630	6	dxdy	dxdy	NOUN
ejpam-4931	630	7	=	=	PUNCT
ejpam-4931	631	1	2r1	2r1	NUM
ejpam-4931	631	2	d	d	NOUN
ejpam-4931	631	3	dt	dt	X
ejpam-4931	631	4	∫	∫	PROPN
ejpam-4931	631	5	ω	ω	PROPN
ejpam-4931	631	6	ln	ln	PROPN
ejpam-4931	631	7	ξdxdy	ξdxdy	PROPN
ejpam-4931	631	8	−	−	PROPN
ejpam-4931	632	1	2r1ϵ	2r1ϵ	NUM
ejpam-4931	632	2	∫	∫	PROPN
ejpam-4931	632	3	ω	ω	NUM
ejpam-4931	632	4	|∇xξ|2	|∇xξ|2	PROPN
ejpam-4931	632	5	ξ2	ξ2	PROPN
ejpam-4931	632	6	dxdy	dxdy	PROPN
ejpam-4931	632	7	.	.	PUNCT
ejpam-4931	633	1	(	(	PUNCT
ejpam-4931	633	2	85	85	NUM
ejpam-4931	633	3	)	)	PUNCT
ejpam-4931	633	4	j.	j.	PROPN
ejpam-4931	633	5	ouya	ouya	PROPN
ejpam-4931	633	6	,	,	PUNCT
ejpam-4931	633	7	a.	a.	NOUN
ejpam-4931	633	8	ouédraogo	ouédraogo	PROPN
ejpam-4931	633	9	/	/	SYM
ejpam-4931	633	10	eur	eur	PROPN
ejpam-4931	633	11	.	.	PUNCT
ejpam-4931	634	1	j.	j.	PROPN
ejpam-4931	634	2	pure	pure	PROPN
ejpam-4931	634	3	appl	appl	PROPN
ejpam-4931	634	4	.	.	PROPN
ejpam-4931	634	5	math	math	PROPN
ejpam-4931	634	6	,	,	PUNCT
ejpam-4931	634	7	16	16	NUM
ejpam-4931	634	8	(	(	PUNCT
ejpam-4931	634	9	4	4	NUM
ejpam-4931	634	10	)	)	PUNCT
ejpam-4931	634	11	(	(	PUNCT
ejpam-4931	634	12	2023	2023	NUM
ejpam-4931	634	13	)	)	PUNCT
ejpam-4931	634	14	,	,	PUNCT
ejpam-4931	634	15	2247	2247	NUM
ejpam-4931	634	16	-	-	SYM
ejpam-4931	634	17	2285	2285	NUM
ejpam-4931	634	18	2270	2270	NUM
ejpam-4931	634	19	substituting	substituting	NOUN
ejpam-4931	634	20	(	(	PUNCT
ejpam-4931	634	21	84	84	NUM
ejpam-4931	634	22	)	)	PUNCT
ejpam-4931	634	23	and	and	CCONJ
ejpam-4931	634	24	(	(	PUNCT
ejpam-4931	634	25	85	85	NUM
ejpam-4931	634	26	)	)	PUNCT
ejpam-4931	634	27	into	into	ADP
ejpam-4931	634	28	(	(	PUNCT
ejpam-4931	634	29	83	83	NUM
ejpam-4931	634	30	)	)	PUNCT
ejpam-4931	634	31	and	and	CCONJ
ejpam-4931	634	32	integrating	integrate	VERB
ejpam-4931	634	33	with	with	ADP
ejpam-4931	634	34	respect	respect	NOUN
ejpam-4931	634	35	to	to	ADP
ejpam-4931	634	36	time	time	NOUN
ejpam-4931	634	37	t	t	PROPN
ejpam-4931	634	38	,	,	PUNCT
ejpam-4931	634	39	we	we	PRON
ejpam-4931	634	40	obtain∫	obtain∫	VERB
ejpam-4931	634	41	ω	ω	X
ejpam-4931	634	42	(	(	PUNCT
ejpam-4931	634	43	1	1	NUM
ejpam-4931	634	44	2	2	NUM
ejpam-4931	634	45	ξ|ψ|2	ξ|ψ|2	ADJ
ejpam-4931	634	46	−	−	PROPN
ejpam-4931	634	47	2r1	2r1	NUM
ejpam-4931	634	48	ln	ln	PROPN
ejpam-4931	634	49	ξ	ξ	PROPN
ejpam-4931	634	50	)	)	PUNCT
ejpam-4931	634	51	dxdy	dxdy	NOUN
ejpam-4931	634	52	+	+	CCONJ
ejpam-4931	634	53	2	2	NUM
ejpam-4931	634	54	∫	∫	NOUN
ejpam-4931	634	55	t	t	PROPN
ejpam-4931	634	56	0	0	NUM
ejpam-4931	634	57	∫	∫	PROPN
ejpam-4931	634	58	ω	ω	NUM
ejpam-4931	634	59	ξ|∂yv|2dxdydt+	ξ|∂yv|2dxdydt+	PROPN
ejpam-4931	635	1	r	r	NOUN
ejpam-4931	635	2	∫	∫	PROPN
ejpam-4931	635	3	t	t	PROPN
ejpam-4931	635	4	0	0	NUM
ejpam-4931	635	5	∫	∫	PROPN
ejpam-4931	635	6	ω	ω	NUM
ejpam-4931	635	7	ξ|u|3dxdydt	ξ|u|3dxdydt	PROPN
ejpam-4931	635	8	+	+	CCONJ
ejpam-4931	635	9	16r2	16r2	NUM
ejpam-4931	635	10	β	β	NOUN
ejpam-4931	635	11	∫	∫	PROPN
ejpam-4931	635	12	t	t	PROPN
ejpam-4931	635	13	0	0	NUM
ejpam-4931	635	14	∫	∫	PROPN
ejpam-4931	636	1	ω	ω	PROPN
ejpam-4931	636	2	|∇xξ	|∇xξ	PROPN
ejpam-4931	636	3	−β/2|2dxdydt+	−β/2|2dxdydt+	PROPN
ejpam-4931	636	4	α	α	NUM
ejpam-4931	636	5	∫	∫	PROPN
ejpam-4931	637	1	t	t	PROPN
ejpam-4931	637	2	0	0	NUM
ejpam-4931	637	3	∫	∫	PROPN
ejpam-4931	637	4	ω	ω	PROPN
ejpam-4931	637	5	|∆xu|2dxdydt+	|∆xu|2dxdydt+	PUNCT
ejpam-4931	638	1	r1	r1	PROPN
ejpam-4931	638	2	∫	∫	PROPN
ejpam-4931	638	3	t	t	PROPN
ejpam-4931	638	4	0	0	NUM
ejpam-4931	638	5	∫	∫	PROPN
ejpam-4931	638	6	ω	ω	PROPN
ejpam-4931	638	7	u2dxdydt	u2dxdydt	PROPN
ejpam-4931	638	8	+	+	PROPN
ejpam-4931	638	9	k1	k1	PROPN
ejpam-4931	638	10	∫	∫	PROPN
ejpam-4931	638	11	t	t	PROPN
ejpam-4931	638	12	0	0	NUM
ejpam-4931	638	13	∫	∫	PROPN
ejpam-4931	638	14	ω	ω	NUM
ejpam-4931	638	15	ξ|∇2	ξ|∇2	PROPN
ejpam-4931	639	1	x	x	SYM
ejpam-4931	639	2	ln	ln	PROPN
ejpam-4931	639	3	ξ|2	ξ|2	PROPN
ejpam-4931	639	4	+	+	CCONJ
ejpam-4931	639	5	2δ	2δ	NUM
ejpam-4931	639	6	∫	∫	PROPN
ejpam-4931	639	7	t	t	PROPN
ejpam-4931	639	8	0	0	NUM
ejpam-4931	639	9	∫	∫	PROPN
ejpam-4931	639	10	ω	ω	PROPN
ejpam-4931	639	11	|∆3	|∆3	NOUN
ejpam-4931	639	12	xξ|2dxdydt+	xξ|2dxdydt+	PROPN
ejpam-4931	639	13	2	2	NUM
ejpam-4931	639	14	∫	∫	NOUN
ejpam-4931	639	15	t	t	PROPN
ejpam-4931	639	16	0	0	NUM
ejpam-4931	639	17	∫	∫	PROPN
ejpam-4931	639	18	ω	ω	PROPN
ejpam-4931	640	1	ξ|ax(u)|2dxdydt	ξ|ax(u)|2dxdydt	PROPN
ejpam-4931	640	2	+	+	NUM
ejpam-4931	640	3	8	8	NUM
ejpam-4931	640	4	∫	∫	NOUN
ejpam-4931	640	5	t	t	PROPN
ejpam-4931	640	6	0	0	NUM
ejpam-4931	640	7	∫	∫	PROPN
ejpam-4931	640	8	ω	ω	NUM
ejpam-4931	640	9	ξ|∇x	ξ|∇x	PROPN
ejpam-4931	641	1	√	√	PROPN
ejpam-4931	641	2	ξ|2dxdydt+	ξ|2dxdydt+	NUM
ejpam-4931	642	1	2r1ϵ	2r1ϵ	NUM
ejpam-4931	642	2	∫	∫	PROPN
ejpam-4931	642	3	t	t	PROPN
ejpam-4931	642	4	0	0	NUM
ejpam-4931	643	1	∫	∫	PROPN
ejpam-4931	644	1	ω	ω	PROPN
ejpam-4931	644	2	|∇xξ|2	|∇xξ|2	NOUN
ejpam-4931	644	3	ξ2	ξ2	PROPN
ejpam-4931	644	4	dxdydt+	dxdydt+	ADP
ejpam-4931	644	5	∫	∫	PROPN
ejpam-4931	644	6	t	t	PROPN
ejpam-4931	644	7	0	0	NUM
ejpam-4931	645	1	∫	∫	PROPN
ejpam-4931	645	2	ω	ω	PROPN
ejpam-4931	645	3	ξ|∂yu|2dxdydt	ξ|∂yu|2dxdydt	PROPN
ejpam-4931	645	4	≤	≤	NUM
ejpam-4931	645	5	∫	∫	PROPN
ejpam-4931	645	6	ω	ω	PROPN
ejpam-4931	645	7	(	(	PUNCT
ejpam-4931	645	8	ξ0u	ξ0u	NOUN
ejpam-4931	645	9	2	2	NUM
ejpam-4931	645	10	0	0	NUM
ejpam-4931	645	11	+	+	CCONJ
ejpam-4931	645	12	10(∇x	10(∇x	NUM
ejpam-4931	645	13	√	√	ADJ
ejpam-4931	645	14	ξ0	ξ0	PROPN
ejpam-4931	645	15	)	)	PUNCT
ejpam-4931	645	16	2	2	NUM
ejpam-4931	645	17	−	−	PROPN
ejpam-4931	645	18	2r1	2r1	NUM
ejpam-4931	645	19	ln	ln	ADJ
ejpam-4931	645	20	ξ0	ξ0	NOUN
ejpam-4931	645	21	)	)	PUNCT
ejpam-4931	645	22	dxdydt+	dxdydt+	NOUN
ejpam-4931	645	23	∫	∫	PROPN
ejpam-4931	645	24	t	t	PROPN
ejpam-4931	645	25	0	0	NUM
ejpam-4931	646	1	(	(	PUNCT
ejpam-4931	646	2	6∑	6∑	NUM
ejpam-4931	646	3	i=2	i=2	PROPN
ejpam-4931	646	4	ii	ii	PROPN
ejpam-4931	646	5	)	)	PUNCT
ejpam-4931	646	6	dt+	dt+	NOUN
ejpam-4931	646	7	e0	e0	PROPN
ejpam-4931	646	8	,	,	PUNCT
ejpam-4931	646	9	(	(	PUNCT
ejpam-4931	646	10	86	86	NUM
ejpam-4931	646	11	)	)	PUNCT
ejpam-4931	646	12	where	where	SCONJ
ejpam-4931	646	13	we	we	PRON
ejpam-4931	646	14	used	use	VERB
ejpam-4931	646	15	the	the	DET
ejpam-4931	646	16	energy	energy	NOUN
ejpam-4931	646	17	inequality	inequality	NOUN
ejpam-4931	646	18	(	(	PUNCT
ejpam-4931	646	19	59	59	NUM
ejpam-4931	646	20	)	)	PUNCT
ejpam-4931	646	21	.	.	PUNCT
ejpam-4931	647	1	now	now	ADV
ejpam-4931	647	2	,	,	PUNCT
ejpam-4931	647	3	we	we	PRON
ejpam-4931	647	4	control	control	VERB
ejpam-4931	647	5	the	the	DET
ejpam-4931	647	6	other	other	ADJ
ejpam-4931	647	7	terms	term	NOUN
ejpam-4931	647	8	ii	ii	VERB
ejpam-4931	647	9	in	in	ADP
ejpam-4931	647	10	(	(	PUNCT
ejpam-4931	647	11	86	86	NUM
ejpam-4931	647	12	)	)	PUNCT
ejpam-4931	647	13	.	.	PUNCT
ejpam-4931	648	1	•	•	NUM
ejpam-4931	648	2	∫	∫	PROPN
ejpam-4931	648	3	t	t	PROPN
ejpam-4931	648	4	0	0	NUM
ejpam-4931	648	5	i2dt	i2dt	PUNCT
ejpam-4931	648	6	=	=	PUNCT
ejpam-4931	649	1	−2α	−2α	PROPN
ejpam-4931	649	2	∫	∫	PROPN
ejpam-4931	649	3	t	t	PROPN
ejpam-4931	649	4	0	0	NUM
ejpam-4931	649	5	∫	∫	PROPN
ejpam-4931	649	6	ω	ω	NUM
ejpam-4931	649	7	∆xu	∆xu	X
ejpam-4931	649	8	·	·	PUNCT
ejpam-4931	649	9	∇x∆x	∇x∆x	ADP
ejpam-4931	649	10	ln	ln	ADJ
ejpam-4931	649	11	ξdxdydt	ξdxdydt	NOUN
ejpam-4931	649	12	=	=	SYM
ejpam-4931	650	1	−2α	−2α	PROPN
ejpam-4931	650	2	∫	∫	PROPN
ejpam-4931	650	3	t	t	PROPN
ejpam-4931	650	4	0	0	NUM
ejpam-4931	650	5	∫	∫	PROPN
ejpam-4931	650	6	ω	ω	NUM
ejpam-4931	650	7	∆xu	∆xu	X
ejpam-4931	650	8	·	·	PUNCT
ejpam-4931	650	9	(	(	PUNCT
ejpam-4931	650	10	∇x∆xξ	∇x∆xξ	PUNCT
ejpam-4931	650	11	ξ	ξ	X
ejpam-4931	650	12	−	−	PROPN
ejpam-4931	650	13	∆xξ∇xξ	∆xξ∇xξ	NOUN
ejpam-4931	650	14	ξ2	ξ2	NOUN
ejpam-4931	650	15	−	−	PROPN
ejpam-4931	650	16	2	2	NUM
ejpam-4931	650	17	(	(	PUNCT
ejpam-4931	650	18	∇xξ.∇xξ)∇xξ	∇xξ.∇xξ)∇xξ	NOUN
ejpam-4931	650	19	ξ2	ξ2	VERB
ejpam-4931	650	20	+	+	CCONJ
ejpam-4931	650	21	2	2	NUM
ejpam-4931	650	22	|∇xξ|2∇xξ	|∇xξ|2∇xξ	NOUN
ejpam-4931	650	23	ξ3	ξ3	NOUN
ejpam-4931	650	24	)	)	PUNCT
ejpam-4931	650	25	dxdydt	dxdydt	NOUN
ejpam-4931	650	26	≤	≤	NUM
ejpam-4931	650	27	cα	cα	ADP
ejpam-4931	650	28	∫	∫	PROPN
ejpam-4931	650	29	t	t	PROPN
ejpam-4931	650	30	0	0	NUM
ejpam-4931	650	31	∫	∫	PROPN
ejpam-4931	651	1	ω	ω	PROPN
ejpam-4931	651	2	|∆xu|	|∆xu|	PROPN
ejpam-4931	651	3	(	(	PUNCT
ejpam-4931	651	4	ξ−1|∇3	ξ−1|∇3	NOUN
ejpam-4931	651	5	xξ|+	xξ|+	NOUN
ejpam-4931	651	6	ξ−2|∇xξ||∇2	ξ−2|∇xξ||∇2	PROPN
ejpam-4931	651	7	xξ|+	xξ|+	PROPN
ejpam-4931	651	8	ξ−3|∇xξ|3	ξ−3|∇xξ|3	PROPN
ejpam-4931	651	9	)	)	PUNCT
ejpam-4931	651	10	dxdzdt	dxdzdt	NOUN
ejpam-4931	651	11	≤	≤	NUM
ejpam-4931	652	1	c	c	NOUN
ejpam-4931	652	2	√	√	PROPN
ejpam-4931	652	3	α∥	α∥	NUM
ejpam-4931	652	4	√	√	NUM
ejpam-4931	652	5	α∆xu∥l2(l2(ω	α∆xu∥l2(l2(ω	NOUN
ejpam-4931	652	6	)	)	PUNCT
ejpam-4931	652	7	)	)	PUNCT
ejpam-4931	653	1	[	[	PUNCT
ejpam-4931	653	2	∥ξ−1∥l∞(l∞(ω))∥∇3	∥ξ−1∥l∞(l∞(ω))∥∇3	NOUN
ejpam-4931	653	3	xξ∥l2(l2(ω	xξ∥l2(l2(ω	NUM
ejpam-4931	653	4	)	)	PUNCT
ejpam-4931	653	5	)	)	PUNCT
ejpam-4931	654	1	+	+	CCONJ
ejpam-4931	654	2	∥ξ−1∥2l∞(l∞(ω))∥∇xξ∥l∞(l∞(ω))∥∇2	∥ξ−1∥2l∞(l∞(ω))∥∇xξ∥l∞(l∞(ω))∥∇2	NOUN
ejpam-4931	654	3	xξ∥l2(l2(ω))+∥ξ−1∥3l∞(l∞(ω))∥∇xξ∥3l6(l6(ω	xξ∥l2(l2(ω))+∥ξ−1∥3l∞(l∞(ω))∥∇xξ∥3l6(l6(ω	X
ejpam-4931	654	4	)	)	PUNCT
ejpam-4931	654	5	)	)	PUNCT
ejpam-4931	654	6	]	]	PUNCT
ejpam-4931	655	1	≤	≤	NUM
ejpam-4931	656	1	c	c	NOUN
ejpam-4931	656	2	√	√	NUM
ejpam-4931	656	3	α∥	α∥	NUM
ejpam-4931	656	4	√	√	NUM
ejpam-4931	656	5	α∆xu∥l2(l2(ω	α∆xu∥l2(l2(ω	NOUN
ejpam-4931	656	6	)	)	PUNCT
ejpam-4931	656	7	)	)	PUNCT
ejpam-4931	657	1	[	[	PUNCT
ejpam-4931	657	2	∥ξ−1∥3l∞(l∞(ω))∥∇	∥ξ−1∥3l∞(l∞(ω))∥∇	ADJ
ejpam-4931	657	3	3	3	NUM
ejpam-4931	657	4	xξ∥l2(l2(ω))+∥ξ−1∥l∞(l∞(ω	xξ∥l2(l2(ω))+∥ξ−1∥l∞(l∞(ω	NUM
ejpam-4931	657	5	)	)	PUNCT
ejpam-4931	657	6	)	)	PUNCT
ejpam-4931	657	7	]	]	PUNCT
ejpam-4931	658	1	≤	≤	PROPN
ejpam-4931	658	2	c(δ	c(δ	PROPN
ejpam-4931	658	3	,	,	PUNCT
ejpam-4931	658	4	r2	r2	PROPN
ejpam-4931	658	5	)	)	PUNCT
ejpam-4931	658	6	√	√	NUM
ejpam-4931	658	7	α	α	X
ejpam-4931	658	8	.	.	PUNCT
ejpam-4931	659	1	(	(	PUNCT
ejpam-4931	659	2	87	87	NUM
ejpam-4931	659	3	)	)	PUNCT
ejpam-4931	659	4	•	•	NUM
ejpam-4931	659	5	∫	∫	PROPN
ejpam-4931	659	6	t	t	NOUN
ejpam-4931	659	7	0	0	NUM
ejpam-4931	659	8	i3dt	i3dt	PUNCT
ejpam-4931	659	9	=	=	SYM
ejpam-4931	660	1	2ϵ	2ϵ	NUM
ejpam-4931	661	1	∫	∫	PROPN
ejpam-4931	661	2	t	t	NOUN
ejpam-4931	661	3	0	0	NUM
ejpam-4931	662	1	∫	∫	PROPN
ejpam-4931	662	2	ω	ω	PROPN
ejpam-4931	662	3	∇xξ	∇xξ	PROPN
ejpam-4931	662	4	·	·	PUNCT
ejpam-4931	662	5	∇2	∇2	PROPN
ejpam-4931	662	6	x	x	SYM
ejpam-4931	662	7	ln	ln	PROPN
ejpam-4931	662	8	ξ	ξ	PROPN
ejpam-4931	662	9	·	·	PUNCT
ejpam-4931	662	10	udxdzdt	udxdzdt	PRON
ejpam-4931	662	11	=	=	PUNCT
ejpam-4931	662	12	−ϵ	−ϵ	PROPN
ejpam-4931	662	13	∫	∫	PROPN
ejpam-4931	663	1	t	t	PROPN
ejpam-4931	663	2	0	0	NUM
ejpam-4931	663	3	∫	∫	PROPN
ejpam-4931	663	4	ω	ω	PROPN
ejpam-4931	663	5	|∇xξ	|∇xξ	PROPN
ejpam-4931	663	6	ξ	ξ	PROPN
ejpam-4931	663	7	|2divx(ξu)dxdzdt	|2divx(ξu)dxdzdt	PUNCT
ejpam-4931	663	8	=	=	SYM
ejpam-4931	664	1	−ϵ	−ϵ	PROPN
ejpam-4931	664	2	∫	∫	PROPN
ejpam-4931	664	3	t	t	PROPN
ejpam-4931	664	4	0	0	NUM
ejpam-4931	665	1	∫	∫	PROPN
ejpam-4931	665	2	ω	ω	PROPN
ejpam-4931	665	3	(	(	PUNCT
ejpam-4931	665	4	|∇xξ|2	|∇xξ|2	ADP
ejpam-4931	665	5	ξ	ξ	PROPN
ejpam-4931	665	6	∇x	∇x	PROPN
ejpam-4931	665	7	·	·	PUNCT
ejpam-4931	665	8	u+	u+	NOUN
ejpam-4931	665	9	|∇xξ|2	|∇xξ|2	NOUN
ejpam-4931	665	10	ξ2	ξ2	PROPN
ejpam-4931	665	11	u∇xξ	u∇xξ	PROPN
ejpam-4931	665	12	)	)	PUNCT
ejpam-4931	665	13	dxdzdt	dxdzdt	NOUN
ejpam-4931	665	14	≤	≤	NUM
ejpam-4931	666	1	ϵ	ϵ	X
ejpam-4931	666	2	∫	∫	PROPN
ejpam-4931	666	3	t	t	PROPN
ejpam-4931	666	4	0	0	NUM
ejpam-4931	667	1	∫	∫	PROPN
ejpam-4931	667	2	ω	ω	PROPN
ejpam-4931	667	3	(	(	PUNCT
ejpam-4931	667	4	∇xξ	∇xξ	PROPN
ejpam-4931	667	5	)	)	PUNCT
ejpam-4931	667	6	2	2	NUM
ejpam-4931	667	7	ξ	ξ	SYM
ejpam-4931	667	8	3	3	NUM
ejpam-4931	667	9	2	2	NUM
ejpam-4931	667	10	√	√	NOUN
ejpam-4931	667	11	ξ∇x	ξ∇x	PROPN
ejpam-4931	667	12	·	·	PUNCT
ejpam-4931	667	13	u+	u+	NUM
ejpam-4931	667	14	(	(	PUNCT
ejpam-4931	667	15	∇xξ	∇xξ	NOUN
ejpam-4931	667	16	)	)	PUNCT
ejpam-4931	667	17	2	2	NUM
ejpam-4931	667	18	ξ	ξ	SYM
ejpam-4931	667	19	5	5	NUM
ejpam-4931	667	20	2	2	NUM
ejpam-4931	667	21	√	√	NUM
ejpam-4931	667	22	ξu	ξu	PROPN
ejpam-4931	667	23	·	·	PUNCT
ejpam-4931	667	24	∇xξdxdzdt	∇xξdxdzdt	VERB
ejpam-4931	667	25	≤	≤	PROPN
ejpam-4931	667	26	ϵ∥1	ϵ∥1	NUM
ejpam-4931	667	27	ξ	ξ	X
ejpam-4931	667	28	∥	∥	NUM
ejpam-4931	667	29	3	3	NUM
ejpam-4931	667	30	2	2	NUM
ejpam-4931	667	31	l∞(l∞(ω))∥∇xξ∥l∞(l∞(ω))∥∇xξ∥l2(l2(ω))∥	l∞(l∞(ω))∥∇xξ∥l∞(l∞(ω))∥∇xξ∥l2(l2(ω))∥	NOUN
ejpam-4931	667	32	√	√	NUM
ejpam-4931	667	33	ξ∇xu∥l2(l2(ω	ξ∇xu∥l2(l2(ω	NUM
ejpam-4931	667	34	)	)	PUNCT
ejpam-4931	667	35	)	)	PUNCT
ejpam-4931	667	36	j.	j.	PROPN
ejpam-4931	667	37	ouya	ouya	PROPN
ejpam-4931	667	38	,	,	PUNCT
ejpam-4931	667	39	a.	a.	NOUN
ejpam-4931	667	40	ouédraogo	ouédraogo	PROPN
ejpam-4931	667	41	/	/	SYM
ejpam-4931	667	42	eur	eur	PROPN
ejpam-4931	667	43	.	.	PUNCT
ejpam-4931	668	1	j.	j.	PROPN
ejpam-4931	668	2	pure	pure	PROPN
ejpam-4931	668	3	appl	appl	PROPN
ejpam-4931	668	4	.	.	PROPN
ejpam-4931	668	5	math	math	PROPN
ejpam-4931	668	6	,	,	PUNCT
ejpam-4931	668	7	16	16	NUM
ejpam-4931	668	8	(	(	PUNCT
ejpam-4931	668	9	4	4	NUM
ejpam-4931	668	10	)	)	PUNCT
ejpam-4931	668	11	(	(	PUNCT
ejpam-4931	668	12	2023	2023	NUM
ejpam-4931	668	13	)	)	PUNCT
ejpam-4931	668	14	,	,	PUNCT
ejpam-4931	668	15	2247	2247	NUM
ejpam-4931	668	16	-	-	SYM
ejpam-4931	668	17	2285	2285	NUM
ejpam-4931	668	18	2271	2271	NUM
ejpam-4931	668	19	+	+	CCONJ
ejpam-4931	668	20	ϵ∥1	ϵ∥1	X
ejpam-4931	668	21	ξ	ξ	X
ejpam-4931	668	22	∥	∥	NUM
ejpam-4931	668	23	5	5	NUM
ejpam-4931	668	24	2	2	NUM
ejpam-4931	668	25	l∞(l∞(ω))∥∇xξ∥2l∞(l∞(ω))∥∇xξ∥l2(l2(ω))∥	l∞(l∞(ω))∥∇xξ∥2l∞(l∞(ω))∥∇xξ∥l2(l2(ω))∥	NOUN
ejpam-4931	668	26	√	√	NUM
ejpam-4931	668	27	ξu∥l2(l2(ω	ξu∥l2(l2(ω	NUM
ejpam-4931	668	28	)	)	PUNCT
ejpam-4931	668	29	)	)	PUNCT
ejpam-4931	668	30	≤	≤	NOUN
ejpam-4931	668	31	ϵc(δ	ϵc(δ	NUM
ejpam-4931	668	32	,	,	PUNCT
ejpam-4931	668	33	r2	r2	PROPN
ejpam-4931	668	34	)	)	PUNCT
ejpam-4931	668	35	(	(	PUNCT
ejpam-4931	668	36	∥	∥	X
ejpam-4931	668	37	√	√	NUM
ejpam-4931	668	38	ξ∇xu∥l2(l2(ω))+1	ξ∇xu∥l2(l2(ω))+1	NOUN
ejpam-4931	668	39	)	)	PUNCT
ejpam-4931	668	40	≤	≤	NUM
ejpam-4931	668	41	1	1	NUM
ejpam-4931	668	42	2	2	NUM
ejpam-4931	668	43	∥	∥	NUM
ejpam-4931	668	44	√	√	NUM
ejpam-4931	668	45	ξax(u)∥2l2(l2(ω))+ϵc(δ	ξax(u)∥2l2(l2(ω))+ϵc(δ	NUM
ejpam-4931	668	46	,	,	PUNCT
ejpam-4931	668	47	r2	r2	PROPN
ejpam-4931	668	48	)	)	PUNCT
ejpam-4931	668	49	,	,	PUNCT
ejpam-4931	668	50	(	(	PUNCT
ejpam-4931	668	51	88	88	NUM
ejpam-4931	668	52	)	)	PUNCT
ejpam-4931	668	53	where	where	SCONJ
ejpam-4931	668	54	we	we	PRON
ejpam-4931	668	55	used	use	VERB
ejpam-4931	668	56	,	,	PUNCT
ejpam-4931	668	57	∥	∥	PROPN
ejpam-4931	668	58	√	√	NUM
ejpam-4931	668	59	ξax(u)∥2l2(l2(ω))+∥	ξax(u)∥2l2(l2(ω))+∥	VERB
ejpam-4931	668	60	√	√	PROPN
ejpam-4931	668	61	ξdx(u)∥2l2(l2(ω))=	ξdx(u)∥2l2(l2(ω))=	PROPN
ejpam-4931	668	62	∥	∥	PROPN
ejpam-4931	668	63	√	√	NUM
ejpam-4931	668	64	ξ∇xu∥2l2(l2(ω	ξ∇xu∥2l2(l2(ω	NUM
ejpam-4931	668	65	)	)	PUNCT
ejpam-4931	668	66	)	)	PUNCT
ejpam-4931	668	67	.	.	PUNCT
ejpam-4931	669	1	in	in	ADP
ejpam-4931	669	2	addition	addition	NOUN
ejpam-4931	669	3	,	,	PUNCT
ejpam-4931	669	4	we	we	PRON
ejpam-4931	669	5	also	also	ADV
ejpam-4931	669	6	have	have	VERB
ejpam-4931	669	7	•	•	NUM
ejpam-4931	669	8	∫	∫	PROPN
ejpam-4931	669	9	t	t	PROPN
ejpam-4931	669	10	0	0	NUM
ejpam-4931	669	11	i4dt	i4dt	NOUN
ejpam-4931	669	12	=	=	SYM
ejpam-4931	669	13	4ϵ	4ϵ	NUM
ejpam-4931	669	14	∫	∫	PROPN
ejpam-4931	669	15	t	t	PROPN
ejpam-4931	669	16	0	0	NUM
ejpam-4931	670	1	∫	∫	PROPN
ejpam-4931	671	1	ω	ω	PROPN
ejpam-4931	671	2	∇xξ	∇xξ	PROPN
ejpam-4931	671	3	·	·	PUNCT
ejpam-4931	671	4	∇2	∇2	PROPN
ejpam-4931	671	5	x	x	SYM
ejpam-4931	671	6	ln	ln	PROPN
ejpam-4931	671	7	ξ	ξ	PROPN
ejpam-4931	671	8	·	·	PUNCT
ejpam-4931	671	9	∇x	∇x	PROPN
ejpam-4931	671	10	ln	ln	ADJ
ejpam-4931	671	11	ξdxdydt	ξdxdydt	NOUN
ejpam-4931	671	12	=	=	SYM
ejpam-4931	671	13	−2ϵ	−2ϵ	PROPN
ejpam-4931	671	14	∫	∫	PROPN
ejpam-4931	671	15	t	t	PROPN
ejpam-4931	671	16	0	0	NUM
ejpam-4931	671	17	∫	∫	PROPN
ejpam-4931	671	18	ω	ω	X
ejpam-4931	671	19	∆xξ	∆xξ	PROPN
ejpam-4931	671	20	·	·	PUNCT
ejpam-4931	671	21	|∇x	|∇x	ADV
ejpam-4931	671	22	ln	ln	ADJ
ejpam-4931	671	23	ξ|2dxdydt	ξ|2dxdydt	NOUN
ejpam-4931	671	24	≤	≤	NUM
ejpam-4931	671	25	2ϵ∥1	2ϵ∥1	NOUN
ejpam-4931	671	26	ξ	ξ	X
ejpam-4931	671	27	∥2l∞(l∞(ω))∥∇xξ∥l∞(l∞(ω))∥∇xξ∥l2(l2(ω))∥∆xξ∥l2(l2(ω	∥2l∞(l∞(ω))∥∇xξ∥l∞(l∞(ω))∥∇xξ∥l2(l2(ω))∥∆xξ∥l2(l2(ω	ADV
ejpam-4931	671	28	)	)	PUNCT
ejpam-4931	671	29	)	)	PUNCT
ejpam-4931	672	1	≤	≤	NOUN
ejpam-4931	672	2	ϵc(δ	ϵc(δ	NUM
ejpam-4931	672	3	,	,	PUNCT
ejpam-4931	672	4	r2	r2	PROPN
ejpam-4931	672	5	)	)	PUNCT
ejpam-4931	672	6	.	.	PUNCT
ejpam-4931	673	1	(	(	PUNCT
ejpam-4931	673	2	89	89	NUM
ejpam-4931	673	3	)	)	PUNCT
ejpam-4931	673	4	furthermore	furthermore	ADV
ejpam-4931	673	5	,	,	PUNCT
ejpam-4931	673	6	we	we	PRON
ejpam-4931	673	7	have	have	VERB
ejpam-4931	673	8	•	•	NUM
ejpam-4931	673	9	∫	∫	PROPN
ejpam-4931	673	10	t	t	PROPN
ejpam-4931	673	11	0	0	NUM
ejpam-4931	673	12	i5dt	i5dt	PUNCT
ejpam-4931	674	1	=	=	PUNCT
ejpam-4931	674	2	2ϵ	2ϵ	NUM
ejpam-4931	675	1	∫	∫	PROPN
ejpam-4931	675	2	t	t	PROPN
ejpam-4931	675	3	0	0	NUM
ejpam-4931	676	1	∫	∫	PROPN
ejpam-4931	677	1	ω	ω	PROPN
ejpam-4931	677	2	∇x∆xξ(u+	∇x∆xξ(u+	PROPN
ejpam-4931	677	3	2∇x	2∇x	NUM
ejpam-4931	677	4	ln	ln	NOUN
ejpam-4931	677	5	ξ)dxdydt	ξ)dxdydt	ADJ
ejpam-4931	677	6	≤	≤	NOUN
ejpam-4931	677	7	2ϵ∥∇x∆xξ∥l2(l2(ω))∥	2ϵ∥∇x∆xξ∥l2(l2(ω))∥	NUM
ejpam-4931	677	8	√	√	ADP
ejpam-4931	678	1	ξu∥l2(l2(ω))∥	ξu∥l2(l2(ω))∥	NOUN
ejpam-4931	678	2	√	√	ADJ
ejpam-4931	678	3	ξ∥l∞(l∞(ω	ξ∥l∞(l∞(ω	NOUN
ejpam-4931	678	4	)	)	PUNCT
ejpam-4931	678	5	)	)	PUNCT
ejpam-4931	679	1	+	+	CCONJ
ejpam-4931	679	2	4ϵ∥∇x∆xξ∥l2(l2(ω))∥∇xξ∥l2(l2(ω))∥ξ−1∥l∞(l∞(ω	4ϵ∥∇x∆xξ∥l2(l2(ω))∥∇xξ∥l2(l2(ω))∥ξ−1∥l∞(l∞(ω	NOUN
ejpam-4931	679	3	)	)	PUNCT
ejpam-4931	679	4	)	)	PUNCT
ejpam-4931	679	5	≤	≤	NUM
ejpam-4931	679	6	ϵc(δ	ϵc(δ	NUM
ejpam-4931	679	7	,	,	PUNCT
ejpam-4931	679	8	r2	r2	PROPN
ejpam-4931	679	9	)	)	PUNCT
ejpam-4931	679	10	(	(	PUNCT
ejpam-4931	679	11	90	90	NUM
ejpam-4931	679	12	)	)	PUNCT
ejpam-4931	679	13	and	and	CCONJ
ejpam-4931	679	14	•	•	NUM
ejpam-4931	679	15	∫	∫	PROPN
ejpam-4931	679	16	t	t	PROPN
ejpam-4931	679	17	0	0	NUM
ejpam-4931	679	18	i6dt	i6dt	PROPN
ejpam-4931	680	1	=	=	SYM
ejpam-4931	681	1	−2rϵ	−2rϵ	NOUN
ejpam-4931	681	2	∫	∫	PROPN
ejpam-4931	681	3	t	t	PROPN
ejpam-4931	681	4	0	0	NUM
ejpam-4931	681	5	∫	∫	PROPN
ejpam-4931	681	6	ω	ω	PROPN
ejpam-4931	681	7	|u|u∇xξdxdydt	|u|u∇xξdxdydt	PROPN
ejpam-4931	681	8	=	=	PUNCT
ejpam-4931	682	1	2rϵ	2rϵ	ADJ
ejpam-4931	682	2	∫	∫	PROPN
ejpam-4931	682	3	t	t	NOUN
ejpam-4931	682	4	0	0	NUM
ejpam-4931	683	1	∫	∫	PROPN
ejpam-4931	683	2	ω	ω	PROPN
ejpam-4931	683	3	divx(|u|u)ξdxdydt	divx(|u|u)ξdxdydt	PROPN
ejpam-4931	683	4	=	=	SYM
ejpam-4931	683	5	2rϵ	2rϵ	ADJ
ejpam-4931	683	6	∫	∫	PROPN
ejpam-4931	683	7	t	t	NOUN
ejpam-4931	683	8	0	0	NUM
ejpam-4931	683	9	∫	∫	PROPN
ejpam-4931	684	1	ω	ω	PROPN
ejpam-4931	684	2	ξ	ξ	X
ejpam-4931	684	3	(	(	PUNCT
ejpam-4931	684	4	|u|divxu+	|u|divxu+	PROPN
ejpam-4931	684	5	u	u	NOUN
ejpam-4931	684	6	u	u	NOUN
ejpam-4931	684	7	|u|	|u|	PROPN
ejpam-4931	684	8	∇xu	∇xu	ADJ
ejpam-4931	684	9	)	)	PUNCT
ejpam-4931	684	10	dxdydt	dxdydt	NOUN
ejpam-4931	684	11	≤	≤	NUM
ejpam-4931	684	12	c∥	c∥	PROPN
ejpam-4931	684	13	√	√	PROPN
ejpam-4931	685	1	ξu∥l2(l2(ω))∥	ξu∥l2(l2(ω))∥	PRON
ejpam-4931	685	2	√	√	NUM
ejpam-4931	685	3	ξ∇xu∥l2(l2(ω	ξ∇xu∥l2(l2(ω	NUM
ejpam-4931	685	4	)	)	PUNCT
ejpam-4931	685	5	)	)	PUNCT
ejpam-4931	686	1	≤	≤	NUM
ejpam-4931	686	2	c	c	NOUN
ejpam-4931	686	3	+	+	NOUN
ejpam-4931	686	4	1	1	NUM
ejpam-4931	686	5	2	2	NUM
ejpam-4931	686	6	∥	∥	NUM
ejpam-4931	686	7	√	√	NUM
ejpam-4931	686	8	ξax(u)∥2l2(l2(ω	ξax(u)∥2l2(l2(ω	PROPN
ejpam-4931	686	9	)	)	PUNCT
ejpam-4931	686	10	)	)	PUNCT
ejpam-4931	686	11	.	.	PUNCT
ejpam-4931	687	1	(	(	PUNCT
ejpam-4931	687	2	91	91	NUM
ejpam-4931	687	3	)	)	PUNCT
ejpam-4931	687	4	so	so	ADV
ejpam-4931	687	5	by	by	ADP
ejpam-4931	687	6	replacing	replace	VERB
ejpam-4931	687	7	(	(	PUNCT
ejpam-4931	687	8	87)-(91	87)-(91	NUM
ejpam-4931	687	9	)	)	PUNCT
ejpam-4931	687	10	in	in	ADP
ejpam-4931	687	11	(	(	PUNCT
ejpam-4931	687	12	86	86	NUM
ejpam-4931	687	13	)	)	PUNCT
ejpam-4931	687	14	,	,	PUNCT
ejpam-4931	687	15	we	we	PRON
ejpam-4931	687	16	get	get	VERB
ejpam-4931	687	17	the	the	DET
ejpam-4931	687	18	b	b	PROPN
ejpam-4931	687	19	-	-	PUNCT
ejpam-4931	687	20	d	d	ADJ
ejpam-4931	687	21	entropy	entropy	NOUN
ejpam-4931	687	22	(	(	PUNCT
ejpam-4931	687	23	65	65	NUM
ejpam-4931	687	24	)	)	PUNCT
ejpam-4931	687	25	.	.	PUNCT
ejpam-4931	688	1	in	in	ADP
ejpam-4931	688	2	the	the	DET
ejpam-4931	688	3	next	next	ADJ
ejpam-4931	688	4	section	section	NOUN
ejpam-4931	688	5	,	,	PUNCT
ejpam-4931	688	6	we	we	PRON
ejpam-4931	688	7	make	make	VERB
ejpam-4931	688	8	the	the	DET
ejpam-4931	688	9	parameters	parameter	NOUN
ejpam-4931	688	10	of	of	ADP
ejpam-4931	688	11	our	our	PRON
ejpam-4931	688	12	approximate	approximate	ADJ
ejpam-4931	688	13	system	system	NOUN
ejpam-4931	688	14	tend	tend	VERB
ejpam-4931	688	15	to	to	ADP
ejpam-4931	688	16	0	0	NUM
ejpam-4931	688	17	.	.	PUNCT
ejpam-4931	689	1	j.	j.	PROPN
ejpam-4931	689	2	ouya	ouya	PROPN
ejpam-4931	689	3	,	,	PUNCT
ejpam-4931	689	4	a.	a.	NOUN
ejpam-4931	689	5	ouédraogo	ouédraogo	PROPN
ejpam-4931	689	6	/	/	SYM
ejpam-4931	689	7	eur	eur	PROPN
ejpam-4931	689	8	.	.	PUNCT
ejpam-4931	690	1	j.	j.	PROPN
ejpam-4931	690	2	pure	pure	PROPN
ejpam-4931	690	3	appl	appl	PROPN
ejpam-4931	690	4	.	.	PROPN
ejpam-4931	690	5	math	math	PROPN
ejpam-4931	690	6	,	,	PUNCT
ejpam-4931	690	7	16	16	NUM
ejpam-4931	690	8	(	(	PUNCT
ejpam-4931	690	9	4	4	NUM
ejpam-4931	690	10	)	)	PUNCT
ejpam-4931	690	11	(	(	PUNCT
ejpam-4931	690	12	2023	2023	NUM
ejpam-4931	690	13	)	)	PUNCT
ejpam-4931	690	14	,	,	PUNCT
ejpam-4931	690	15	2247	2247	NUM
ejpam-4931	690	16	-	-	SYM
ejpam-4931	690	17	2285	2285	NUM
ejpam-4931	690	18	2272	2272	NUM
ejpam-4931	690	19	5	5	NUM
ejpam-4931	690	20	.	.	PUNCT
ejpam-4931	691	1	proof	proof	NOUN
ejpam-4931	691	2	of	of	ADP
ejpam-4931	691	3	mains	main	NOUN
ejpam-4931	691	4	results	result	VERB
ejpam-4931	691	5	5.1	5.1	NUM
ejpam-4931	691	6	.	.	PUNCT
ejpam-4931	692	1	proof	proof	NOUN
ejpam-4931	692	2	of	of	ADP
ejpam-4931	692	3	theorem	theorem	NOUN
ejpam-4931	692	4	1	1	NUM
ejpam-4931	692	5	we	we	PRON
ejpam-4931	692	6	make	make	VERB
ejpam-4931	692	7	the	the	DET
ejpam-4931	692	8	proof	proof	NOUN
ejpam-4931	692	9	of	of	ADP
ejpam-4931	692	10	theorem	theorem	NOUN
ejpam-4931	692	11	1	1	NUM
ejpam-4931	692	12	in	in	ADP
ejpam-4931	692	13	several	several	ADJ
ejpam-4931	692	14	steps	step	NOUN
ejpam-4931	692	15	.	.	PUNCT
ejpam-4931	693	1	5.1.1	5.1.1	NOUN
ejpam-4931	693	2	.	.	PUNCT
ejpam-4931	694	1	passing	pass	VERB
ejpam-4931	694	2	to	to	ADP
ejpam-4931	694	3	the	the	DET
ejpam-4931	694	4	limits	limit	NOUN
ejpam-4931	694	5	as	as	ADP
ejpam-4931	694	6	ϵ	ϵ	NOUN
ejpam-4931	694	7	,	,	PUNCT
ejpam-4931	694	8	α	α	PROPN
ejpam-4931	694	9	−→	−→	NOUN
ejpam-4931	694	10	0	0	NUM
ejpam-4931	695	1	we	we	PRON
ejpam-4931	695	2	denote	denote	VERB
ejpam-4931	695	3	the	the	DET
ejpam-4931	695	4	solution	solution	NOUN
ejpam-4931	695	5	to	to	ADP
ejpam-4931	695	6	(	(	PUNCT
ejpam-4931	695	7	60	60	NUM
ejpam-4931	695	8	)	)	PUNCT
ejpam-4931	695	9	at	at	ADP
ejpam-4931	695	10	this	this	DET
ejpam-4931	695	11	level	level	NOUN
ejpam-4931	695	12	of	of	ADP
ejpam-4931	695	13	approximation	approximation	NOUN
ejpam-4931	695	14	as	as	ADP
ejpam-4931	695	15	(	(	PUNCT
ejpam-4931	695	16	ξα,ϵ	ξα,ϵ	NOUN
ejpam-4931	695	17	,	,	PUNCT
ejpam-4931	695	18	uα,ϵ	uα,ϵ	NOUN
ejpam-4931	695	19	,	,	PUNCT
ejpam-4931	695	20	vα,ϵ	vα,ϵ	NOUN
ejpam-4931	695	21	)	)	PUNCT
ejpam-4931	695	22	.	.	PUNCT
ejpam-4931	696	1	from	from	ADP
ejpam-4931	696	2	the	the	DET
ejpam-4931	696	3	energy	energy	NOUN
ejpam-4931	696	4	inequality	inequality	NOUN
ejpam-4931	696	5	(	(	PUNCT
ejpam-4931	696	6	59	59	NUM
ejpam-4931	696	7	)	)	PUNCT
ejpam-4931	696	8	,	,	PUNCT
ejpam-4931	696	9	we	we	PRON
ejpam-4931	696	10	obtain	obtain	VERB
ejpam-4931	696	11	the	the	DET
ejpam-4931	696	12	following	follow	VERB
ejpam-4931	696	13	uniform	uniform	NOUN
ejpam-4931	696	14	regularities.	regularities.	PROPN
ejpam-4931	696	15	√	√	ADP
ejpam-4931	696	16	ξα,ϵuα,ϵ	ξα,ϵuα,ϵ	PROPN
ejpam-4931	696	17	∈	∈	PROPN
ejpam-4931	696	18	l∞	l∞	NOUN
ejpam-4931	696	19	(	(	PUNCT
ejpam-4931	696	20	[	[	X
ejpam-4931	696	21	0	0	NUM
ejpam-4931	696	22	,	,	PUNCT
ejpam-4931	696	23	t	t	X
ejpam-4931	696	24	]	]	PUNCT
ejpam-4931	696	25	;	;	PUNCT
ejpam-4931	696	26	l2(ω	l2(ω	NUM
ejpam-4931	696	27	)	)	PUNCT
ejpam-4931	696	28	)	)	PUNCT
ejpam-4931	696	29	,	,	PUNCT
ejpam-4931	696	30	r2ξ	r2ξ	ADP
ejpam-4931	696	31	−β	−β	NOUN
ejpam-4931	696	32	α,ϵ	α,ϵ	PROPN
ejpam-4931	696	33	∈	∈	PROPN
ejpam-4931	696	34	l∞	l∞	NOUN
ejpam-4931	696	35	(	(	PUNCT
ejpam-4931	696	36	[	[	X
ejpam-4931	696	37	0	0	NUM
ejpam-4931	696	38	,	,	PUNCT
ejpam-4931	696	39	t	t	X
ejpam-4931	696	40	]	]	PUNCT
ejpam-4931	696	41	;	;	PUNCT
ejpam-4931	696	42	l1(ω	l1(ω	X
ejpam-4931	696	43	)	)	PUNCT
ejpam-4931	696	44	)	)	PUNCT
ejpam-4931	696	45	,	,	PUNCT
ejpam-4931	696	46	√	√	NUM
ejpam-4931	696	47	ξα,ϵdx(uα,ϵ	ξα,ϵdx(uα,ϵ	NUM
ejpam-4931	696	48	)	)	PUNCT
ejpam-4931	696	49	∈	∈	NOUN
ejpam-4931	696	50	l2	l2	NOUN
ejpam-4931	696	51	(	(	PUNCT
ejpam-4931	696	52	[	[	X
ejpam-4931	696	53	0	0	NUM
ejpam-4931	696	54	,	,	PUNCT
ejpam-4931	696	55	t	t	X
ejpam-4931	696	56	]	]	PUNCT
ejpam-4931	696	57	;	;	PUNCT
ejpam-4931	696	58	l2(ω	l2(ω	NUM
ejpam-4931	696	59	)	)	PUNCT
ejpam-4931	696	60	)	)	PUNCT
ejpam-4931	696	61	,	,	PUNCT
ejpam-4931	696	62	√	√	NUM
ejpam-4931	696	63	ξα,ϵ∂yuα,ϵ	ξα,ϵ∂yuα,ϵ	NOUN
ejpam-4931	696	64	∈	∈	NOUN
ejpam-4931	696	65	l2	l2	NOUN
ejpam-4931	696	66	(	(	PUNCT
ejpam-4931	696	67	[	[	X
ejpam-4931	696	68	0	0	NUM
ejpam-4931	696	69	,	,	PUNCT
ejpam-4931	696	70	t	t	X
ejpam-4931	696	71	]	]	PUNCT
ejpam-4931	696	72	;	;	PUNCT
ejpam-4931	696	73	l2(ω	l2(ω	NUM
ejpam-4931	696	74	)	)	PUNCT
ejpam-4931	696	75	)	)	PUNCT
ejpam-4931	696	76	,	,	PUNCT
ejpam-4931	696	77	√	√	PUNCT
ejpam-4931	696	78	δξα,ϵ	δξα,ϵ	ADP
ejpam-4931	696	79	∈	∈	PROPN
ejpam-4931	696	80	l∞	l∞	NOUN
ejpam-4931	696	81	(	(	PUNCT
ejpam-4931	696	82	[	[	X
ejpam-4931	696	83	0	0	NUM
ejpam-4931	696	84	,	,	PUNCT
ejpam-4931	696	85	t	t	X
ejpam-4931	696	86	]	]	PUNCT
ejpam-4931	696	87	;	;	PUNCT
ejpam-4931	696	88	h5(ω	h5(ω	NUM
ejpam-4931	696	89	)	)	PUNCT
ejpam-4931	696	90	)	)	PUNCT
ejpam-4931	696	91	,	,	PUNCT
ejpam-4931	696	92	√	√	NUM
ejpam-4931	696	93	r1uα,ϵ	r1uα,ϵ	NOUN
ejpam-4931	696	94	∈	∈	NOUN
ejpam-4931	696	95	l2	l2	NOUN
ejpam-4931	696	96	(	(	PUNCT
ejpam-4931	696	97	[	[	X
ejpam-4931	696	98	0	0	NUM
ejpam-4931	696	99	,	,	PUNCT
ejpam-4931	696	100	t	t	X
ejpam-4931	696	101	]	]	PUNCT
ejpam-4931	696	102	;	;	PUNCT
ejpam-4931	696	103	l2(ω	l2(ω	NUM
ejpam-4931	696	104	)	)	PUNCT
ejpam-4931	696	105	)	)	PUNCT
ejpam-4931	696	106	,	,	PUNCT
ejpam-4931	696	107	√	√	PUNCT
ejpam-4931	696	108	α∆uα,ϵ	α∆uα,ϵ	PROPN
ejpam-4931	696	109	∈	∈	NOUN
ejpam-4931	696	110	l2	l2	NOUN
ejpam-4931	696	111	(	(	PUNCT
ejpam-4931	696	112	[	[	X
ejpam-4931	696	113	0	0	NUM
ejpam-4931	696	114	,	,	PUNCT
ejpam-4931	696	115	t	t	X
ejpam-4931	696	116	]	]	PUNCT
ejpam-4931	696	117	;	;	PUNCT
ejpam-4931	696	118	l2(ω	l2(ω	NUM
ejpam-4931	696	119	)	)	PUNCT
ejpam-4931	696	120	)	)	PUNCT
ejpam-4931	696	121	,	,	PUNCT
ejpam-4931	697	1	ξ	ξ	PROPN
ejpam-4931	697	2	1	1	NUM
ejpam-4931	697	3	3	3	NUM
ejpam-4931	697	4	α,ϵuα,ϵ	α,ϵuα,ϵ	NOUN
ejpam-4931	697	5	∈	∈	PROPN
ejpam-4931	697	6	l3	l3	X
ejpam-4931	697	7	(	(	PUNCT
ejpam-4931	697	8	[	[	X
ejpam-4931	697	9	0	0	NUM
ejpam-4931	697	10	,	,	PUNCT
ejpam-4931	697	11	t	t	X
ejpam-4931	697	12	]	]	PUNCT
ejpam-4931	697	13	;	;	PUNCT
ejpam-4931	697	14	l3(ω	l3(ω	X
ejpam-4931	697	15	)	)	PUNCT
ejpam-4931	697	16	)	)	PUNCT
ejpam-4931	697	17	.	.	PUNCT
ejpam-4931	698	1	(	(	PUNCT
ejpam-4931	698	2	92	92	NUM
ejpam-4931	698	3	)	)	PUNCT
ejpam-4931	698	4	the	the	DET
ejpam-4931	698	5	b	b	PROPN
ejpam-4931	698	6	-	-	PUNCT
ejpam-4931	698	7	d	d	ADJ
ejpam-4931	698	8	entropy	entropy	NOUN
ejpam-4931	698	9	(	(	PUNCT
ejpam-4931	698	10	65	65	NUM
ejpam-4931	698	11	)	)	PUNCT
ejpam-4931	698	12	gives	give	VERB
ejpam-4931	698	13	the	the	DET
ejpam-4931	698	14	following	follow	VERB
ejpam-4931	698	15	additional	additional	ADJ
ejpam-4931	698	16	uniform	uniform	ADJ
ejpam-4931	698	17	regularities:	regularities:	NOUN
ejpam-4931	698	18	√	√	ADP
ejpam-4931	698	19	δξα,ϵ	δξα,ϵ	NOUN
ejpam-4931	698	20	∈	∈	NOUN
ejpam-4931	698	21	l2	l2	NOUN
ejpam-4931	698	22	(	(	PUNCT
ejpam-4931	698	23	[	[	X
ejpam-4931	698	24	0	0	NUM
ejpam-4931	698	25	,	,	PUNCT
ejpam-4931	698	26	t	t	X
ejpam-4931	698	27	]	]	PUNCT
ejpam-4931	698	28	;	;	PUNCT
ejpam-4931	698	29	h6(ω	h6(ω	X
ejpam-4931	698	30	)	)	PUNCT
ejpam-4931	698	31	)	)	PUNCT
ejpam-4931	698	32	,	,	PUNCT
ejpam-4931	698	33	∇xξα,ϵ	∇xξα,ϵ	PROPN
ejpam-4931	698	34	∈	∈	NOUN
ejpam-4931	698	35	l2	l2	NOUN
ejpam-4931	698	36	(	(	PUNCT
ejpam-4931	698	37	[	[	X
ejpam-4931	698	38	0	0	NUM
ejpam-4931	698	39	,	,	PUNCT
ejpam-4931	698	40	t	t	X
ejpam-4931	698	41	]	]	PUNCT
ejpam-4931	698	42	;	;	PUNCT
ejpam-4931	698	43	l2(ω	l2(ω	NUM
ejpam-4931	698	44	)	)	PUNCT
ejpam-4931	698	45	)	)	PUNCT
ejpam-4931	699	1	√	√	VERB
ejpam-4931	699	2	r2∇xξ	r2∇xξ	NOUN
ejpam-4931	699	3	−β/2	−β/2	NOUN
ejpam-4931	699	4	α,ϵ	α,ϵ	NOUN
ejpam-4931	699	5	∈	∈	NOUN
ejpam-4931	699	6	l2	l2	NOUN
ejpam-4931	699	7	(	(	PUNCT
ejpam-4931	699	8	[	[	X
ejpam-4931	699	9	0	0	NUM
ejpam-4931	699	10	,	,	PUNCT
ejpam-4931	699	11	t	t	X
ejpam-4931	699	12	]	]	PUNCT
ejpam-4931	699	13	;	;	PUNCT
ejpam-4931	699	14	l2(ω	l2(ω	NUM
ejpam-4931	699	15	)	)	PUNCT
ejpam-4931	699	16	)	)	PUNCT
ejpam-4931	699	17	,	,	PUNCT
ejpam-4931	699	18	√	√	NUM
ejpam-4931	699	19	ξα,ϵax(uα,ϵ	ξα,ϵax(uα,ϵ	NUM
ejpam-4931	699	20	)	)	PUNCT
ejpam-4931	699	21	∈	∈	NOUN
ejpam-4931	699	22	l2	l2	NOUN
ejpam-4931	699	23	(	(	PUNCT
ejpam-4931	699	24	[	[	X
ejpam-4931	699	25	0	0	NUM
ejpam-4931	699	26	,	,	PUNCT
ejpam-4931	699	27	t	t	X
ejpam-4931	699	28	]	]	PUNCT
ejpam-4931	699	29	;	;	PUNCT
ejpam-4931	699	30	l2(ω	l2(ω	NUM
ejpam-4931	699	31	)	)	PUNCT
ejpam-4931	699	32	)	)	PUNCT
ejpam-4931	699	33	,	,	PUNCT
ejpam-4931	699	34	√	√	NUM
ejpam-4931	699	35	ξα,ϵ∂yuα,ϵ	ξα,ϵ∂yuα,ϵ	NOUN
ejpam-4931	699	36	∈	∈	NOUN
ejpam-4931	699	37	l2	l2	NOUN
ejpam-4931	699	38	(	(	PUNCT
ejpam-4931	699	39	[	[	X
ejpam-4931	699	40	0	0	NUM
ejpam-4931	699	41	,	,	PUNCT
ejpam-4931	699	42	t	t	X
ejpam-4931	699	43	]	]	PUNCT
ejpam-4931	699	44	;	;	PUNCT
ejpam-4931	699	45	l2(ω	l2(ω	NUM
ejpam-4931	699	46	)	)	PUNCT
ejpam-4931	699	47	)	)	PUNCT
ejpam-4931	699	48	,	,	PUNCT
ejpam-4931	699	49	ξ2α,ϵ	ξ2α,ϵ	NOUN
ejpam-4931	699	50	∈	∈	PROPN
ejpam-4931	699	51	l∞	l∞	NOUN
ejpam-4931	699	52	(	(	PUNCT
ejpam-4931	699	53	[	[	X
ejpam-4931	699	54	0	0	NUM
ejpam-4931	699	55	,	,	PUNCT
ejpam-4931	699	56	t	t	X
ejpam-4931	699	57	]	]	PUNCT
ejpam-4931	699	58	;	;	PUNCT
ejpam-4931	699	59	l1(ω	l1(ω	X
ejpam-4931	699	60	)	)	PUNCT
ejpam-4931	699	61	)	)	PUNCT
ejpam-4931	699	62	,	,	PUNCT
ejpam-4931	699	63	√	√	NUM
ejpam-4931	699	64	ξα,ϵ∇x	ξα,ϵ∇x	NOUN
ejpam-4931	699	65	√	√	NUM
ejpam-4931	699	66	ξα,ϵ	ξα,ϵ	SYM
ejpam-4931	699	67	∈	∈	PROPN
ejpam-4931	699	68	l∞	l∞	NOUN
ejpam-4931	699	69	(	(	PUNCT
ejpam-4931	699	70	[	[	X
ejpam-4931	699	71	0	0	NUM
ejpam-4931	699	72	,	,	PUNCT
ejpam-4931	699	73	t	t	X
ejpam-4931	699	74	]	]	PUNCT
ejpam-4931	699	75	;	;	PUNCT
ejpam-4931	699	76	l2(ω	l2(ω	NUM
ejpam-4931	699	77	)	)	PUNCT
ejpam-4931	699	78	)	)	PUNCT
ejpam-4931	699	79	.	.	PUNCT
ejpam-4931	700	1	(	(	PUNCT
ejpam-4931	700	2	93	93	NUM
ejpam-4931	700	3	)	)	PUNCT
ejpam-4931	700	4	similar	similar	ADJ
ejpam-4931	700	5	to	to	ADP
ejpam-4931	700	6	the	the	DET
ejpam-4931	700	7	proof	proof	NOUN
ejpam-4931	700	8	of	of	ADP
ejpam-4931	700	9	lemma	lemma	PROPN
ejpam-4931	700	10	5	5	NUM
ejpam-4931	700	11	,	,	PUNCT
ejpam-4931	700	12	we	we	PRON
ejpam-4931	700	13	have	have	VERB
ejpam-4931	700	14	the	the	DET
ejpam-4931	700	15	following	following	ADJ
ejpam-4931	700	16	uniform	uniform	NOUN
ejpam-4931	700	17	boundedness:√	boundedness:√	PROPN
ejpam-4931	700	18	k1	k1	PROPN
ejpam-4931	700	19	√	√	NUM
ejpam-4931	700	20	ξα,ϵ	ξα,ϵ	NOUN
ejpam-4931	700	21	∈	∈	NOUN
ejpam-4931	700	22	l2	l2	NOUN
ejpam-4931	700	23	(	(	PUNCT
ejpam-4931	700	24	[	[	X
ejpam-4931	700	25	0	0	NUM
ejpam-4931	700	26	,	,	PUNCT
ejpam-4931	700	27	t	t	X
ejpam-4931	700	28	]	]	PUNCT
ejpam-4931	700	29	;	;	PUNCT
ejpam-4931	700	30	h2(ω	h2(ω	NUM
ejpam-4931	700	31	)	)	PUNCT
ejpam-4931	700	32	)	)	PUNCT
ejpam-4931	701	1	;	;	PUNCT
ejpam-4931	701	2	k	k	PROPN
ejpam-4931	701	3	1	1	NUM
ejpam-4931	701	4	4	4	NUM
ejpam-4931	701	5	1	1	NUM
ejpam-4931	701	6	∇xξ	∇xξ	NUM
ejpam-4931	701	7	1	1	NUM
ejpam-4931	701	8	4	4	NUM
ejpam-4931	701	9	α,ϵ	α,ϵ	PROPN
ejpam-4931	701	10	∈	∈	PROPN
ejpam-4931	701	11	l4	l4	PROPN
ejpam-4931	701	12	(	(	PUNCT
ejpam-4931	701	13	[	[	X
ejpam-4931	701	14	0	0	NUM
ejpam-4931	701	15	,	,	PUNCT
ejpam-4931	701	16	t	t	X
ejpam-4931	701	17	]	]	PUNCT
ejpam-4931	701	18	;	;	PUNCT
ejpam-4931	701	19	l4(ω	l4(ω	X
ejpam-4931	701	20	)	)	PUNCT
ejpam-4931	701	21	)	)	PUNCT
ejpam-4931	701	22	.	.	PUNCT
ejpam-4931	702	1	with	with	ADP
ejpam-4931	702	2	the	the	DET
ejpam-4931	702	3	above	above	ADJ
ejpam-4931	702	4	regularities	regularity	NOUN
ejpam-4931	702	5	,	,	PUNCT
ejpam-4931	702	6	we	we	PRON
ejpam-4931	702	7	can	can	AUX
ejpam-4931	702	8	show	show	VERB
ejpam-4931	702	9	the	the	DET
ejpam-4931	702	10	following	follow	VERB
ejpam-4931	702	11	uniform	uniform	ADJ
ejpam-4931	702	12	compactness	compactness	NOUN
ejpam-4931	702	13	results	result	NOUN
ejpam-4931	702	14	.	.	PUNCT
ejpam-4931	703	1	lemma	lemma	PROPN
ejpam-4931	703	2	12	12	NUM
ejpam-4931	703	3	.	.	PUNCT
ejpam-4931	704	1	let	let	VERB
ejpam-4931	704	2	(	(	PUNCT
ejpam-4931	704	3	ξα,ϵ	ξα,ϵ	NOUN
ejpam-4931	704	4	,	,	PUNCT
ejpam-4931	704	5	uα,ϵ	uα,ϵ	NOUN
ejpam-4931	704	6	,	,	PUNCT
ejpam-4931	704	7	vα,ϵ	vα,ϵ	NOUN
ejpam-4931	704	8	)	)	PUNCT
ejpam-4931	704	9	the	the	DET
ejpam-4931	704	10	weak	weak	ADJ
ejpam-4931	704	11	solution	solution	NOUN
ejpam-4931	704	12	of	of	ADP
ejpam-4931	704	13	(	(	PUNCT
ejpam-4931	704	14	60	60	NUM
ejpam-4931	704	15	)	)	PUNCT
ejpam-4931	704	16	satisfying	satisfying	NOUN
ejpam-4931	704	17	(	(	PUNCT
ejpam-4931	704	18	92	92	NUM
ejpam-4931	704	19	)	)	PUNCT
ejpam-4931	704	20	and	and	CCONJ
ejpam-4931	704	21	(	(	PUNCT
ejpam-4931	704	22	93	93	NUM
ejpam-4931	704	23	)	)	PUNCT
ejpam-4931	704	24	,	,	PUNCT
ejpam-4931	704	25	then	then	ADV
ejpam-4931	704	26	the	the	DET
ejpam-4931	704	27	following	follow	VERB
ejpam-4931	704	28	estimates	estimate	NOUN
ejpam-4931	704	29	hold:	hold:	PROPN
ejpam-4931	704	30	∥∂t	∥∂t	NOUN
ejpam-4931	704	31	√	√	PROPN
ejpam-4931	704	32	ξα,ϵ∥	ξα,ϵ∥	PROPN
ejpam-4931	704	33	l∞	l∞	PROPN
ejpam-4931	704	34	(	(	PUNCT
ejpam-4931	704	35	[	[	X
ejpam-4931	704	36	0,t	0,t	X
ejpam-4931	704	37	]	]	X
ejpam-4931	704	38	;	;	PUNCT
ejpam-4931	704	39	w−1	w−1	PROPN
ejpam-4931	704	40	,	,	PUNCT
ejpam-4931	704	41	32	32	NUM
ejpam-4931	704	42	(	(	PUNCT
ejpam-4931	704	43	ω	ω	NOUN
ejpam-4931	704	44	)	)	PUNCT
ejpam-4931	704	45	)	)	PUNCT
ejpam-4931	705	1	+	+	X
ejpam-4931	705	2	∥	∥	PRON
ejpam-4931	705	3	√	√	VERB
ejpam-4931	705	4	ξα,ϵ∥l2	ξα,ϵ∥l2	PROPN
ejpam-4931	705	5	(	(	PUNCT
ejpam-4931	705	6	[	[	X
ejpam-4931	705	7	0,t	0,t	X
ejpam-4931	705	8	]	]	X
ejpam-4931	705	9	;	;	PUNCT
ejpam-4931	705	10	h2(ω	h2(ω	NUM
ejpam-4931	705	11	)	)	PUNCT
ejpam-4931	705	12	)	)	PUNCT
ejpam-4931	705	13	≤	≤	PUNCT
ejpam-4931	706	1	k	k	PROPN
ejpam-4931	706	2	∥ξα,ϵ∥l2	∥ξα,ϵ∥l2	PROPN
ejpam-4931	706	3	(	(	PUNCT
ejpam-4931	706	4	[	[	X
ejpam-4931	706	5	0,t	0,t	X
ejpam-4931	706	6	]	]	X
ejpam-4931	706	7	;	;	PUNCT
ejpam-4931	706	8	h6(ω	h6(ω	PROPN
ejpam-4931	706	9	)	)	PUNCT
ejpam-4931	706	10	)	)	PUNCT
ejpam-4931	707	1	+	+	X
ejpam-4931	707	2	∥∂tξα,ϵ∥l2	∥∂tξα,ϵ∥l2	ADJ
ejpam-4931	707	3	(	(	PUNCT
ejpam-4931	707	4	[	[	X
ejpam-4931	707	5	0,t	0,t	X
ejpam-4931	707	6	]	]	X
ejpam-4931	707	7	;	;	PUNCT
ejpam-4931	707	8	h−1(ω	h−1(ω	PROPN
ejpam-4931	707	9	)	)	PUNCT
ejpam-4931	707	10	)	)	PUNCT
ejpam-4931	707	11	≤	≤	NUM
ejpam-4931	708	1	k	k	PUNCT
ejpam-4931	708	2	∥ξ−β	∥ξ−β	NOUN
ejpam-4931	708	3	α,ϵ∥	α,ϵ∥	NOUN
ejpam-4931	708	4	l	l	NOUN
ejpam-4931	708	5	5	5	NUM
ejpam-4931	708	6	3	3	NUM
ejpam-4931	708	7	(	(	PUNCT
ejpam-4931	708	8	[	[	X
ejpam-4931	708	9	0,t	0,t	X
ejpam-4931	708	10	]	]	X
ejpam-4931	708	11	;	;	PUNCT
ejpam-4931	708	12	l	l	NOUN
ejpam-4931	708	13	5	5	NUM
ejpam-4931	708	14	3	3	NUM
ejpam-4931	708	15	(	(	PUNCT
ejpam-4931	708	16	ω	ω	NOUN
ejpam-4931	708	17	)	)	PUNCT
ejpam-4931	708	18	)	)	PUNCT
ejpam-4931	708	19	≤	≤	PUNCT
ejpam-4931	708	20	k	k	X
ejpam-4931	708	21	∥ξα,ϵuα,ϵ∥	∥ξα,ϵuα,ϵ∥	PROPN
ejpam-4931	708	22	l2	l2	NOUN
ejpam-4931	708	23	(	(	PUNCT
ejpam-4931	708	24	[	[	X
ejpam-4931	708	25	0,t	0,t	X
ejpam-4931	708	26	]	]	X
ejpam-4931	708	27	;	;	PUNCT
ejpam-4931	708	28	w	w	PROPN
ejpam-4931	708	29	1	1	NUM
ejpam-4931	708	30	,	,	PUNCT
ejpam-4931	708	31	32	32	NUM
ejpam-4931	708	32	(	(	PUNCT
ejpam-4931	708	33	ω	ω	NOUN
ejpam-4931	708	34	)	)	PUNCT
ejpam-4931	708	35	)	)	PUNCT
ejpam-4931	709	1	+	+	X
ejpam-4931	709	2	∥∂t(ξα,ϵuα,ϵ)∥l2	∥∂t(ξα,ϵuα,ϵ)∥l2	PART
ejpam-4931	709	3	(	(	PUNCT
ejpam-4931	709	4	[	[	X
ejpam-4931	709	5	0,t	0,t	X
ejpam-4931	709	6	]	]	X
ejpam-4931	709	7	;	;	PUNCT
ejpam-4931	709	8	h−5(ω	h−5(ω	PROPN
ejpam-4931	709	9	)	)	PUNCT
ejpam-4931	709	10	)	)	PUNCT
ejpam-4931	709	11	≤	≤	PUNCT
ejpam-4931	710	1	k	k	X
ejpam-4931	710	2	,	,	PUNCT
ejpam-4931	710	3	(	(	PUNCT
ejpam-4931	710	4	94	94	NUM
ejpam-4931	710	5	)	)	PUNCT
ejpam-4931	710	6	where	where	SCONJ
ejpam-4931	710	7	k	k	PROPN
ejpam-4931	710	8	is	be	AUX
ejpam-4931	710	9	independent	independent	ADJ
ejpam-4931	710	10	of	of	ADP
ejpam-4931	710	11	ϵ	ϵ	NUM
ejpam-4931	710	12	,	,	PUNCT
ejpam-4931	710	13	α	α	PROPN
ejpam-4931	710	14	.	.	PUNCT
ejpam-4931	710	15	j.	j.	PROPN
ejpam-4931	710	16	ouya	ouya	PROPN
ejpam-4931	710	17	,	,	PUNCT
ejpam-4931	710	18	a.	a.	NOUN
ejpam-4931	710	19	ouédraogo	ouédraogo	PROPN
ejpam-4931	710	20	/	/	SYM
ejpam-4931	710	21	eur	eur	PROPN
ejpam-4931	710	22	.	.	PUNCT
ejpam-4931	711	1	j.	j.	PROPN
ejpam-4931	711	2	pure	pure	PROPN
ejpam-4931	711	3	appl	appl	PROPN
ejpam-4931	711	4	.	.	PROPN
ejpam-4931	711	5	math	math	PROPN
ejpam-4931	711	6	,	,	PUNCT
ejpam-4931	711	7	16	16	NUM
ejpam-4931	711	8	(	(	PUNCT
ejpam-4931	711	9	4	4	NUM
ejpam-4931	711	10	)	)	PUNCT
ejpam-4931	711	11	(	(	PUNCT
ejpam-4931	711	12	2023	2023	NUM
ejpam-4931	711	13	)	)	PUNCT
ejpam-4931	711	14	,	,	PUNCT
ejpam-4931	711	15	2247	2247	NUM
ejpam-4931	711	16	-	-	SYM
ejpam-4931	711	17	2285	2285	NUM
ejpam-4931	711	18	2273	2273	NUM
ejpam-4931	711	19	proof	proof	NOUN
ejpam-4931	711	20	.	.	PUNCT
ejpam-4931	712	1	the	the	DET
ejpam-4931	712	2	proof	proof	NOUN
ejpam-4931	712	3	of	of	ADP
ejpam-4931	712	4	lemma	lemma	PROPN
ejpam-4931	712	5	12	12	NUM
ejpam-4931	712	6	follows	follow	VERB
ejpam-4931	712	7	the	the	DET
ejpam-4931	712	8	same	same	ADJ
ejpam-4931	712	9	lines	line	NOUN
ejpam-4931	712	10	as	as	ADP
ejpam-4931	712	11	the	the	DET
ejpam-4931	712	12	proof	proof	NOUN
ejpam-4931	712	13	of	of	ADP
ejpam-4931	712	14	lemma	lemma	PROPN
ejpam-4931	712	15	6	6	NUM
ejpam-4931	712	16	.	.	PUNCT
ejpam-4931	712	17	thanks	thank	NOUN
ejpam-4931	712	18	to	to	ADP
ejpam-4931	712	19	lemmas	lemmas	PROPN
ejpam-4931	712	20	1	1	NUM
ejpam-4931	712	21	and	and	CCONJ
ejpam-4931	712	22	12	12	NUM
ejpam-4931	712	23	,	,	PUNCT
ejpam-4931	712	24	when	when	SCONJ
ejpam-4931	712	25	α→	α→	PROPN
ejpam-4931	712	26	0	0	NUM
ejpam-4931	712	27	and	and	CCONJ
ejpam-4931	712	28	ϵ→	ϵ→	PROPN
ejpam-4931	712	29	0	0	NUM
ejpam-4931	712	30	,	,	PUNCT
ejpam-4931	712	31	we	we	PRON
ejpam-4931	712	32	have	have	VERB
ejpam-4931	712	33	the	the	DET
ejpam-4931	712	34	following	follow	VERB
ejpam-4931	712	35	compactness	compactness	NOUN
ejpam-4931	712	36	results	results	PROPN
ejpam-4931	712	37	√	√	ADP
ejpam-4931	712	38	ξα,ϵ	ξα,ϵ	NOUN
ejpam-4931	712	39	−→	−→	NOUN
ejpam-4931	712	40	√	√	NUM
ejpam-4931	712	41	ξ	ξ	ADP
ejpam-4931	712	42	strongly	strongly	ADV
ejpam-4931	712	43	in	in	ADP
ejpam-4931	712	44	l2	l2	NOUN
ejpam-4931	712	45	(	(	PUNCT
ejpam-4931	712	46	[	[	X
ejpam-4931	712	47	0	0	NUM
ejpam-4931	712	48	,	,	PUNCT
ejpam-4931	712	49	t	t	X
ejpam-4931	712	50	]	]	PUNCT
ejpam-4931	712	51	;	;	PUNCT
ejpam-4931	712	52	h1(ω	h1(ω	PROPN
ejpam-4931	712	53	)	)	PUNCT
ejpam-4931	712	54	)	)	PUNCT
ejpam-4931	712	55	,	,	PUNCT
ejpam-4931	712	56	ξα,ϵ	ξα,ϵ	AUX
ejpam-4931	712	57	−→	−→	NOUN
ejpam-4931	712	58	ξ	ξ	X
ejpam-4931	712	59	strongly	strongly	ADV
ejpam-4931	712	60	in	in	ADP
ejpam-4931	712	61	c	c	PROPN
ejpam-4931	712	62	(	(	PUNCT
ejpam-4931	712	63	[	[	X
ejpam-4931	712	64	0	0	NUM
ejpam-4931	712	65	,	,	PUNCT
ejpam-4931	712	66	t	t	X
ejpam-4931	712	67	]	]	PUNCT
ejpam-4931	712	68	;	;	PUNCT
ejpam-4931	712	69	h5(ω	h5(ω	NUM
ejpam-4931	712	70	)	)	PUNCT
ejpam-4931	712	71	)	)	PUNCT
ejpam-4931	712	72	,	,	PUNCT
ejpam-4931	712	73	ξα,ϵ	ξα,ϵ	X
ejpam-4931	713	1	⇀	⇀	PUNCT
ejpam-4931	713	2	ξ	ξ	PUNCT
ejpam-4931	713	3	weakly	weakly	ADJ
ejpam-4931	713	4	in	in	ADP
ejpam-4931	713	5	l2	l2	NOUN
ejpam-4931	713	6	(	(	PUNCT
ejpam-4931	713	7	[	[	X
ejpam-4931	713	8	0	0	NUM
ejpam-4931	713	9	,	,	PUNCT
ejpam-4931	713	10	t	t	X
ejpam-4931	713	11	]	]	PUNCT
ejpam-4931	713	12	;	;	PUNCT
ejpam-4931	713	13	h6(ω	h6(ω	X
ejpam-4931	713	14	)	)	PUNCT
ejpam-4931	713	15	)	)	PUNCT
ejpam-4931	713	16	,	,	PUNCT
ejpam-4931	713	17	uα,ϵ	uα,ϵ	PUNCT
ejpam-4931	713	18	⇀	⇀	PUNCT
ejpam-4931	713	19	u	u	NOUN
ejpam-4931	713	20	weakly	weakly	ADJ
ejpam-4931	713	21	in	in	ADP
ejpam-4931	713	22	l2	l2	NOUN
ejpam-4931	713	23	(	(	PUNCT
ejpam-4931	713	24	[	[	X
ejpam-4931	713	25	0	0	NUM
ejpam-4931	713	26	,	,	PUNCT
ejpam-4931	713	27	t	t	X
ejpam-4931	713	28	]	]	PUNCT
ejpam-4931	713	29	;	;	PUNCT
ejpam-4931	713	30	l2(ω	l2(ω	NUM
ejpam-4931	713	31	)	)	PUNCT
ejpam-4931	713	32	)	)	PUNCT
ejpam-4931	713	33	,	,	PUNCT
ejpam-4931	713	34	√	√	NUM
ejpam-4931	713	35	ξα,ϵ	ξα,ϵ	PUNCT
ejpam-4931	713	36	⇀	⇀	NUM
ejpam-4931	713	37	√	√	NUM
ejpam-4931	713	38	ξ	ξ	X
ejpam-4931	713	39	weakly	weakly	ADJ
ejpam-4931	713	40	in	in	ADP
ejpam-4931	713	41	l2	l2	NOUN
ejpam-4931	713	42	(	(	PUNCT
ejpam-4931	713	43	[	[	X
ejpam-4931	713	44	0	0	NUM
ejpam-4931	713	45	,	,	PUNCT
ejpam-4931	713	46	t	t	X
ejpam-4931	713	47	]	]	PUNCT
ejpam-4931	713	48	;	;	PUNCT
ejpam-4931	713	49	h2(ω	h2(ω	NUM
ejpam-4931	713	50	)	)	PUNCT
ejpam-4931	713	51	)	)	PUNCT
ejpam-4931	713	52	,	,	PUNCT
ejpam-4931	713	53	ξα,ϵuα,ϵ	ξα,ϵuα,ϵ	PROPN
ejpam-4931	713	54	−→	−→	NOUN
ejpam-4931	713	55	ξu	ξu	VERB
ejpam-4931	713	56	strongly	strongly	ADV
ejpam-4931	713	57	in	in	ADP
ejpam-4931	713	58	l2	l2	NOUN
ejpam-4931	713	59	(	(	PUNCT
ejpam-4931	713	60	[	[	X
ejpam-4931	713	61	0	0	NUM
ejpam-4931	713	62	,	,	PUNCT
ejpam-4931	713	63	t	t	X
ejpam-4931	713	64	]	]	PUNCT
ejpam-4931	713	65	;	;	PUNCT
ejpam-4931	713	66	lp(ω	lp(ω	X
ejpam-4931	713	67	)	)	PUNCT
ejpam-4931	713	68	)	)	PUNCT
ejpam-4931	714	1	,	,	PUNCT
ejpam-4931	714	2	∀1	∀1	VERB
ejpam-4931	714	3	≤	≤	PUNCT
ejpam-4931	714	4	p	p	X
ejpam-4931	714	5	<	<	X
ejpam-4931	714	6	3	3	NUM
ejpam-4931	714	7	,	,	PUNCT
ejpam-4931	714	8	ξ−β	ξ−β	VERB
ejpam-4931	714	9	α,ϵ	α,ϵ	PRON
ejpam-4931	714	10	−→	−→	NOUN
ejpam-4931	714	11	ξ−β	ξ−β	VERB
ejpam-4931	714	12	strongly	strongly	ADV
ejpam-4931	714	13	in	in	ADP
ejpam-4931	714	14	l1	l1	PROPN
ejpam-4931	714	15	(	(	PUNCT
ejpam-4931	714	16	[	[	X
ejpam-4931	714	17	0	0	NUM
ejpam-4931	714	18	,	,	PUNCT
ejpam-4931	714	19	t	t	X
ejpam-4931	714	20	]	]	PUNCT
ejpam-4931	714	21	;	;	PUNCT
ejpam-4931	714	22	l1(ω	l1(ω	X
ejpam-4931	714	23	)	)	PUNCT
ejpam-4931	714	24	)	)	PUNCT
ejpam-4931	714	25	,	,	PUNCT
ejpam-4931	714	26	√	√	PUNCT
ejpam-4931	714	27	ξα,ϵuα,ϵ	ξα,ϵuα,ϵ	PROPN
ejpam-4931	714	28	−→	−→	ADJ
ejpam-4931	714	29	√	√	PUNCT
ejpam-4931	714	30	ξu	ξu	VERB
ejpam-4931	714	31	strongly	strongly	ADV
ejpam-4931	714	32	in	in	ADP
ejpam-4931	714	33	l2	l2	NOUN
ejpam-4931	714	34	(	(	PUNCT
ejpam-4931	714	35	[	[	X
ejpam-4931	714	36	0	0	NUM
ejpam-4931	714	37	,	,	PUNCT
ejpam-4931	714	38	t	t	X
ejpam-4931	714	39	]	]	PUNCT
ejpam-4931	714	40	;	;	PUNCT
ejpam-4931	714	41	l2(ω	l2(ω	NUM
ejpam-4931	714	42	)	)	PUNCT
ejpam-4931	714	43	)	)	PUNCT
ejpam-4931	714	44	.	.	PUNCT
ejpam-4931	715	1	(	(	PUNCT
ejpam-4931	715	2	95	95	NUM
ejpam-4931	715	3	)	)	PUNCT
ejpam-4931	715	4	hence	hence	ADV
ejpam-4931	715	5	,	,	PUNCT
ejpam-4931	715	6	√	√	NUM
ejpam-4931	715	7	ξα,ϵ	ξα,ϵ	NOUN
ejpam-4931	715	8	−→	−→	ADJ
ejpam-4931	715	9	√	√	NUM
ejpam-4931	715	10	ξ	ξ	PROPN
ejpam-4931	715	11	,	,	PUNCT
ejpam-4931	715	12	ξα,ϵ	ξα,ϵ	VERB
ejpam-4931	715	13	−→	−→	NOUN
ejpam-4931	715	14	ξ	ξ	PROPN
ejpam-4931	715	15	and	and	CCONJ
ejpam-4931	715	16	ξ−β	ξ−β	VERB
ejpam-4931	715	17	α,ϵ	α,ϵ	PRON
ejpam-4931	715	18	−→	−→	NOUN
ejpam-4931	715	19	ξ−β	ξ−β	VERB
ejpam-4931	715	20	almost	almost	ADV
ejpam-4931	715	21	everywhere	everywhere	ADV
ejpam-4931	715	22	(	(	PUNCT
ejpam-4931	715	23	t	t	PROPN
ejpam-4931	715	24	,	,	PUNCT
ejpam-4931	715	25	x	x	NOUN
ejpam-4931	715	26	)	)	PUNCT
ejpam-4931	715	27	.	.	PUNCT
ejpam-4931	716	1	by	by	ADP
ejpam-4931	716	2	the	the	DET
ejpam-4931	716	3	results	result	NOUN
ejpam-4931	716	4	of	of	ADP
ejpam-4931	716	5	regularities	regularity	NOUN
ejpam-4931	716	6	above	above	ADV
ejpam-4931	716	7	,	,	PUNCT
ejpam-4931	716	8	we	we	PRON
ejpam-4931	716	9	can	can	AUX
ejpam-4931	716	10	pass	pass	VERB
ejpam-4931	716	11	to	to	ADP
ejpam-4931	716	12	the	the	DET
ejpam-4931	716	13	limits	limit	NOUN
ejpam-4931	716	14	in	in	ADP
ejpam-4931	716	15	(	(	PUNCT
ejpam-4931	716	16	60	60	NUM
ejpam-4931	716	17	)	)	PUNCT
ejpam-4931	716	18	as	as	ADP
ejpam-4931	716	19	α→	α→	PROPN
ejpam-4931	716	20	0	0	NUM
ejpam-4931	716	21	and	and	CCONJ
ejpam-4931	716	22	ϵ→	ϵ→	PROPN
ejpam-4931	716	23	0	0	NUM
ejpam-4931	716	24	.	.	PUNCT
ejpam-4931	717	1	for	for	ADP
ejpam-4931	717	2	any	any	DET
ejpam-4931	717	3	test	test	NOUN
ejpam-4931	717	4	function	function	NOUN
ejpam-4931	717	5	φ	φ	PROPN
ejpam-4931	717	6	∈	∈	PROPN
ejpam-4931	717	7	c∞	c∞	PROPN
ejpam-4931	717	8	c	c	NOUN
ejpam-4931	717	9	(	(	PUNCT
ejpam-4931	717	10	[	[	X
ejpam-4931	717	11	0	0	NUM
ejpam-4931	717	12	,	,	PUNCT
ejpam-4931	717	13	t	t	X
ejpam-4931	717	14	]	]	X
ejpam-4931	717	15	×	×	PROPN
ejpam-4931	717	16	ω	ω	PROPN
ejpam-4931	717	17	)	)	PUNCT
ejpam-4931	717	18	,	,	PUNCT
ejpam-4931	717	19	we	we	PRON
ejpam-4931	717	20	have∫	have∫	VERB
ejpam-4931	717	21	t	t	PROPN
ejpam-4931	717	22	0	0	NUM
ejpam-4931	717	23	∫	∫	PROPN
ejpam-4931	717	24	ω	ω	PROPN
ejpam-4931	717	25	∂y(ξα,ϵuα,ϵvα,ϵ)φdxdydt	∂y(ξα,ϵuα,ϵvα,ϵ)φdxdydt	PROPN
ejpam-4931	717	26	=	=	PUNCT
ejpam-4931	718	1	−	−	PROPN
ejpam-4931	718	2	∫	∫	PROPN
ejpam-4931	718	3	t	t	PROPN
ejpam-4931	718	4	0	0	NUM
ejpam-4931	718	5	∫	∫	PROPN
ejpam-4931	719	1	ω	ω	NUM
ejpam-4931	719	2	ξα,ϵuα,ϵvα,ϵ∂yφdxdydt	ξα,ϵuα,ϵvα,ϵ∂yφdxdydt	PROPN
ejpam-4931	719	3	−→	−→	NOUN
ejpam-4931	719	4	−	−	PROPN
ejpam-4931	719	5	∫	∫	PROPN
ejpam-4931	719	6	t	t	PROPN
ejpam-4931	719	7	0	0	NUM
ejpam-4931	719	8	∫	∫	PROPN
ejpam-4931	719	9	ω	ω	PROPN
ejpam-4931	719	10	ξuv∂yφdxdydt	ξuv∂yφdxdydt	PROPN
ejpam-4931	719	11	.	.	PUNCT
ejpam-4931	720	1	(	(	PUNCT
ejpam-4931	720	2	96	96	NUM
ejpam-4931	720	3	)	)	PUNCT
ejpam-4931	720	4	moreover	moreover	ADV
ejpam-4931	720	5	,	,	PUNCT
ejpam-4931	720	6	when	when	SCONJ
ejpam-4931	720	7	ϵ	ϵ	X
ejpam-4931	720	8	,	,	PUNCT
ejpam-4931	720	9	α	α	PRON
ejpam-4931	720	10	−→	−→	NOUN
ejpam-4931	720	11	0	0	NUM
ejpam-4931	720	12	,	,	PUNCT
ejpam-4931	720	13	we	we	PRON
ejpam-4931	720	14	have	have	VERB
ejpam-4931	720	15	ϵ	ϵ	X
ejpam-4931	720	16	∫	∫	PROPN
ejpam-4931	720	17	t	t	PROPN
ejpam-4931	720	18	0	0	NUM
ejpam-4931	721	1	∫	∫	PROPN
ejpam-4931	721	2	ω	ω	X
ejpam-4931	721	3	∇xξα,ϵ	∇xξα,ϵ	X
ejpam-4931	721	4	·	·	PUNCT
ejpam-4931	721	5	∇xuα,ϵφdxdydt	∇xuα,ϵφdxdydt	PROPN
ejpam-4931	721	6	=	=	SYM
ejpam-4931	721	7	−ϵ	−ϵ	PROPN
ejpam-4931	721	8	∫	∫	PROPN
ejpam-4931	721	9	t	t	PROPN
ejpam-4931	721	10	0	0	NUM
ejpam-4931	722	1	∫	∫	PROPN
ejpam-4931	722	2	ω	ω	NUM
ejpam-4931	722	3	∇x(∇xξα,ϵφ)uα,ϵdxdydt	∇x(∇xξα,ϵφ)uα,ϵdxdydt	PROPN
ejpam-4931	722	4	=	=	PUNCT
ejpam-4931	723	1	−ϵ	−ϵ	PROPN
ejpam-4931	723	2	∫	∫	PROPN
ejpam-4931	723	3	t	t	PROPN
ejpam-4931	723	4	0	0	NUM
ejpam-4931	723	5	∫	∫	PROPN
ejpam-4931	723	6	ω	ω	PROPN
ejpam-4931	723	7	∆xξα,ϵ	∆xξα,ϵ	PROPN
ejpam-4931	723	8	·	·	PUNCT
ejpam-4931	723	9	uα,ϵφdxdydt−	uα,ϵφdxdydt−	ADP
ejpam-4931	724	1	ϵ	ϵ	X
ejpam-4931	724	2	∫	∫	PROPN
ejpam-4931	724	3	t	t	PROPN
ejpam-4931	724	4	0	0	NUM
ejpam-4931	724	5	∫	∫	PROPN
ejpam-4931	724	6	ω	ω	PROPN
ejpam-4931	724	7	∇xξα,ϵuα,ϵdivxφdxdydt	∇xξα,ϵuα,ϵdivxφdxdydt	PROPN
ejpam-4931	724	8	≤	≤	NOUN
ejpam-4931	724	9	ϵ∥∆xξα,ϵ∥l2	ϵ∥∆xξα,ϵ∥l2	NOUN
ejpam-4931	725	1	(	(	PUNCT
ejpam-4931	725	2	[	[	X
ejpam-4931	725	3	0,t	0,t	X
ejpam-4931	725	4	]	]	X
ejpam-4931	725	5	;	;	PUNCT
ejpam-4931	725	6	l2(ω	l2(ω	NUM
ejpam-4931	725	7	)	)	PUNCT
ejpam-4931	725	8	)	)	PUNCT
ejpam-4931	726	1	∥uα,ϵ∥l2	∥uα,ϵ∥l2	PROPN
ejpam-4931	726	2	(	(	PUNCT
ejpam-4931	726	3	[	[	X
ejpam-4931	726	4	0,t	0,t	X
ejpam-4931	726	5	]	]	X
ejpam-4931	726	6	;	;	PUNCT
ejpam-4931	726	7	l2(ω	l2(ω	NUM
ejpam-4931	726	8	)	)	PUNCT
ejpam-4931	726	9	)	)	PUNCT
ejpam-4931	726	10	∥φ∥	∥φ∥	VERB
ejpam-4931	726	11	l∞	l∞	NOUN
ejpam-4931	726	12	(	(	PUNCT
ejpam-4931	726	13	[	[	X
ejpam-4931	726	14	0,t	0,t	X
ejpam-4931	726	15	]	]	X
ejpam-4931	726	16	;	;	PUNCT
ejpam-4931	726	17	l∞(ω	l∞(ω	X
ejpam-4931	726	18	)	)	PUNCT
ejpam-4931	726	19	)	)	PUNCT
ejpam-4931	727	1	+	+	PUNCT
ejpam-4931	727	2	ϵ∥∇xξα,ϵ∥l2	ϵ∥∇xξα,ϵ∥l2	NUM
ejpam-4931	727	3	(	(	PUNCT
ejpam-4931	727	4	[	[	X
ejpam-4931	727	5	0,t	0,t	X
ejpam-4931	727	6	]	]	X
ejpam-4931	727	7	;	;	PUNCT
ejpam-4931	727	8	l2(ω	l2(ω	NUM
ejpam-4931	727	9	)	)	PUNCT
ejpam-4931	727	10	)	)	PUNCT
ejpam-4931	728	1	∥uα,ϵ∥l2	∥uα,ϵ∥l2	PROPN
ejpam-4931	728	2	(	(	PUNCT
ejpam-4931	728	3	[	[	X
ejpam-4931	728	4	0,t	0,t	X
ejpam-4931	728	5	]	]	X
ejpam-4931	728	6	;	;	PUNCT
ejpam-4931	728	7	l2(ω	l2(ω	NUM
ejpam-4931	728	8	)	)	PUNCT
ejpam-4931	728	9	)	)	PUNCT
ejpam-4931	728	10	∥divxφ∥l∞	∥divxφ∥l∞	NUM
ejpam-4931	729	1	(	(	PUNCT
ejpam-4931	729	2	[	[	X
ejpam-4931	729	3	0,t	0,t	X
ejpam-4931	729	4	]	]	X
ejpam-4931	729	5	;	;	PUNCT
ejpam-4931	729	6	l∞(ω	l∞(ω	X
ejpam-4931	729	7	)	)	PUNCT
ejpam-4931	729	8	)	)	PUNCT
ejpam-4931	730	1	−→	−→	NOUN
ejpam-4931	730	2	0	0	NUM
ejpam-4931	730	3	(	(	PUNCT
ejpam-4931	730	4	97	97	NUM
ejpam-4931	730	5	)	)	PUNCT
ejpam-4931	730	6	and	and	CCONJ
ejpam-4931	730	7	α	α	DET
ejpam-4931	730	8	∫	∫	PROPN
ejpam-4931	731	1	t	t	PROPN
ejpam-4931	731	2	0	0	NUM
ejpam-4931	731	3	∫	∫	PROPN
ejpam-4931	731	4	ω	ω	PROPN
ejpam-4931	731	5	∆2uα,ϵ	∆2uα,ϵ	PROPN
ejpam-4931	731	6	·	·	PUNCT
ejpam-4931	731	7	φdxdydt	φdxdydt	ADJ
ejpam-4931	731	8	=	=	SYM
ejpam-4931	731	9	α	α	NUM
ejpam-4931	731	10	∫	∫	PROPN
ejpam-4931	731	11	t	t	PROPN
ejpam-4931	731	12	0	0	NUM
ejpam-4931	731	13	∫	∫	PROPN
ejpam-4931	732	1	ω	ω	PROPN
ejpam-4931	732	2	∆uα,ϵ	∆uα,ϵ	PROPN
ejpam-4931	732	3	·	·	PUNCT
ejpam-4931	732	4	∆ϕdxdydt	∆ϕdxdydt	ADJ
ejpam-4931	732	5	j.	j.	PROPN
ejpam-4931	732	6	ouya	ouya	PROPN
ejpam-4931	732	7	,	,	PUNCT
ejpam-4931	732	8	a.	a.	NOUN
ejpam-4931	732	9	ouédraogo	ouédraogo	PROPN
ejpam-4931	732	10	/	/	SYM
ejpam-4931	732	11	eur	eur	PROPN
ejpam-4931	732	12	.	.	PUNCT
ejpam-4931	733	1	j.	j.	PROPN
ejpam-4931	733	2	pure	pure	PROPN
ejpam-4931	733	3	appl	appl	PROPN
ejpam-4931	733	4	.	.	PROPN
ejpam-4931	733	5	math	math	PROPN
ejpam-4931	733	6	,	,	PUNCT
ejpam-4931	733	7	16	16	NUM
ejpam-4931	733	8	(	(	PUNCT
ejpam-4931	733	9	4	4	NUM
ejpam-4931	733	10	)	)	PUNCT
ejpam-4931	733	11	(	(	PUNCT
ejpam-4931	733	12	2023	2023	NUM
ejpam-4931	733	13	)	)	PUNCT
ejpam-4931	733	14	,	,	PUNCT
ejpam-4931	733	15	2247	2247	NUM
ejpam-4931	733	16	-	-	SYM
ejpam-4931	733	17	2285	2285	NUM
ejpam-4931	733	18	2274	2274	NUM
ejpam-4931	733	19	≤	≤	NOUN
ejpam-4931	733	20	√	√	NUM
ejpam-4931	734	1	α∥	α∥	ADP
ejpam-4931	734	2	√	√	PROPN
ejpam-4931	734	3	α∆uα,ϵ∥l2	α∆uα,ϵ∥l2	PROPN
ejpam-4931	734	4	(	(	PUNCT
ejpam-4931	734	5	[	[	X
ejpam-4931	734	6	0,t	0,t	X
ejpam-4931	734	7	]	]	X
ejpam-4931	734	8	;	;	PUNCT
ejpam-4931	734	9	l2(ω	l2(ω	NUM
ejpam-4931	734	10	)	)	PUNCT
ejpam-4931	734	11	)	)	PUNCT
ejpam-4931	734	12	∥∆φ∥	∥∆φ∥	VERB
ejpam-4931	734	13	l2	l2	NOUN
ejpam-4931	734	14	(	(	PUNCT
ejpam-4931	734	15	[	[	X
ejpam-4931	734	16	0,t	0,t	X
ejpam-4931	734	17	]	]	X
ejpam-4931	734	18	;	;	PUNCT
ejpam-4931	734	19	l2(ω	l2(ω	NUM
ejpam-4931	734	20	)	)	PUNCT
ejpam-4931	734	21	)	)	PUNCT
ejpam-4931	735	1	−→	−→	NOUN
ejpam-4931	735	2	0	0	NUM
ejpam-4931	735	3	.	.	PUNCT
ejpam-4931	736	1	(	(	PUNCT
ejpam-4931	736	2	98	98	NUM
ejpam-4931	736	3	)	)	PUNCT
ejpam-4931	736	4	so	so	ADV
ejpam-4931	736	5	,	,	PUNCT
ejpam-4931	736	6	taking	take	VERB
ejpam-4931	736	7	α	α	PRON
ejpam-4931	736	8	,	,	PUNCT
ejpam-4931	736	9	ϵ	ϵ	X
ejpam-4931	736	10	−→	−→	NOUN
ejpam-4931	736	11	0	0	NUM
ejpam-4931	736	12	in	in	ADP
ejpam-4931	736	13	(	(	PUNCT
ejpam-4931	736	14	60	60	NUM
ejpam-4931	736	15	)	)	PUNCT
ejpam-4931	736	16	,	,	PUNCT
ejpam-4931	736	17	the	the	DET
ejpam-4931	736	18	system	system	PROPN
ejpam-4931	736	19	∂tξ	∂tξ	VERB
ejpam-4931	736	20	+	+	CCONJ
ejpam-4931	736	21	divx(ξu	divx(ξu	NOUN
ejpam-4931	736	22	)	)	PUNCT
ejpam-4931	736	23	+	+	SYM
ejpam-4931	736	24	∂y(ξv	∂y(ξv	NOUN
ejpam-4931	736	25	)	)	PUNCT
ejpam-4931	736	26	=	=	SYM
ejpam-4931	736	27	0	0	NUM
ejpam-4931	736	28	,	,	PUNCT
ejpam-4931	736	29	∂t(ξu	∂t(ξu	X
ejpam-4931	736	30	)	)	PUNCT
ejpam-4931	736	31	+	+	CCONJ
ejpam-4931	736	32	divx(ξu⊗	divx(ξu⊗	NOUN
ejpam-4931	736	33	u	u	NOUN
ejpam-4931	736	34	)	)	PUNCT
ejpam-4931	736	35	+	+	CCONJ
ejpam-4931	736	36	∂y(ξuv	∂y(ξuv	X
ejpam-4931	736	37	)	)	PUNCT
ejpam-4931	737	1	+	+	X
ejpam-4931	737	2	∇xξ	∇xξ	PROPN
ejpam-4931	737	3	2	2	NUM
ejpam-4931	737	4	+	+	NUM
ejpam-4931	737	5	r1u+	r1u+	NOUN
ejpam-4931	737	6	rξ|u|u	rξ|u|u	NOUN
ejpam-4931	737	7	=	=	SYM
ejpam-4931	737	8	2divx	2divx	NUM
ejpam-4931	737	9	(	(	PUNCT
ejpam-4931	737	10	ξdx(u	ξdx(u	PROPN
ejpam-4931	737	11	)	)	PUNCT
ejpam-4931	737	12	)	)	PUNCT
ejpam-4931	738	1	+	+	CCONJ
ejpam-4931	738	2	∂y(ξ∂yu	∂y(ξ∂yu	NOUN
ejpam-4931	738	3	)	)	PUNCT
ejpam-4931	739	1	+	+	CCONJ
ejpam-4931	739	2	r2∇xξ	r2∇xξ	NOUN
ejpam-4931	739	3	−β	−β	NOUN
ejpam-4931	739	4	+	+	CCONJ
ejpam-4931	739	5	k1ξ∇x	k1ξ∇x	PROPN
ejpam-4931	739	6	(	(	PUNCT
ejpam-4931	739	7	∆x	∆x	PROPN
ejpam-4931	739	8	√	√	PROPN
ejpam-4931	739	9	ξ√	ξ√	PROPN
ejpam-4931	739	10	ξ	ξ	PROPN
ejpam-4931	739	11	)	)	PUNCT
ejpam-4931	740	1	+	+	CCONJ
ejpam-4931	740	2	δξ∇x∆	δξ∇x∆	PROPN
ejpam-4931	740	3	5	5	NUM
ejpam-4931	740	4	xξ	xξ	NOUN
ejpam-4931	740	5	,	,	PUNCT
ejpam-4931	740	6	∂yξ	∂yξ	PROPN
ejpam-4931	740	7	=	=	SYM
ejpam-4931	740	8	0	0	NUM
ejpam-4931	740	9	(	(	PUNCT
ejpam-4931	740	10	99	99	NUM
ejpam-4931	740	11	)	)	PUNCT
ejpam-4931	740	12	holds	hold	VERB
ejpam-4931	740	13	in	in	ADP
ejpam-4931	740	14	the	the	DET
ejpam-4931	740	15	sense	sense	NOUN
ejpam-4931	740	16	of	of	ADP
ejpam-4931	740	17	distribution	distribution	NOUN
ejpam-4931	740	18	on	on	ADP
ejpam-4931	740	19	[	[	X
ejpam-4931	740	20	0	0	NUM
ejpam-4931	740	21	,	,	PUNCT
ejpam-4931	740	22	t	t	X
ejpam-4931	740	23	]	]	X
ejpam-4931	740	24	×	×	PROPN
ejpam-4931	740	25	ω	ω	X
ejpam-4931	740	26	.	.	PUNCT
ejpam-4931	741	1	moreover	moreover	ADV
ejpam-4931	741	2	,	,	PUNCT
ejpam-4931	741	3	thanks	thank	NOUN
ejpam-4931	741	4	to	to	ADP
ejpam-4931	741	5	the	the	DET
ejpam-4931	741	6	lower	low	ADJ
ejpam-4931	741	7	semi	semi	NOUN
ejpam-4931	741	8	-	-	NOUN
ejpam-4931	741	9	continuity	continuity	NOUN
ejpam-4931	741	10	of	of	ADP
ejpam-4931	741	11	convex	convex	NOUN
ejpam-4931	741	12	functions	function	NOUN
ejpam-4931	741	13	and	and	CCONJ
ejpam-4931	741	14	the	the	DET
ejpam-4931	741	15	strong	strong	ADJ
ejpam-4931	741	16	convergence	convergence	NOUN
ejpam-4931	741	17	of	of	ADP
ejpam-4931	741	18	(	(	PUNCT
ejpam-4931	741	19	ξα,ϵ	ξα,ϵ	NOUN
ejpam-4931	741	20	,	,	PUNCT
ejpam-4931	741	21	uα,ϵ	uα,ϵ	NOUN
ejpam-4931	741	22	,	,	PUNCT
ejpam-4931	741	23	vα,ϵ	vα,ϵ	NOUN
ejpam-4931	741	24	)	)	PUNCT
ejpam-4931	741	25	,	,	PUNCT
ejpam-4931	741	26	we	we	PRON
ejpam-4931	741	27	can	can	AUX
ejpam-4931	741	28	pass	pass	VERB
ejpam-4931	741	29	to	to	ADP
ejpam-4931	741	30	the	the	DET
ejpam-4931	741	31	limits	limit	NOUN
ejpam-4931	741	32	in	in	ADP
ejpam-4931	741	33	the	the	DET
ejpam-4931	741	34	energy	energy	NOUN
ejpam-4931	741	35	inequality	inequality	NOUN
ejpam-4931	741	36	(	(	PUNCT
ejpam-4931	741	37	59	59	NUM
ejpam-4931	741	38	)	)	PUNCT
ejpam-4931	741	39	and	and	CCONJ
ejpam-4931	741	40	the	the	DET
ejpam-4931	741	41	b	b	PROPN
ejpam-4931	741	42	-	-	PUNCT
ejpam-4931	741	43	d	d	ADJ
ejpam-4931	741	44	entropy	entropy	NOUN
ejpam-4931	741	45	(	(	PUNCT
ejpam-4931	741	46	65	65	NUM
ejpam-4931	741	47	)	)	PUNCT
ejpam-4931	741	48	as	as	ADP
ejpam-4931	741	49	α	α	NOUN
ejpam-4931	741	50	=	=	NOUN
ejpam-4931	741	51	ϵ	ϵ	X
ejpam-4931	741	52	−→	−→	NOUN
ejpam-4931	741	53	0	0	NUM
ejpam-4931	741	54	with	with	ADP
ejpam-4931	741	55	δ	δ	PROPN
ejpam-4931	741	56	,	,	PUNCT
ejpam-4931	741	57	r2	r2	PROPN
ejpam-4931	741	58	,	,	PUNCT
ejpam-4931	741	59	r0	r0	NOUN
ejpam-4931	741	60	,	,	PUNCT
ejpam-4931	741	61	k1	k1	NOUN
ejpam-4931	741	62	being	be	AUX
ejpam-4931	741	63	fixed	fix	VERB
ejpam-4931	741	64	,	,	PUNCT
ejpam-4931	741	65	to	to	PART
ejpam-4931	741	66	obtain	obtain	VERB
ejpam-4931	741	67	e(ξ	e(ξ	PROPN
ejpam-4931	741	68	,	,	PUNCT
ejpam-4931	741	69	u	u	NOUN
ejpam-4931	741	70	)	)	PUNCT
ejpam-4931	741	71	+	+	CCONJ
ejpam-4931	742	1	r1	r1	PROPN
ejpam-4931	742	2	∫	∫	PROPN
ejpam-4931	742	3	t	t	PROPN
ejpam-4931	742	4	0	0	NUM
ejpam-4931	742	5	∫	∫	PROPN
ejpam-4931	742	6	ω	ω	NUM
ejpam-4931	742	7	u2dxdt+	u2dxdt+	PROPN
ejpam-4931	742	8	r	r	NOUN
ejpam-4931	742	9	∫	∫	PROPN
ejpam-4931	742	10	t	t	PROPN
ejpam-4931	742	11	0	0	NUM
ejpam-4931	742	12	∫	∫	PROPN
ejpam-4931	742	13	ω	ω	NUM
ejpam-4931	742	14	ξ|u|3dxdt	ξ|u|3dxdt	PROPN
ejpam-4931	742	15	+	+	CCONJ
ejpam-4931	742	16	∫	∫	PROPN
ejpam-4931	742	17	t	t	PROPN
ejpam-4931	742	18	0	0	NUM
ejpam-4931	742	19	∫	∫	PROPN
ejpam-4931	742	20	ω	ω	NUM
ejpam-4931	742	21	2ξ|dx(u)|2dxdt+	2ξ|dx(u)|2dxdt+	NUM
ejpam-4931	742	22	∫	∫	PROPN
ejpam-4931	742	23	t	t	PROPN
ejpam-4931	742	24	0	0	NUM
ejpam-4931	742	25	∫	∫	PROPN
ejpam-4931	742	26	ω	ω	NUM
ejpam-4931	742	27	ξ|∂yu|2dxdt	ξ|∂yu|2dxdt	PROPN
ejpam-4931	742	28	≤	≤	PROPN
ejpam-4931	742	29	e(ξ0	e(ξ0	NOUN
ejpam-4931	742	30	,	,	PUNCT
ejpam-4931	742	31	u0	u0	ADJ
ejpam-4931	742	32	)	)	PUNCT
ejpam-4931	742	33	(	(	PUNCT
ejpam-4931	742	34	100	100	NUM
ejpam-4931	742	35	)	)	PUNCT
ejpam-4931	742	36	and∫	and∫	PROPN
ejpam-4931	743	1	ω	ω	PROPN
ejpam-4931	743	2	(	(	PUNCT
ejpam-4931	743	3	1	1	NUM
ejpam-4931	743	4	2	2	NUM
ejpam-4931	743	5	ξ|u+	ξ|u+	NOUN
ejpam-4931	743	6	2∇x	2∇x	NUM
ejpam-4931	743	7	ln	ln	PROPN
ejpam-4931	743	8	ξ|2	ξ|2	PROPN
ejpam-4931	743	9	−	−	PROPN
ejpam-4931	743	10	2r1	2r1	NUM
ejpam-4931	743	11	ln	ln	PROPN
ejpam-4931	743	12	ξ	ξ	PROPN
ejpam-4931	743	13	)	)	PUNCT
ejpam-4931	743	14	dxdy	dxdy	NOUN
ejpam-4931	743	15	+	+	CCONJ
ejpam-4931	744	1	2	2	NUM
ejpam-4931	744	2	∫	∫	NOUN
ejpam-4931	744	3	t	t	PROPN
ejpam-4931	744	4	0	0	NUM
ejpam-4931	744	5	∫	∫	PROPN
ejpam-4931	744	6	ω	ω	NUM
ejpam-4931	744	7	ξ|∂yv|2dxdydt+	ξ|∂yv|2dxdydt+	PROPN
ejpam-4931	744	8	r	r	NOUN
ejpam-4931	744	9	∫	∫	PROPN
ejpam-4931	744	10	t	t	PROPN
ejpam-4931	744	11	0	0	NUM
ejpam-4931	744	12	∫	∫	PROPN
ejpam-4931	744	13	ω	ω	NUM
ejpam-4931	744	14	ξ|u|3dxdydt	ξ|u|3dxdydt	PROPN
ejpam-4931	744	15	+	+	CCONJ
ejpam-4931	744	16	16r2	16r2	NUM
ejpam-4931	744	17	β	β	NOUN
ejpam-4931	744	18	∫	∫	PROPN
ejpam-4931	744	19	t	t	PROPN
ejpam-4931	744	20	0	0	NUM
ejpam-4931	744	21	∫	∫	PROPN
ejpam-4931	744	22	ω	ω	PROPN
ejpam-4931	744	23	|∇xξ	|∇xξ	PROPN
ejpam-4931	744	24	−β/2|2dxdydt+	−β/2|2dxdydt+	PROPN
ejpam-4931	744	25	r1	r1	PROPN
ejpam-4931	744	26	∫	∫	PROPN
ejpam-4931	744	27	t	t	PROPN
ejpam-4931	744	28	0	0	NUM
ejpam-4931	744	29	∫	∫	PROPN
ejpam-4931	745	1	ω	ω	PROPN
ejpam-4931	745	2	u2dxdydt+	u2dxdydt+	PROPN
ejpam-4931	745	3	∫	∫	PROPN
ejpam-4931	745	4	t	t	PROPN
ejpam-4931	745	5	0	0	NUM
ejpam-4931	745	6	∫	∫	PROPN
ejpam-4931	745	7	ω	ω	X
ejpam-4931	745	8	ξ|∂yu|2dxdy	ξ|∂yu|2dxdy	X
ejpam-4931	745	9	+	+	CCONJ
ejpam-4931	745	10	k1	k1	PROPN
ejpam-4931	745	11	∫	∫	PROPN
ejpam-4931	745	12	t	t	PROPN
ejpam-4931	745	13	0	0	NUM
ejpam-4931	745	14	∫	∫	PROPN
ejpam-4931	745	15	ω	ω	NUM
ejpam-4931	745	16	ξ|∇2	ξ|∇2	PROPN
ejpam-4931	746	1	x	x	SYM
ejpam-4931	746	2	ln	ln	NOUN
ejpam-4931	746	3	ξ|2dxdydt+	ξ|2dxdydt+	NUM
ejpam-4931	746	4	2δ	2δ	NUM
ejpam-4931	747	1	∫	∫	PROPN
ejpam-4931	747	2	t	t	PROPN
ejpam-4931	747	3	0	0	NUM
ejpam-4931	747	4	∫	∫	PROPN
ejpam-4931	747	5	ω	ω	PROPN
ejpam-4931	747	6	|∆3	|∆3	NOUN
ejpam-4931	747	7	xξ|2dxdydt+	xξ|2dxdydt+	PROPN
ejpam-4931	747	8	2	2	NUM
ejpam-4931	747	9	∫	∫	NOUN
ejpam-4931	747	10	t	t	PROPN
ejpam-4931	747	11	0	0	NUM
ejpam-4931	747	12	∫	∫	PROPN
ejpam-4931	747	13	ω	ω	PROPN
ejpam-4931	748	1	ξ|ax(u)|2dxdydt	ξ|ax(u)|2dxdydt	PROPN
ejpam-4931	748	2	+	+	NUM
ejpam-4931	748	3	8	8	NUM
ejpam-4931	748	4	∫	∫	NOUN
ejpam-4931	748	5	t	t	PROPN
ejpam-4931	748	6	0	0	NUM
ejpam-4931	748	7	∫	∫	PROPN
ejpam-4931	748	8	ω	ω	NUM
ejpam-4931	748	9	ξ|∇x	ξ|∇x	ADJ
ejpam-4931	748	10	√	√	PROPN
ejpam-4931	748	11	ξ|2dxdydt	ξ|2dxdydt	NOUN
ejpam-4931	748	12	≤	≤	NUM
ejpam-4931	748	13	∫	∫	PROPN
ejpam-4931	748	14	ω	ω	PROPN
ejpam-4931	748	15	(	(	PUNCT
ejpam-4931	748	16	ξ0u	ξ0u	NOUN
ejpam-4931	748	17	2	2	NUM
ejpam-4931	748	18	0	0	NUM
ejpam-4931	748	19	+	+	CCONJ
ejpam-4931	748	20	10(∇x	10(∇x	NUM
ejpam-4931	748	21	√	√	ADJ
ejpam-4931	748	22	ξ0	ξ0	PROPN
ejpam-4931	748	23	)	)	PUNCT
ejpam-4931	748	24	2	2	NUM
ejpam-4931	748	25	−	−	PROPN
ejpam-4931	748	26	2r1	2r1	NUM
ejpam-4931	748	27	ln	ln	PROPN
ejpam-4931	748	28	ξ0	ξ0	PROPN
ejpam-4931	748	29	)	)	PUNCT
ejpam-4931	748	30	dxdy	dxdy	PROPN
ejpam-4931	748	31	+	+	CCONJ
ejpam-4931	748	32	e0	e0	PROPN
ejpam-4931	748	33	+	+	CCONJ
ejpam-4931	748	34	c.	c.	PROPN
ejpam-4931	748	35	(	(	PUNCT
ejpam-4931	748	36	101	101	NUM
ejpam-4931	748	37	)	)	PUNCT
ejpam-4931	748	38	thus	thus	ADV
ejpam-4931	748	39	,	,	PUNCT
ejpam-4931	748	40	to	to	PART
ejpam-4931	748	41	conclude	conclude	VERB
ejpam-4931	748	42	this	this	DET
ejpam-4931	748	43	part	part	NOUN
ejpam-4931	748	44	,	,	PUNCT
ejpam-4931	748	45	we	we	PRON
ejpam-4931	748	46	give	give	VERB
ejpam-4931	748	47	an	an	DET
ejpam-4931	748	48	existence	existence	NOUN
ejpam-4931	748	49	result	result	NOUN
ejpam-4931	748	50	of	of	ADP
ejpam-4931	748	51	weak	weak	ADJ
ejpam-4931	748	52	solutions	solution	NOUN
ejpam-4931	748	53	to	to	ADP
ejpam-4931	748	54	the	the	DET
ejpam-4931	748	55	system	system	NOUN
ejpam-4931	748	56	(	(	PUNCT
ejpam-4931	748	57	99	99	NUM
ejpam-4931	748	58	)	)	PUNCT
ejpam-4931	748	59	.	.	PUNCT
ejpam-4931	749	1	proposition	proposition	NOUN
ejpam-4931	749	2	5.1	5.1	NUM
ejpam-4931	749	3	.	.	PUNCT
ejpam-4931	750	1	for	for	ADP
ejpam-4931	750	2	any	any	DET
ejpam-4931	750	3	t	t	PROPN
ejpam-4931	750	4	>	>	X
ejpam-4931	750	5	0	0	PROPN
ejpam-4931	750	6	,	,	PUNCT
ejpam-4931	750	7	the	the	DET
ejpam-4931	750	8	system	system	PROPN
ejpam-4931	750	9	∂tξ	∂tξ	VERB
ejpam-4931	750	10	+	+	CCONJ
ejpam-4931	750	11	divx(ξu	divx(ξu	NOUN
ejpam-4931	750	12	)	)	PUNCT
ejpam-4931	750	13	+	+	SYM
ejpam-4931	750	14	∂y(ξv	∂y(ξv	NOUN
ejpam-4931	750	15	)	)	PUNCT
ejpam-4931	750	16	=	=	SYM
ejpam-4931	750	17	0	0	NUM
ejpam-4931	750	18	,	,	PUNCT
ejpam-4931	750	19	∂t(ξu	∂t(ξu	X
ejpam-4931	750	20	)	)	PUNCT
ejpam-4931	751	1	+	+	CCONJ
ejpam-4931	751	2	divx(ξu⊗	divx(ξu⊗	NOUN
ejpam-4931	751	3	u	u	NOUN
ejpam-4931	751	4	)	)	PUNCT
ejpam-4931	751	5	+	+	CCONJ
ejpam-4931	751	6	∂y(ξuv	∂y(ξuv	X
ejpam-4931	751	7	)	)	PUNCT
ejpam-4931	752	1	+	+	X
ejpam-4931	752	2	∇xξ	∇xξ	PROPN
ejpam-4931	752	3	2	2	NUM
ejpam-4931	752	4	+	+	NUM
ejpam-4931	752	5	rξ|u|u+	rξ|u|u+	ADJ
ejpam-4931	752	6	r1u	r1u	NOUN
ejpam-4931	752	7	=	=	SYM
ejpam-4931	752	8	2divx	2divx	NUM
ejpam-4931	752	9	(	(	PUNCT
ejpam-4931	752	10	ξdx(u	ξdx(u	PROPN
ejpam-4931	752	11	)	)	PUNCT
ejpam-4931	752	12	)	)	PUNCT
ejpam-4931	753	1	+	+	CCONJ
ejpam-4931	753	2	∂y(ξ∂yu	∂y(ξ∂yu	NOUN
ejpam-4931	753	3	)	)	PUNCT
ejpam-4931	754	1	+	+	CCONJ
ejpam-4931	754	2	r2∇xξ	r2∇xξ	NOUN
ejpam-4931	754	3	−β	−β	NOUN
ejpam-4931	754	4	+	+	CCONJ
ejpam-4931	754	5	k1ξ∇x	k1ξ∇x	PROPN
ejpam-4931	754	6	(	(	PUNCT
ejpam-4931	754	7	∆x	∆x	PROPN
ejpam-4931	754	8	√	√	PROPN
ejpam-4931	754	9	ξ√	ξ√	PROPN
ejpam-4931	754	10	ξ	ξ	PROPN
ejpam-4931	754	11	)	)	PUNCT
ejpam-4931	755	1	+	+	CCONJ
ejpam-4931	755	2	δξ∇x∆	δξ∇x∆	PROPN
ejpam-4931	755	3	5	5	NUM
ejpam-4931	755	4	xξ	xξ	NOUN
ejpam-4931	755	5	,	,	PUNCT
ejpam-4931	755	6	∂yξ	∂yξ	PROPN
ejpam-4931	755	7	=	=	SYM
ejpam-4931	755	8	0	0	NUM
ejpam-4931	755	9	,	,	PUNCT
ejpam-4931	755	10	(	(	PUNCT
ejpam-4931	755	11	102	102	NUM
ejpam-4931	755	12	)	)	PUNCT
ejpam-4931	755	13	with	with	ADP
ejpam-4931	755	14	(	(	PUNCT
ejpam-4931	755	15	t	t	PROPN
ejpam-4931	755	16	,	,	PUNCT
ejpam-4931	755	17	x	x	NOUN
ejpam-4931	755	18	,	,	PUNCT
ejpam-4931	755	19	y	y	NOUN
ejpam-4931	755	20	)	)	PUNCT
ejpam-4931	755	21	∈	∈	PROPN
ejpam-4931	756	1	[	[	X
ejpam-4931	756	2	0	0	NUM
ejpam-4931	756	3	,	,	PUNCT
ejpam-4931	756	4	t	t	X
ejpam-4931	756	5	]	]	PUNCT
ejpam-4931	756	6	×ω	×ω	PUNCT
ejpam-4931	756	7	,	,	PUNCT
ejpam-4931	756	8	admits	admit	VERB
ejpam-4931	756	9	a	a	DET
ejpam-4931	756	10	weak	weak	ADJ
ejpam-4931	756	11	solution	solution	NOUN
ejpam-4931	756	12	with	with	ADP
ejpam-4931	756	13	appropriate	appropriate	ADJ
ejpam-4931	756	14	initial	initial	ADJ
ejpam-4931	756	15	data	datum	NOUN
ejpam-4931	756	16	.	.	PUNCT
ejpam-4931	757	1	in	in	ADP
ejpam-4931	757	2	particular	particular	ADJ
ejpam-4931	757	3	the	the	DET
ejpam-4931	757	4	weak	weak	ADJ
ejpam-4931	757	5	solution	solution	NOUN
ejpam-4931	757	6	(	(	PUNCT
ejpam-4931	757	7	ξ	ξ	X
ejpam-4931	757	8	,	,	PUNCT
ejpam-4931	757	9	u	u	NOUN
ejpam-4931	757	10	,	,	PUNCT
ejpam-4931	757	11	v	v	NOUN
ejpam-4931	757	12	)	)	PUNCT
ejpam-4931	757	13	satisfies	satisfy	VERB
ejpam-4931	757	14	the	the	DET
ejpam-4931	757	15	energy	energy	NOUN
ejpam-4931	757	16	inequality	inequality	NOUN
ejpam-4931	757	17	(	(	PUNCT
ejpam-4931	757	18	100	100	NUM
ejpam-4931	757	19	)	)	PUNCT
ejpam-4931	757	20	and	and	CCONJ
ejpam-4931	757	21	the	the	DET
ejpam-4931	757	22	b	b	PROPN
ejpam-4931	757	23	-	-	PUNCT
ejpam-4931	757	24	d	d	ADJ
ejpam-4931	757	25	entropy	entropy	NOUN
ejpam-4931	757	26	(	(	PUNCT
ejpam-4931	757	27	101	101	NUM
ejpam-4931	757	28	)	)	PUNCT
ejpam-4931	757	29	.	.	PUNCT
ejpam-4931	758	1	j.	j.	PROPN
ejpam-4931	758	2	ouya	ouya	PROPN
ejpam-4931	758	3	,	,	PUNCT
ejpam-4931	758	4	a.	a.	NOUN
ejpam-4931	758	5	ouédraogo	ouédraogo	PROPN
ejpam-4931	758	6	/	/	SYM
ejpam-4931	758	7	eur	eur	PROPN
ejpam-4931	758	8	.	.	PUNCT
ejpam-4931	759	1	j.	j.	PROPN
ejpam-4931	759	2	pure	pure	PROPN
ejpam-4931	759	3	appl	appl	PROPN
ejpam-4931	759	4	.	.	PROPN
ejpam-4931	759	5	math	math	PROPN
ejpam-4931	759	6	,	,	PUNCT
ejpam-4931	759	7	16	16	NUM
ejpam-4931	759	8	(	(	PUNCT
ejpam-4931	759	9	4	4	NUM
ejpam-4931	759	10	)	)	PUNCT
ejpam-4931	759	11	(	(	PUNCT
ejpam-4931	759	12	2023	2023	NUM
ejpam-4931	759	13	)	)	PUNCT
ejpam-4931	759	14	,	,	PUNCT
ejpam-4931	759	15	2247	2247	NUM
ejpam-4931	759	16	-	-	SYM
ejpam-4931	759	17	2285	2285	NUM
ejpam-4931	759	18	2275	2275	NUM
ejpam-4931	759	19	5.1.2	5.1.2	NOUN
ejpam-4931	759	20	.	.	PUNCT
ejpam-4931	760	1	passing	pass	VERB
ejpam-4931	760	2	to	to	ADP
ejpam-4931	760	3	the	the	DET
ejpam-4931	760	4	limits	limit	NOUN
ejpam-4931	760	5	as	as	ADP
ejpam-4931	760	6	r2	r2	NOUN
ejpam-4931	760	7	,	,	PUNCT
ejpam-4931	760	8	δ	δ	PROPN
ejpam-4931	760	9	−→	−→	NOUN
ejpam-4931	760	10	0	0	NUM
ejpam-4931	760	11	in	in	ADP
ejpam-4931	760	12	this	this	DET
ejpam-4931	760	13	step	step	NOUN
ejpam-4931	760	14	,	,	PUNCT
ejpam-4931	760	15	we	we	PRON
ejpam-4931	760	16	pass	pass	VERB
ejpam-4931	760	17	to	to	ADP
ejpam-4931	760	18	the	the	DET
ejpam-4931	760	19	limit	limit	NOUN
ejpam-4931	760	20	as	as	ADP
ejpam-4931	760	21	r2	r2	PROPN
ejpam-4931	760	22	−→	−→	NOUN
ejpam-4931	760	23	0	0	NUM
ejpam-4931	760	24	,	,	PUNCT
ejpam-4931	760	25	δ	δ	PROPN
ejpam-4931	760	26	−→	−→	NOUN
ejpam-4931	760	27	0	0	NUM
ejpam-4931	760	28	with	with	ADP
ejpam-4931	760	29	k1	k1	NOUN
ejpam-4931	760	30	,	,	PUNCT
ejpam-4931	760	31	r1	r1	PROPN
ejpam-4931	760	32	fixed	fix	VERB
ejpam-4931	760	33	.	.	PUNCT
ejpam-4931	761	1	we	we	PRON
ejpam-4931	761	2	denote	denote	VERB
ejpam-4931	761	3	by	by	ADP
ejpam-4931	761	4	(	(	PUNCT
ejpam-4931	761	5	ξr2,δ	ξr2,δ	PROPN
ejpam-4931	761	6	,	,	PUNCT
ejpam-4931	761	7	ur2,δ	ur2,δ	PROPN
ejpam-4931	761	8	,	,	PUNCT
ejpam-4931	761	9	vr2,δ	vr2,δ	PROPN
ejpam-4931	761	10	)	)	PUNCT
ejpam-4931	761	11	the	the	DET
ejpam-4931	761	12	weak	weak	ADJ
ejpam-4931	761	13	solution	solution	NOUN
ejpam-4931	761	14	at	at	ADP
ejpam-4931	761	15	this	this	DET
ejpam-4931	761	16	level	level	NOUN
ejpam-4931	761	17	.	.	PUNCT
ejpam-4931	762	1	from	from	ADP
ejpam-4931	762	2	proposition	proposition	NOUN
ejpam-4931	762	3	5.1	5.1	NUM
ejpam-4931	762	4	,	,	PUNCT
ejpam-4931	762	5	we	we	PRON
ejpam-4931	762	6	have	have	VERB
ejpam-4931	762	7	the	the	DET
ejpam-4931	762	8	following	follow	VERB
ejpam-4931	762	9	regularity	regularity	NOUN
ejpam-4931	762	10	results:	results:	PROPN
ejpam-4931	762	11	√	√	VERB
ejpam-4931	762	12	ξr2,δur2,δ	ξr2,δur2,δ	PROPN
ejpam-4931	762	13	∈	∈	PROPN
ejpam-4931	762	14	l∞	l∞	PROPN
ejpam-4931	762	15	(	(	PUNCT
ejpam-4931	762	16	[	[	X
ejpam-4931	762	17	0	0	NUM
ejpam-4931	762	18	,	,	PUNCT
ejpam-4931	762	19	t	t	X
ejpam-4931	762	20	]	]	PUNCT
ejpam-4931	762	21	;	;	PUNCT
ejpam-4931	762	22	l2(ω	l2(ω	NUM
ejpam-4931	762	23	)	)	PUNCT
ejpam-4931	762	24	)	)	PUNCT
ejpam-4931	762	25	,	,	PUNCT
ejpam-4931	762	26	√	√	NUM
ejpam-4931	762	27	ξr2,δdx(ur2,,δ	ξr2,δdx(ur2,,δ	ADJ
ejpam-4931	762	28	)	)	PUNCT
ejpam-4931	762	29	∈	∈	NOUN
ejpam-4931	762	30	l2	l2	NOUN
ejpam-4931	762	31	(	(	PUNCT
ejpam-4931	762	32	[	[	X
ejpam-4931	762	33	0	0	NUM
ejpam-4931	762	34	,	,	PUNCT
ejpam-4931	762	35	t	t	X
ejpam-4931	762	36	]	]	PUNCT
ejpam-4931	762	37	;	;	PUNCT
ejpam-4931	762	38	l2(ω	l2(ω	NUM
ejpam-4931	762	39	)	)	PUNCT
ejpam-4931	762	40	)	)	PUNCT
ejpam-4931	762	41	,	,	PUNCT
ejpam-4931	762	42	√	√	NUM
ejpam-4931	762	43	ξr2,δ∂yur2,δ	ξr2,δ∂yur2,δ	PROPN
ejpam-4931	762	44	∈	∈	PROPN
ejpam-4931	762	45	l2	l2	NOUN
ejpam-4931	762	46	(	(	PUNCT
ejpam-4931	762	47	[	[	X
ejpam-4931	762	48	0	0	NUM
ejpam-4931	762	49	,	,	PUNCT
ejpam-4931	762	50	t	t	X
ejpam-4931	762	51	]	]	PUNCT
ejpam-4931	762	52	;	;	PUNCT
ejpam-4931	762	53	l2(ω	l2(ω	NUM
ejpam-4931	762	54	)	)	PUNCT
ejpam-4931	762	55	)	)	PUNCT
ejpam-4931	762	56	,	,	PUNCT
ejpam-4931	762	57	√	√	NUM
ejpam-4931	762	58	ξr2,δ∇x	ξr2,δ∇x	NOUN
ejpam-4931	762	59	√	√	NOUN
ejpam-4931	762	60	ξr2,δ	ξr2,δ	PROPN
ejpam-4931	762	61	∈	∈	PROPN
ejpam-4931	762	62	l∞	l∞	NOUN
ejpam-4931	762	63	(	(	PUNCT
ejpam-4931	762	64	[	[	X
ejpam-4931	762	65	0	0	NUM
ejpam-4931	762	66	,	,	PUNCT
ejpam-4931	762	67	t	t	X
ejpam-4931	762	68	]	]	PUNCT
ejpam-4931	762	69	;	;	PUNCT
ejpam-4931	762	70	l2(ω	l2(ω	NUM
ejpam-4931	762	71	)	)	PUNCT
ejpam-4931	762	72	)	)	PUNCT
ejpam-4931	762	73	,	,	PUNCT
ejpam-4931	762	74	√	√	NUM
ejpam-4931	762	75	δξr2,δ	δξr2,δ	PROPN
ejpam-4931	762	76	∈	∈	PROPN
ejpam-4931	762	77	l∞	l∞	PROPN
ejpam-4931	762	78	(	(	PUNCT
ejpam-4931	762	79	[	[	X
ejpam-4931	762	80	0	0	NUM
ejpam-4931	762	81	,	,	PUNCT
ejpam-4931	762	82	t	t	X
ejpam-4931	762	83	]	]	PUNCT
ejpam-4931	762	84	;	;	PUNCT
ejpam-4931	762	85	h5(ω	h5(ω	NUM
ejpam-4931	762	86	)	)	PUNCT
ejpam-4931	762	87	)	)	PUNCT
ejpam-4931	762	88	,	,	PUNCT
ejpam-4931	762	89	√	√	NUM
ejpam-4931	762	90	δξr2,δ	δξr2,δ	PROPN
ejpam-4931	762	91	∈	∈	PROPN
ejpam-4931	762	92	l2	l2	NOUN
ejpam-4931	762	93	(	(	PUNCT
ejpam-4931	762	94	[	[	X
ejpam-4931	762	95	0	0	NUM
ejpam-4931	762	96	,	,	PUNCT
ejpam-4931	762	97	t	t	X
ejpam-4931	762	98	]	]	PUNCT
ejpam-4931	762	99	;	;	PUNCT
ejpam-4931	762	100	h6(ω	h6(ω	X
ejpam-4931	762	101	)	)	PUNCT
ejpam-4931	762	102	)	)	PUNCT
ejpam-4931	762	103	,	,	PUNCT
ejpam-4931	762	104	ur2,δ	ur2,δ	PROPN
ejpam-4931	762	105	∈	∈	PROPN
ejpam-4931	762	106	l2	l2	NOUN
ejpam-4931	762	107	(	(	PUNCT
ejpam-4931	762	108	[	[	X
ejpam-4931	762	109	0	0	NUM
ejpam-4931	762	110	,	,	PUNCT
ejpam-4931	762	111	t	t	X
ejpam-4931	762	112	]	]	PUNCT
ejpam-4931	762	113	;	;	PUNCT
ejpam-4931	762	114	l2(ω	l2(ω	NUM
ejpam-4931	762	115	)	)	PUNCT
ejpam-4931	762	116	)	)	PUNCT
ejpam-4931	762	117	,	,	PUNCT
ejpam-4931	762	118	ξ	ξ	PROPN
ejpam-4931	762	119	1	1	NUM
ejpam-4931	762	120	3	3	NUM
ejpam-4931	762	121	r2,δ	r2,δ	PROPN
ejpam-4931	762	122	ur2,δ	ur2,δ	PROPN
ejpam-4931	762	123	∈	∈	PROPN
ejpam-4931	762	124	l3	l3	NOUN
ejpam-4931	762	125	(	(	PUNCT
ejpam-4931	762	126	[	[	X
ejpam-4931	762	127	0	0	NUM
ejpam-4931	762	128	,	,	PUNCT
ejpam-4931	762	129	t	t	X
ejpam-4931	762	130	]	]	PUNCT
ejpam-4931	762	131	;	;	PUNCT
ejpam-4931	762	132	l3(ω	l3(ω	X
ejpam-4931	762	133	)	)	PUNCT
ejpam-4931	762	134	)	)	PUNCT
ejpam-4931	762	135	,	,	PUNCT
ejpam-4931	762	136	√	√	NUM
ejpam-4931	762	137	ξr2,δ∇xur2,δ	ξr2,δ∇xur2,δ	PROPN
ejpam-4931	762	138	∈	∈	PROPN
ejpam-4931	762	139	l2	l2	NOUN
ejpam-4931	762	140	(	(	PUNCT
ejpam-4931	762	141	[	[	X
ejpam-4931	762	142	0	0	NUM
ejpam-4931	762	143	,	,	PUNCT
ejpam-4931	762	144	t	t	X
ejpam-4931	762	145	]	]	PUNCT
ejpam-4931	762	146	;	;	PUNCT
ejpam-4931	762	147	l2(ω	l2(ω	NUM
ejpam-4931	762	148	)	)	PUNCT
ejpam-4931	762	149	)	)	PUNCT
ejpam-4931	762	150	,	,	PUNCT
ejpam-4931	762	151	√	√	PROPN
ejpam-4931	762	152	k1	k1	PROPN
ejpam-4931	762	153	√	√	PROPN
ejpam-4931	762	154	ξr2,δ	ξr2,δ	PROPN
ejpam-4931	762	155	∈	∈	PROPN
ejpam-4931	762	156	l2	l2	NOUN
ejpam-4931	762	157	(	(	PUNCT
ejpam-4931	762	158	[	[	X
ejpam-4931	762	159	0	0	NUM
ejpam-4931	762	160	,	,	PUNCT
ejpam-4931	762	161	t	t	X
ejpam-4931	762	162	]	]	PUNCT
ejpam-4931	762	163	;	;	PUNCT
ejpam-4931	762	164	h2(ω	h2(ω	NUM
ejpam-4931	762	165	)	)	PUNCT
ejpam-4931	762	166	)	)	PUNCT
ejpam-4931	762	167	,	,	PUNCT
ejpam-4931	762	168	4	4	NUM
ejpam-4931	762	169	√	√	NOUN
ejpam-4931	762	170	k1∇xξ	k1∇xξ	PROPN
ejpam-4931	762	171	1	1	NUM
ejpam-4931	762	172	4	4	NUM
ejpam-4931	762	173	r2,δ	r2,δ	PROPN
ejpam-4931	762	174	∈	∈	PROPN
ejpam-4931	762	175	l4	l4	PROPN
ejpam-4931	762	176	(	(	PUNCT
ejpam-4931	762	177	[	[	X
ejpam-4931	762	178	0	0	NUM
ejpam-4931	762	179	,	,	PUNCT
ejpam-4931	762	180	t	t	X
ejpam-4931	762	181	]	]	PUNCT
ejpam-4931	762	182	;	;	PUNCT
ejpam-4931	762	183	l4(ω	l4(ω	X
ejpam-4931	762	184	)	)	PUNCT
ejpam-4931	762	185	)	)	PUNCT
ejpam-4931	762	186	,	,	PUNCT
ejpam-4931	762	187	√	√	NUM
ejpam-4931	762	188	δ∆3	δ∆3	NUM
ejpam-4931	762	189	xξr2,δ	xξr2,δ	PROPN
ejpam-4931	762	190	∈	∈	PROPN
ejpam-4931	762	191	l2	l2	NOUN
ejpam-4931	762	192	(	(	PUNCT
ejpam-4931	762	193	[	[	X
ejpam-4931	762	194	0	0	NUM
ejpam-4931	762	195	,	,	PUNCT
ejpam-4931	762	196	t	t	X
ejpam-4931	762	197	]	]	PUNCT
ejpam-4931	762	198	;	;	PUNCT
ejpam-4931	762	199	l2(ω	l2(ω	NUM
ejpam-4931	762	200	)	)	PUNCT
ejpam-4931	762	201	)	)	PUNCT
ejpam-4931	762	202	,	,	PUNCT
ejpam-4931	762	203	√	√	PUNCT
ejpam-4931	762	204	r2∇xξ	r2∇xξ	NOUN
ejpam-4931	762	205	−β/2	−β/2	NOUN
ejpam-4931	762	206	r2,δ	r2,δ	PROPN
ejpam-4931	762	207	∈	∈	PROPN
ejpam-4931	762	208	l2	l2	NOUN
ejpam-4931	762	209	(	(	PUNCT
ejpam-4931	762	210	[	[	X
ejpam-4931	762	211	0	0	NUM
ejpam-4931	762	212	,	,	PUNCT
ejpam-4931	762	213	t	t	X
ejpam-4931	762	214	]	]	PUNCT
ejpam-4931	762	215	;	;	PUNCT
ejpam-4931	762	216	l2(ω	l2(ω	NUM
ejpam-4931	762	217	)	)	PUNCT
ejpam-4931	762	218	)	)	PUNCT
ejpam-4931	762	219	,	,	PUNCT
ejpam-4931	762	220	√	√	NUM
ejpam-4931	762	221	ξr2,δ∂yvr2,δ	ξr2,δ∂yvr2,δ	PROPN
ejpam-4931	762	222	∈	∈	PROPN
ejpam-4931	762	223	l2	l2	NOUN
ejpam-4931	762	224	(	(	PUNCT
ejpam-4931	762	225	[	[	X
ejpam-4931	762	226	0	0	NUM
ejpam-4931	762	227	,	,	PUNCT
ejpam-4931	762	228	t	t	X
ejpam-4931	762	229	]	]	PUNCT
ejpam-4931	762	230	;	;	PUNCT
ejpam-4931	762	231	l2(ω	l2(ω	NUM
ejpam-4931	762	232	)	)	PUNCT
ejpam-4931	762	233	)	)	PUNCT
ejpam-4931	762	234	,	,	PUNCT
ejpam-4931	762	235	r2ξ	r2ξ	ADP
ejpam-4931	762	236	−β	−β	PROPN
ejpam-4931	762	237	r2,δ	r2,δ	PROPN
ejpam-4931	762	238	∈	∈	PROPN
ejpam-4931	762	239	l∞	l∞	NOUN
ejpam-4931	762	240	(	(	PUNCT
ejpam-4931	762	241	[	[	X
ejpam-4931	762	242	0	0	NUM
ejpam-4931	762	243	,	,	PUNCT
ejpam-4931	762	244	t	t	X
ejpam-4931	762	245	]	]	PUNCT
ejpam-4931	762	246	;	;	PUNCT
ejpam-4931	762	247	l1(ω	l1(ω	X
ejpam-4931	762	248	)	)	PUNCT
ejpam-4931	762	249	)	)	PUNCT
ejpam-4931	762	250	,	,	PUNCT
ejpam-4931	762	251	r1	r1	PROPN
ejpam-4931	762	252	ln	ln	PROPN
ejpam-4931	762	253	ξr2,δ	ξr2,δ	PROPN
ejpam-4931	762	254	∈	∈	PROPN
ejpam-4931	762	255	l∞	l∞	NOUN
ejpam-4931	762	256	(	(	PUNCT
ejpam-4931	762	257	[	[	X
ejpam-4931	762	258	0	0	NUM
ejpam-4931	762	259	,	,	PUNCT
ejpam-4931	762	260	t	t	X
ejpam-4931	762	261	]	]	PUNCT
ejpam-4931	762	262	;	;	PUNCT
ejpam-4931	762	263	l1(ω	l1(ω	X
ejpam-4931	762	264	)	)	PUNCT
ejpam-4931	762	265	)	)	PUNCT
ejpam-4931	762	266	.	.	PUNCT
ejpam-4931	763	1	(	(	PUNCT
ejpam-4931	763	2	103	103	NUM
ejpam-4931	763	3	)	)	PUNCT
ejpam-4931	763	4	the	the	DET
ejpam-4931	763	5	inequality	inequality	NOUN
ejpam-4931	763	6	(	(	PUNCT
ejpam-4931	763	7	46	46	NUM
ejpam-4931	763	8	)	)	PUNCT
ejpam-4931	763	9	remains	remain	VERB
ejpam-4931	763	10	true	true	ADJ
ejpam-4931	763	11	for	for	ADP
ejpam-4931	763	12	r2	r2	NOUN
ejpam-4931	763	13	,	,	PUNCT
ejpam-4931	763	14	δ	δ	PROPN
ejpam-4931	763	15	−→	−→	NOUN
ejpam-4931	763	16	0	0	NUM
ejpam-4931	763	17	.	.	PUNCT
ejpam-4931	764	1	thus	thus	ADV
ejpam-4931	764	2	,	,	PUNCT
ejpam-4931	764	3	we	we	PRON
ejpam-4931	764	4	have	have	VERB
ejpam-4931	764	5	the	the	DET
ejpam-4931	764	6	uniform	uniform	ADJ
ejpam-4931	764	7	estimates	estimate	NOUN
ejpam-4931	764	8	similar	similar	ADJ
ejpam-4931	764	9	to	to	ADP
ejpam-4931	764	10	the	the	DET
ejpam-4931	764	11	lemma	lemma	PROPN
ejpam-4931	764	12	12	12	NUM
ejpam-4931	764	13	with	with	ADP
ejpam-4931	764	14	δ	δ	PROPN
ejpam-4931	764	15	and	and	CCONJ
ejpam-4931	764	16	r2	r2	PROPN
ejpam-4931	764	17	.	.	PUNCT
ejpam-4931	765	1	moreover	moreover	ADV
ejpam-4931	765	2	,	,	PUNCT
ejpam-4931	765	3	we	we	PRON
ejpam-4931	765	4	deduce	deduce	VERB
ejpam-4931	765	5	the	the	DET
ejpam-4931	765	6	same	same	ADJ
ejpam-4931	765	7	compactness	compactness	NOUN
ejpam-4931	765	8	for	for	ADP
ejpam-4931	765	9	(	(	PUNCT
ejpam-4931	765	10	ξr2	ξr2	NOUN
ejpam-4931	765	11	,	,	PUNCT
ejpam-4931	765	12	ur2	ur2	NOUN
ejpam-4931	765	13	,	,	PUNCT
ejpam-4931	765	14	vr2	vr2	PROPN
ejpam-4931	765	15	)	)	PUNCT
ejpam-4931	765	16	and	and	CCONJ
ejpam-4931	765	17	for	for	ADP
ejpam-4931	765	18	(	(	PUNCT
ejpam-4931	765	19	ξδ	ξδ	ADP
ejpam-4931	765	20	,	,	PUNCT
ejpam-4931	765	21	uδ	uδ	PROPN
ejpam-4931	765	22	,	,	PUNCT
ejpam-4931	765	23	vδ	vδ	NOUN
ejpam-4931	765	24	)	)	PUNCT
ejpam-4931	765	25	.	.	PUNCT
ejpam-4931	766	1	therefore	therefore	ADV
ejpam-4931	766	2	at	at	ADP
ejpam-4931	766	3	this	this	DET
ejpam-4931	766	4	level	level	NOUN
ejpam-4931	766	5	of	of	ADP
ejpam-4931	766	6	approximation	approximation	NOUN
ejpam-4931	766	7	,	,	PUNCT
ejpam-4931	766	8	we	we	PRON
ejpam-4931	766	9	focus	focus	VERB
ejpam-4931	766	10	only	only	ADV
ejpam-4931	766	11	on	on	ADP
ejpam-4931	766	12	the	the	DET
ejpam-4931	766	13	convergence	convergence	NOUN
ejpam-4931	766	14	of	of	ADP
ejpam-4931	766	15	r2∇ξ−β	r2∇ξ−β	PROPN
ejpam-4931	766	16	and	and	CCONJ
ejpam-4931	766	17	that	that	PRON
ejpam-4931	766	18	of	of	ADP
ejpam-4931	766	19	δξ∇x∆	δξ∇x∆	PROPN
ejpam-4931	766	20	5	5	NUM
ejpam-4931	766	21	xξ	xξ	NOUN
ejpam-4931	766	22	.	.	PUNCT
ejpam-4931	767	1	here	here	ADV
ejpam-4931	767	2	we	we	PRON
ejpam-4931	767	3	state	state	VERB
ejpam-4931	767	4	the	the	DET
ejpam-4931	767	5	following	follow	VERB
ejpam-4931	767	6	two	two	NUM
ejpam-4931	767	7	lemmas	lemma	NOUN
ejpam-4931	767	8	.	.	PUNCT
ejpam-4931	768	1	lemma	lemma	PROPN
ejpam-4931	768	2	13	13	NUM
ejpam-4931	768	3	.	.	PUNCT
ejpam-4931	769	1	:	:	PUNCT
ejpam-4931	769	2	for	for	ADP
ejpam-4931	769	3	any	any	DET
ejpam-4931	769	4	ξr2	ξr2	NOUN
ejpam-4931	769	5	defined	define	VERB
ejpam-4931	769	6	as	as	ADP
ejpam-4931	769	7	in	in	ADP
ejpam-4931	769	8	proposition	proposition	NOUN
ejpam-4931	769	9	5.1	5.1	NUM
ejpam-4931	769	10	,	,	PUNCT
ejpam-4931	769	11	we	we	PRON
ejpam-4931	769	12	have	have	VERB
ejpam-4931	769	13	r2	r2	PROPN
ejpam-4931	769	14	∫	∫	PROPN
ejpam-4931	770	1	t	t	PROPN
ejpam-4931	770	2	0	0	NUM
ejpam-4931	770	3	∫	∫	PROPN
ejpam-4931	770	4	ω	ω	PROPN
ejpam-4931	770	5	ξ−β	ξ−β	PROPN
ejpam-4931	770	6	r2	r2	PROPN
ejpam-4931	770	7	dxdydt	dxdydt	NOUN
ejpam-4931	770	8	−→	−→	NOUN
ejpam-4931	770	9	0	0	NUM
ejpam-4931	770	10	as	as	ADP
ejpam-4931	770	11	r2	r2	PROPN
ejpam-4931	770	12	−→	−→	NOUN
ejpam-4931	770	13	0	0	NUM
ejpam-4931	770	14	.	.	PUNCT
ejpam-4931	771	1	proof	proof	NOUN
ejpam-4931	771	2	.	.	PUNCT
ejpam-4931	772	1	the	the	DET
ejpam-4931	772	2	proof	proof	NOUN
ejpam-4931	772	3	is	be	AUX
ejpam-4931	772	4	motivated	motivate	VERB
ejpam-4931	772	5	by	by	ADP
ejpam-4931	772	6	the	the	DET
ejpam-4931	772	7	method	method	NOUN
ejpam-4931	772	8	in	in	ADP
ejpam-4931	772	9	[	[	X
ejpam-4931	772	10	18	18	NUM
ejpam-4931	772	11	,	,	PUNCT
ejpam-4931	772	12	19	19	NUM
ejpam-4931	772	13	]	]	PUNCT
ejpam-4931	772	14	.	.	PUNCT
ejpam-4931	773	1	from	from	ADP
ejpam-4931	773	2	the	the	DET
ejpam-4931	773	3	entropy	entropy	PROPN
ejpam-4931	773	4	b	b	PROPN
ejpam-4931	773	5	-	-	PUNCT
ejpam-4931	773	6	d	d	X
ejpam-4931	773	7	(	(	PUNCT
ejpam-4931	773	8	101	101	NUM
ejpam-4931	773	9	)	)	PUNCT
ejpam-4931	773	10	,	,	PUNCT
ejpam-4931	773	11	we	we	PRON
ejpam-4931	773	12	have	have	VERB
ejpam-4931	773	13	:	:	PUNCT
ejpam-4931	773	14	sup	sup	PROPN
ejpam-4931	773	15	t∈[0,t	t∈[0,t	PROPN
ejpam-4931	773	16	]	]	PUNCT
ejpam-4931	774	1	∫	∫	PROPN
ejpam-4931	775	1	ω	ω	INTJ
ejpam-4931	776	1	(	(	PUNCT
ejpam-4931	776	2	ln	ln	ADJ
ejpam-4931	776	3	(	(	PUNCT
ejpam-4931	776	4	1	1	NUM
ejpam-4931	776	5	ξr2	ξr2	NOUN
ejpam-4931	776	6	)	)	PUNCT
ejpam-4931	776	7	)	)	PUNCT
ejpam-4931	777	1	+	+	CCONJ
ejpam-4931	777	2	dxdy	dxdy	PROPN
ejpam-4931	777	3	≤	≤	PROPN
ejpam-4931	777	4	c(r1	c(r1	NOUN
ejpam-4931	777	5	)	)	PUNCT
ejpam-4931	777	6	<	<	X
ejpam-4931	778	1	+	+	PRON
ejpam-4931	778	2	∞.	∞.	PROPN
ejpam-4931	778	3	(	(	PUNCT
ejpam-4931	778	4	104	104	NUM
ejpam-4931	778	5	)	)	PUNCT
ejpam-4931	778	6	note	note	NOUN
ejpam-4931	778	7	that	that	SCONJ
ejpam-4931	778	8	y	y	PROPN
ejpam-4931	778	9	∈	∈	PROPN
ejpam-4931	778	10	r+	r+	PUNCT
ejpam-4931	778	11	7−→	7−→	PROPN
ejpam-4931	778	12	ln	ln	PROPN
ejpam-4931	778	13	(	(	PUNCT
ejpam-4931	778	14	1y	1y	NUM
ejpam-4931	778	15	)	)	PUNCT
ejpam-4931	778	16	+	+	CCONJ
ejpam-4931	778	17	is	be	AUX
ejpam-4931	778	18	a	a	DET
ejpam-4931	778	19	continuous	continuous	ADJ
ejpam-4931	778	20	convex	convex	NOUN
ejpam-4931	778	21	function	function	NOUN
ejpam-4931	778	22	.	.	PUNCT
ejpam-4931	779	1	moreover	moreover	ADV
ejpam-4931	779	2	,	,	PUNCT
ejpam-4931	779	3	in	in	ADP
ejpam-4931	779	4	combination	combination	NOUN
ejpam-4931	779	5	with	with	ADP
ejpam-4931	779	6	the	the	DET
ejpam-4931	779	7	convex	convex	PROPN
ejpam-4931	779	8	function	function	NOUN
ejpam-4931	779	9	property	property	NOUN
ejpam-4931	779	10	and	and	CCONJ
ejpam-4931	779	11	fatou	fatou	NOUN
ejpam-4931	779	12	’s	’s	PART
ejpam-4931	779	13	lemma	lemma	PROPN
ejpam-4931	779	14	,	,	PUNCT
ejpam-4931	779	15	it	it	PRON
ejpam-4931	779	16	follows	follow	VERB
ejpam-4931	779	17	that:∫	that:∫	NOUN
ejpam-4931	779	18	ω	ω	PROPN
ejpam-4931	779	19	(	(	PUNCT
ejpam-4931	779	20	ln	ln	ADJ
ejpam-4931	779	21	(	(	PUNCT
ejpam-4931	779	22	1	1	NUM
ejpam-4931	779	23	ξ	ξ	PROPN
ejpam-4931	779	24	)	)	PUNCT
ejpam-4931	779	25	)	)	PUNCT
ejpam-4931	780	1	+	+	CCONJ
ejpam-4931	780	2	dxdy	dxdy	PROPN
ejpam-4931	780	3	≤	≤	PROPN
ejpam-4931	780	4	∫	∫	PROPN
ejpam-4931	780	5	ω	ω	PROPN
ejpam-4931	780	6	lim	lim	PROPN
ejpam-4931	780	7	inf	inf	PROPN
ejpam-4931	781	1	r2→0	r2→0	PROPN
ejpam-4931	781	2	(	(	PUNCT
ejpam-4931	781	3	ln	ln	ADJ
ejpam-4931	781	4	(	(	PUNCT
ejpam-4931	781	5	1	1	NUM
ejpam-4931	781	6	ξr2	ξr2	NOUN
ejpam-4931	781	7	)	)	PUNCT
ejpam-4931	781	8	)	)	PUNCT
ejpam-4931	782	1	+	+	CCONJ
ejpam-4931	782	2	dxdy	dxdy	PROPN
ejpam-4931	782	3	≤	≤	PROPN
ejpam-4931	782	4	lim	lim	PROPN
ejpam-4931	782	5	inf	inf	PROPN
ejpam-4931	782	6	r2→0	r2→0	PROPN
ejpam-4931	782	7	∫	∫	PROPN
ejpam-4931	782	8	ω	ω	PROPN
ejpam-4931	782	9	(	(	PUNCT
ejpam-4931	782	10	ln	ln	ADJ
ejpam-4931	782	11	(	(	PUNCT
ejpam-4931	782	12	1	1	NUM
ejpam-4931	782	13	ξr2	ξr2	NOUN
ejpam-4931	782	14	)	)	PUNCT
ejpam-4931	782	15	)	)	PUNCT
ejpam-4931	783	1	+	+	CCONJ
ejpam-4931	783	2	dxdy	dxdy	PROPN
ejpam-4931	783	3	≤	≤	PROPN
ejpam-4931	783	4	c(r1	c(r1	NOUN
ejpam-4931	783	5	)	)	PUNCT
ejpam-4931	783	6	<	<	X
ejpam-4931	784	1	+	+	PRON
ejpam-4931	784	2	∞.	∞.	PROPN
ejpam-4931	784	3	(	(	PUNCT
ejpam-4931	784	4	105	105	NUM
ejpam-4931	784	5	)	)	PUNCT
ejpam-4931	784	6	this	this	PRON
ejpam-4931	784	7	means	mean	VERB
ejpam-4931	784	8	that	that	SCONJ
ejpam-4931	784	9	(	(	PUNCT
ejpam-4931	784	10	ln(1ξ	ln(1ξ	ADP
ejpam-4931	784	11	)	)	PUNCT
ejpam-4931	784	12	)	)	PUNCT
ejpam-4931	785	1	+	+	CCONJ
ejpam-4931	785	2	is	be	AUX
ejpam-4931	785	3	bounded	bound	VERB
ejpam-4931	785	4	in	in	ADP
ejpam-4931	785	5	l∞	l∞	PROPN
ejpam-4931	785	6	(	(	PUNCT
ejpam-4931	785	7	[	[	X
ejpam-4931	785	8	0	0	NUM
ejpam-4931	785	9	,	,	PUNCT
ejpam-4931	785	10	t	t	X
ejpam-4931	785	11	]	]	PUNCT
ejpam-4931	785	12	;	;	PUNCT
ejpam-4931	785	13	l1(ω	l1(ω	X
ejpam-4931	785	14	)	)	PUNCT
ejpam-4931	785	15	)	)	PUNCT
ejpam-4931	785	16	.	.	PUNCT
ejpam-4931	786	1	this	this	PRON
ejpam-4931	786	2	allows	allow	VERB
ejpam-4931	786	3	us	we	PRON
ejpam-4931	786	4	to	to	PART
ejpam-4931	786	5	deduce	deduce	VERB
ejpam-4931	786	6	that∣∣{x	that∣∣{x	PROPN
ejpam-4931	786	7	/	/	SYM
ejpam-4931	786	8	ξ(t	ξ(t	PROPN
ejpam-4931	786	9	,	,	PUNCT
ejpam-4931	786	10	x	x	X
ejpam-4931	786	11	)	)	PUNCT
ejpam-4931	786	12	=	=	SYM
ejpam-4931	786	13	0	0	X
ejpam-4931	786	14	}	}	PUNCT
ejpam-4931	786	15	∣∣	∣∣	X
ejpam-4931	786	16	=	=	SYM
ejpam-4931	786	17	0	0	NUM
ejpam-4931	786	18	for	for	ADP
ejpam-4931	786	19	almost	almost	ADV
ejpam-4931	786	20	every	every	PRON
ejpam-4931	786	21	t	t	NOUN
ejpam-4931	786	22	∈	∈	PROPN
ejpam-4931	787	1	[	[	X
ejpam-4931	787	2	0	0	NUM
ejpam-4931	787	3	,	,	PUNCT
ejpam-4931	787	4	t	t	X
ejpam-4931	787	5	]	]	PUNCT
ejpam-4931	787	6	,	,	PUNCT
ejpam-4931	787	7	(	(	PUNCT
ejpam-4931	787	8	106	106	NUM
ejpam-4931	787	9	)	)	PUNCT
ejpam-4931	787	10	j.	j.	PROPN
ejpam-4931	787	11	ouya	ouya	PROPN
ejpam-4931	787	12	,	,	PUNCT
ejpam-4931	787	13	a.	a.	NOUN
ejpam-4931	787	14	ouédraogo	ouédraogo	PROPN
ejpam-4931	787	15	/	/	SYM
ejpam-4931	787	16	eur	eur	PROPN
ejpam-4931	787	17	.	.	PUNCT
ejpam-4931	788	1	j.	j.	PROPN
ejpam-4931	788	2	pure	pure	PROPN
ejpam-4931	788	3	appl	appl	PROPN
ejpam-4931	788	4	.	.	PROPN
ejpam-4931	788	5	math	math	PROPN
ejpam-4931	788	6	,	,	PUNCT
ejpam-4931	788	7	16	16	NUM
ejpam-4931	788	8	(	(	PUNCT
ejpam-4931	788	9	4	4	NUM
ejpam-4931	788	10	)	)	PUNCT
ejpam-4931	788	11	(	(	PUNCT
ejpam-4931	788	12	2023	2023	NUM
ejpam-4931	788	13	)	)	PUNCT
ejpam-4931	788	14	,	,	PUNCT
ejpam-4931	788	15	2247	2247	NUM
ejpam-4931	788	16	-	-	SYM
ejpam-4931	788	17	2285	2285	NUM
ejpam-4931	788	18	2276	2276	NUM
ejpam-4931	788	19	where	where	SCONJ
ejpam-4931	788	20	|b|	|b|	PROPN
ejpam-4931	788	21	denotes	denote	VERB
ejpam-4931	788	22	the	the	DET
ejpam-4931	788	23	measure	measure	NOUN
ejpam-4931	788	24	of	of	ADP
ejpam-4931	788	25	set	set	PROPN
ejpam-4931	788	26	b.	b.	PROPN
ejpam-4931	788	27	due	due	ADP
ejpam-4931	788	28	to	to	PART
ejpam-4931	788	29	ξr2	ξr2	VERB
ejpam-4931	788	30	−→	−→	ADV
ejpam-4931	788	31	ξ	ξ	X
ejpam-4931	788	32	strongly	strongly	ADV
ejpam-4931	788	33	in	in	ADP
ejpam-4931	788	34	c	c	PROPN
ejpam-4931	788	35	(	(	PUNCT
ejpam-4931	788	36	[	[	X
ejpam-4931	788	37	0	0	NUM
ejpam-4931	788	38	,	,	PUNCT
ejpam-4931	788	39	t	t	X
ejpam-4931	788	40	]	]	PUNCT
ejpam-4931	788	41	;	;	PUNCT
ejpam-4931	788	42	h5(ω	h5(ω	NUM
ejpam-4931	788	43	)	)	PUNCT
ejpam-4931	788	44	)	)	PUNCT
ejpam-4931	789	1	,	,	PUNCT
ejpam-4931	789	2	hence	hence	ADV
ejpam-4931	789	3	ξr2	ξr2	VERB
ejpam-4931	789	4	−→	−→	NOUN
ejpam-4931	789	5	ξ	ξ	X
ejpam-4931	789	6	a.e	a.e	PROPN
ejpam-4931	789	7	.	.	PUNCT
ejpam-4931	790	1	thus	thus	ADV
ejpam-4931	790	2	the	the	DET
ejpam-4931	790	3	above	above	ADJ
ejpam-4931	790	4	limits	limit	NOUN
ejpam-4931	790	5	and	and	CCONJ
ejpam-4931	790	6	(	(	PUNCT
ejpam-4931	790	7	106	106	NUM
ejpam-4931	790	8	)	)	PUNCT
ejpam-4931	790	9	deduce	deduce	ADV
ejpam-4931	790	10	r2ξ	r2ξ	ADP
ejpam-4931	790	11	−β	−β	PROPN
ejpam-4931	790	12	r2	r2	PROPN
ejpam-4931	791	1	−→	−→	NOUN
ejpam-4931	791	2	0	0	NUM
ejpam-4931	792	1	a.e	a.e	NOUN
ejpam-4931	792	2	as	as	ADP
ejpam-4931	792	3	r2	r2	PROPN
ejpam-4931	792	4	−→	−→	NOUN
ejpam-4931	792	5	0	0	NUM
ejpam-4931	792	6	.	.	PUNCT
ejpam-4931	793	1	(	(	PUNCT
ejpam-4931	793	2	107	107	NUM
ejpam-4931	793	3	)	)	PUNCT
ejpam-4931	793	4	moreover	moreover	ADV
ejpam-4931	793	5	,	,	PUNCT
ejpam-4931	793	6	using	use	VERB
ejpam-4931	793	7	the	the	DET
ejpam-4931	793	8	lemma	lemma	PROPN
ejpam-4931	793	9	3	3	NUM
ejpam-4931	793	10	(	(	PUNCT
ejpam-4931	793	11	interpolation	interpolation	NOUN
ejpam-4931	793	12	inequality	inequality	NOUN
ejpam-4931	793	13	)	)	PUNCT
ejpam-4931	793	14	,	,	PUNCT
ejpam-4931	793	15	we	we	PRON
ejpam-4931	793	16	have	have	VERB
ejpam-4931	793	17	∥r2ξ−β	∥r2ξ−β	NUM
ejpam-4931	793	18	r2	r2	PROPN
ejpam-4931	793	19	∥	∥	PUNCT
ejpam-4931	793	20	l	l	NOUN
ejpam-4931	793	21	5	5	NUM
ejpam-4931	793	22	3	3	NUM
ejpam-4931	793	23	(	(	PUNCT
ejpam-4931	793	24	[	[	X
ejpam-4931	793	25	0,t	0,t	X
ejpam-4931	793	26	]	]	X
ejpam-4931	793	27	;	;	PUNCT
ejpam-4931	793	28	l	l	NOUN
ejpam-4931	793	29	5	5	NUM
ejpam-4931	793	30	3	3	NUM
ejpam-4931	793	31	(	(	PUNCT
ejpam-4931	793	32	ω	ω	NOUN
ejpam-4931	793	33	)	)	PUNCT
ejpam-4931	793	34	)	)	PUNCT
ejpam-4931	793	35	≤	≤	NOUN
ejpam-4931	793	36	∥r2ξ−β	∥r2ξ−β	PUNCT
ejpam-4931	793	37	r2	r2	PROPN
ejpam-4931	793	38	∥	∥	PUNCT
ejpam-4931	793	39	2	2	NUM
ejpam-4931	793	40	5	5	NUM
ejpam-4931	793	41	l∞	l∞	NOUN
ejpam-4931	793	42	(	(	PUNCT
ejpam-4931	793	43	[	[	X
ejpam-4931	793	44	0,t	0,t	X
ejpam-4931	793	45	]	]	X
ejpam-4931	793	46	;	;	PUNCT
ejpam-4931	793	47	l1(ω	l1(ω	X
ejpam-4931	793	48	)	)	PUNCT
ejpam-4931	793	49	)	)	PUNCT
ejpam-4931	793	50	∥r2ξ−β	∥r2ξ−β	PUNCT
ejpam-4931	794	1	r2	r2	PROPN
ejpam-4931	794	2	∥	∥	PUNCT
ejpam-4931	794	3	3	3	NUM
ejpam-4931	794	4	5	5	NUM
ejpam-4931	794	5	l1	l1	PROPN
ejpam-4931	794	6	(	(	PUNCT
ejpam-4931	794	7	[	[	X
ejpam-4931	794	8	0,t	0,t	X
ejpam-4931	794	9	]	]	X
ejpam-4931	794	10	;	;	PUNCT
ejpam-4931	794	11	l3(ω	l3(ω	X
ejpam-4931	794	12	)	)	PUNCT
ejpam-4931	794	13	)	)	PUNCT
ejpam-4931	794	14	≤	≤	NOUN
ejpam-4931	795	1	c	c	X
ejpam-4931	795	2	,	,	PUNCT
ejpam-4931	795	3	(	(	PUNCT
ejpam-4931	795	4	108	108	NUM
ejpam-4931	795	5	)	)	PUNCT
ejpam-4931	795	6	which	which	PRON
ejpam-4931	795	7	combines	combine	VERB
ejpam-4931	795	8	with	with	ADP
ejpam-4931	795	9	(	(	PUNCT
ejpam-4931	795	10	107	107	NUM
ejpam-4931	795	11	)	)	PUNCT
ejpam-4931	795	12	and	and	CCONJ
ejpam-4931	795	13	lemma	lemma	PROPN
ejpam-4931	795	14	2	2	NUM
ejpam-4931	795	15	,	,	PUNCT
ejpam-4931	795	16	and	and	CCONJ
ejpam-4931	795	17	we	we	PRON
ejpam-4931	795	18	have	have	VERB
ejpam-4931	795	19	r2ξ	r2ξ	ADJ
ejpam-4931	795	20	−β	−β	ADJ
ejpam-4931	795	21	r2	r2	PROPN
ejpam-4931	796	1	−→	−→	ADV
ejpam-4931	796	2	0	0	NUM
ejpam-4931	796	3	strongly	strongly	ADV
ejpam-4931	796	4	in	in	ADP
ejpam-4931	796	5	l1	l1	PROPN
ejpam-4931	796	6	(	(	PUNCT
ejpam-4931	797	1	[	[	X
ejpam-4931	797	2	0	0	NUM
ejpam-4931	797	3	,	,	PUNCT
ejpam-4931	797	4	t	t	X
ejpam-4931	797	5	]	]	PUNCT
ejpam-4931	797	6	;	;	PUNCT
ejpam-4931	797	7	l1(ω	l1(ω	X
ejpam-4931	797	8	)	)	PUNCT
ejpam-4931	797	9	)	)	PUNCT
ejpam-4931	797	10	.	.	PUNCT
ejpam-4931	798	1	lemma	lemma	PROPN
ejpam-4931	798	2	14	14	NUM
ejpam-4931	798	3	.	.	PUNCT
ejpam-4931	799	1	for	for	ADP
ejpam-4931	799	2	any	any	PRON
ejpam-4931	799	3	ξδ	ξδ	ADV
ejpam-4931	799	4	defined	define	VERB
ejpam-4931	799	5	as	as	ADP
ejpam-4931	799	6	in	in	ADP
ejpam-4931	799	7	the	the	DET
ejpam-4931	799	8	proposition	proposition	NOUN
ejpam-4931	799	9	5.1	5.1	NUM
ejpam-4931	799	10	,	,	PUNCT
ejpam-4931	799	11	we	we	PRON
ejpam-4931	799	12	have	have	VERB
ejpam-4931	799	13	,	,	PUNCT
ejpam-4931	799	14	for	for	ADP
ejpam-4931	799	15	any	any	DET
ejpam-4931	799	16	test	test	NOUN
ejpam-4931	799	17	function	function	NOUN
ejpam-4931	799	18	φ	φ	PROPN
ejpam-4931	799	19	δ	δ	PROPN
ejpam-4931	800	1	∫	∫	PROPN
ejpam-4931	800	2	t	t	PROPN
ejpam-4931	800	3	0	0	NUM
ejpam-4931	801	1	∫	∫	PROPN
ejpam-4931	801	2	ω	ω	NUM
ejpam-4931	802	1	ξδ∇x∆	ξδ∇x∆	CCONJ
ejpam-4931	802	2	5	5	NUM
ejpam-4931	802	3	xξδφdxdydt	xξδφdxdydt	ADV
ejpam-4931	802	4	−→	−→	ADV
ejpam-4931	802	5	0	0	PUNCT
ejpam-4931	802	6	as	as	SCONJ
ejpam-4931	802	7	δ	δ	PROPN
ejpam-4931	802	8	−→	−→	NOUN
ejpam-4931	802	9	0	0	NUM
ejpam-4931	802	10	.	.	PUNCT
ejpam-4931	803	1	(	(	PUNCT
ejpam-4931	803	2	109	109	NUM
ejpam-4931	803	3	)	)	PUNCT
ejpam-4931	803	4	proof	proof	NOUN
ejpam-4931	803	5	.	.	PUNCT
ejpam-4931	804	1	by	by	ADP
ejpam-4931	804	2	(	(	PUNCT
ejpam-4931	804	3	103	103	NUM
ejpam-4931	804	4	)	)	PUNCT
ejpam-4931	804	5	(	(	PUNCT
ejpam-4931	804	6	where	where	SCONJ
ejpam-4931	804	7	δ	δ	PROPN
ejpam-4931	804	8	appears	appear	VERB
ejpam-4931	804	9	)	)	PUNCT
ejpam-4931	804	10	and	and	CCONJ
ejpam-4931	804	11	using	use	VERB
ejpam-4931	804	12	the	the	DET
ejpam-4931	804	13	gagliardo	gagliardo	NOUN
ejpam-4931	804	14	-	-	PUNCT
ejpam-4931	804	15	nirenberg	nirenberg	PROPN
ejpam-4931	804	16	interpolation	interpolation	NOUN
ejpam-4931	804	17	inequality	inequality	NOUN
ejpam-4931	804	18	,	,	PUNCT
ejpam-4931	804	19	we	we	PRON
ejpam-4931	804	20	have	have	AUX
ejpam-4931	804	21	∥∇5	∥∇5	VERB
ejpam-4931	804	22	xξδ∥l2≤	xξδ∥l2≤	PROPN
ejpam-4931	804	23	c∥∇6	c∥∇6	NOUN
ejpam-4931	804	24	xξδ∥	xξδ∥	PROPN
ejpam-4931	804	25	9	9	NUM
ejpam-4931	804	26	11	11	NUM
ejpam-4931	804	27	l2	l2	NOUN
ejpam-4931	804	28	∥ξδ∥	∥ξδ∥	NOUN
ejpam-4931	804	29	2	2	NUM
ejpam-4931	804	30	11	11	NUM
ejpam-4931	804	31	l3	l3	NOUN
ejpam-4931	804	32	.	.	PUNCT
ejpam-4931	805	1	(	(	PUNCT
ejpam-4931	805	2	110	110	NUM
ejpam-4931	805	3	)	)	PUNCT
ejpam-4931	805	4	thus	thus	ADV
ejpam-4931	805	5	,	,	PUNCT
ejpam-4931	805	6	∫	∫	PROPN
ejpam-4931	805	7	t	t	PROPN
ejpam-4931	805	8	0	0	NUM
ejpam-4931	805	9	δ	δ	PROPN
ejpam-4931	805	10	(	(	PUNCT
ejpam-4931	805	11	∫	∫	PROPN
ejpam-4931	805	12	ω	ω	PROPN
ejpam-4931	805	13	|∇5	|∇5	X
ejpam-4931	805	14	xξδ|2dxdy	xξδ|2dxdy	PROPN
ejpam-4931	805	15	)	)	PUNCT
ejpam-4931	806	1	11	11	NUM
ejpam-4931	806	2	9	9	NUM
ejpam-4931	806	3	dt	dt	NOUN
ejpam-4931	806	4	≤	≤	NUM
ejpam-4931	806	5	c	c	NOUN
ejpam-4931	806	6	(	(	PUNCT
ejpam-4931	806	7	sup	sup	NOUN
ejpam-4931	806	8	t∈[0,t	t∈[0,t	NOUN
ejpam-4931	806	9	]	]	X
ejpam-4931	806	10	∥ξδ∥l3	∥ξδ∥l3	X
ejpam-4931	806	11	)	)	PUNCT
ejpam-4931	806	12	4	4	NUM
ejpam-4931	806	13	9	9	NUM
ejpam-4931	806	14	∫	∫	NOUN
ejpam-4931	806	15	t	t	PROPN
ejpam-4931	806	16	0	0	NUM
ejpam-4931	807	1	δ	δ	PROPN
ejpam-4931	807	2	∫	∫	PROPN
ejpam-4931	807	3	ω	ω	NUM
ejpam-4931	807	4	|∇6	|∇6	PROPN
ejpam-4931	807	5	xξδ|2dxdydt	xξδ|2dxdydt	PROPN
ejpam-4931	807	6	.	.	PUNCT
ejpam-4931	808	1	(	(	PUNCT
ejpam-4931	808	2	111	111	NUM
ejpam-4931	808	3	)	)	PUNCT
ejpam-4931	808	4	this	this	PRON
ejpam-4931	808	5	implies	imply	VERB
ejpam-4931	808	6	δ	δ	PROPN
ejpam-4931	808	7	9	9	NUM
ejpam-4931	808	8	22∇5	22∇5	NUM
ejpam-4931	808	9	xξδ	xξδ	PUNCT
ejpam-4931	808	10	∈	∈	PROPN
ejpam-4931	808	11	l	l	NOUN
ejpam-4931	808	12	22	22	NUM
ejpam-4931	808	13	9	9	NUM
ejpam-4931	808	14	(	(	PUNCT
ejpam-4931	808	15	[	[	X
ejpam-4931	808	16	0	0	NUM
ejpam-4931	808	17	,	,	PUNCT
ejpam-4931	808	18	t	t	X
ejpam-4931	808	19	]	]	PUNCT
ejpam-4931	808	20	;	;	PUNCT
ejpam-4931	808	21	l2(ω	l2(ω	NUM
ejpam-4931	808	22	)	)	PUNCT
ejpam-4931	808	23	)	)	PUNCT
ejpam-4931	808	24	.	.	PUNCT
ejpam-4931	809	1	for	for	ADP
ejpam-4931	809	2	any	any	DET
ejpam-4931	809	3	test	test	NOUN
ejpam-4931	809	4	function	function	NOUN
ejpam-4931	809	5	φ	φ	PROPN
ejpam-4931	809	6	∈	∈	PROPN
ejpam-4931	809	7	c∞	c∞	PROPN
ejpam-4931	809	8	c	c	NOUN
ejpam-4931	809	9	(	(	PUNCT
ejpam-4931	809	10	[	[	X
ejpam-4931	809	11	0	0	NUM
ejpam-4931	809	12	,	,	PUNCT
ejpam-4931	809	13	t	t	X
ejpam-4931	809	14	]	]	PUNCT
ejpam-4931	809	15	;	;	PUNCT
ejpam-4931	809	16	ω	ω	X
ejpam-4931	809	17	)	)	PUNCT
ejpam-4931	809	18	,	,	PUNCT
ejpam-4931	809	19	we	we	PRON
ejpam-4931	809	20	have	have	VERB
ejpam-4931	809	21	δ	δ	PROPN
ejpam-4931	809	22	∫	∫	PROPN
ejpam-4931	809	23	t	t	PROPN
ejpam-4931	809	24	0	0	NUM
ejpam-4931	810	1	∫	∫	PROPN
ejpam-4931	810	2	ω	ω	NUM
ejpam-4931	810	3	ξδ∇x∆	ξδ∇x∆	CCONJ
ejpam-4931	810	4	5	5	NUM
ejpam-4931	810	5	xξδφdxdydt	xξδφdxdydt	NOUN
ejpam-4931	810	6	=	=	SYM
ejpam-4931	811	1	−δ	−δ	ADJ
ejpam-4931	811	2	∫	∫	PROPN
ejpam-4931	811	3	t	t	PROPN
ejpam-4931	811	4	0	0	NUM
ejpam-4931	811	5	∫	∫	PROPN
ejpam-4931	811	6	ω	ω	PROPN
ejpam-4931	811	7	∆2	∆2	PROPN
ejpam-4931	811	8	xdivx(ξδφ)∆	xdivx(ξδφ)∆	PROPN
ejpam-4931	811	9	3	3	NUM
ejpam-4931	811	10	xξδdxdydt	xξδdxdydt	NOUN
ejpam-4931	811	11	=	=	PUNCT
ejpam-4931	811	12	−δ	−δ	ADJ
ejpam-4931	811	13	∫	∫	PROPN
ejpam-4931	811	14	t	t	PROPN
ejpam-4931	811	15	0	0	NUM
ejpam-4931	811	16	∫	∫	PROPN
ejpam-4931	811	17	ω	ω	PROPN
ejpam-4931	811	18	∆2	∆2	PROPN
ejpam-4931	811	19	x	x	PROPN
ejpam-4931	811	20	(	(	PUNCT
ejpam-4931	811	21	φ∇xξδ	φ∇xξδ	X
ejpam-4931	811	22	+	+	CCONJ
ejpam-4931	811	23	ξδdivxφ	ξδdivxφ	VERB
ejpam-4931	811	24	)	)	PUNCT
ejpam-4931	812	1	∆3	∆3	ADV
ejpam-4931	812	2	xξδdxdydt	xξδdxdydt	PROPN
ejpam-4931	812	3	.	.	PUNCT
ejpam-4931	813	1	(	(	PUNCT
ejpam-4931	813	2	112	112	NUM
ejpam-4931	813	3	)	)	PUNCT
ejpam-4931	813	4	j.	j.	PROPN
ejpam-4931	813	5	ouya	ouya	PROPN
ejpam-4931	813	6	,	,	PUNCT
ejpam-4931	813	7	a.	a.	NOUN
ejpam-4931	813	8	ouédraogo	ouédraogo	PROPN
ejpam-4931	813	9	/	/	SYM
ejpam-4931	813	10	eur	eur	PROPN
ejpam-4931	813	11	.	.	PUNCT
ejpam-4931	814	1	j.	j.	PROPN
ejpam-4931	814	2	pure	pure	PROPN
ejpam-4931	814	3	appl	appl	PROPN
ejpam-4931	814	4	.	.	PROPN
ejpam-4931	814	5	math	math	PROPN
ejpam-4931	814	6	,	,	PUNCT
ejpam-4931	814	7	16	16	NUM
ejpam-4931	814	8	(	(	PUNCT
ejpam-4931	814	9	4	4	NUM
ejpam-4931	814	10	)	)	PUNCT
ejpam-4931	814	11	(	(	PUNCT
ejpam-4931	814	12	2023	2023	NUM
ejpam-4931	814	13	)	)	PUNCT
ejpam-4931	814	14	,	,	PUNCT
ejpam-4931	814	15	2247	2247	NUM
ejpam-4931	814	16	-	-	SYM
ejpam-4931	814	17	2285	2285	NUM
ejpam-4931	814	18	2277	2277	NUM
ejpam-4931	814	19	now	now	ADV
ejpam-4931	814	20	we	we	PRON
ejpam-4931	814	21	treat	treat	VERB
ejpam-4931	814	22	the	the	DET
ejpam-4931	814	23	term∣∣∣δ	term∣∣∣δ	PROPN
ejpam-4931	814	24	∫	∫	PROPN
ejpam-4931	814	25	t	t	PROPN
ejpam-4931	814	26	0	0	NUM
ejpam-4931	814	27	∫	∫	PROPN
ejpam-4931	815	1	ω	ω	PROPN
ejpam-4931	815	2	∆2	∆2	PROPN
ejpam-4931	815	3	x(∇xξδ)∆	x(∇xξδ)∆	VERB
ejpam-4931	815	4	3	3	NUM
ejpam-4931	815	5	xξδφdxdydt	xξδφdxdydt	NOUN
ejpam-4931	815	6	∣∣∣	∣∣∣	NOUN
ejpam-4931	815	7	≤	≤	NUM
ejpam-4931	815	8	cδ	cδ	NOUN
ejpam-4931	816	1	1	1	NUM
ejpam-4931	816	2	11	11	NUM
ejpam-4931	816	3	∥	∥	PUNCT
ejpam-4931	816	4	√	√	ADP
ejpam-4931	816	5	δ∇6	δ∇6	NOUN
ejpam-4931	816	6	xξδ∥l2(l2)∥δ	xξδ∥l2(l2)∥δ	NOUN
ejpam-4931	816	7	9	9	NUM
ejpam-4931	816	8	22∇5	22∇5	NUM
ejpam-4931	816	9	xξδ∥	xξδ∥	PUNCT
ejpam-4931	816	10	l	l	NOUN
ejpam-4931	816	11	22	22	NUM
ejpam-4931	816	12	9	9	NUM
ejpam-4931	816	13	(	(	PUNCT
ejpam-4931	816	14	l2	l2	NOUN
ejpam-4931	816	15	)	)	PUNCT
ejpam-4931	816	16	∥φ∥l11(l∞)−→	∥φ∥l11(l∞)−→	NOUN
ejpam-4931	816	17	0	0	NUM
ejpam-4931	816	18	,	,	PUNCT
ejpam-4931	816	19	(	(	PUNCT
ejpam-4931	816	20	113	113	NUM
ejpam-4931	816	21	)	)	PUNCT
ejpam-4931	816	22	as	as	ADP
ejpam-4931	816	23	δ	δ	PROPN
ejpam-4931	816	24	−→	−→	NOUN
ejpam-4931	816	25	0	0	NUM
ejpam-4931	816	26	.	.	PUNCT
ejpam-4931	817	1	as	as	ADP
ejpam-4931	817	2	before	before	ADV
ejpam-4931	817	3	,	,	PUNCT
ejpam-4931	817	4	we	we	PRON
ejpam-4931	817	5	can	can	AUX
ejpam-4931	817	6	control	control	VERB
ejpam-4931	817	7	the	the	DET
ejpam-4931	817	8	other	other	ADJ
ejpam-4931	817	9	term	term	NOUN
ejpam-4931	817	10	of	of	ADP
ejpam-4931	817	11	δ	δ	PROPN
ejpam-4931	817	12	∫	∫	PROPN
ejpam-4931	818	1	t	t	PROPN
ejpam-4931	818	2	0	0	NUM
ejpam-4931	818	3	∫	∫	PROPN
ejpam-4931	819	1	ω	ω	NUM
ejpam-4931	819	2	ξδ∇x∆	ξδ∇x∆	CCONJ
ejpam-4931	819	3	5	5	NUM
ejpam-4931	819	4	xξδφdxdydt	xξδφdxdydt	NOUN
ejpam-4931	819	5	.	.	PUNCT
ejpam-4931	820	1	thus	thus	ADV
ejpam-4931	820	2	,	,	PUNCT
ejpam-4931	820	3	we	we	PRON
ejpam-4931	820	4	have	have	VERB
ejpam-4931	820	5	:	:	PUNCT
ejpam-4931	821	1	δ	δ	PROPN
ejpam-4931	821	2	∫	∫	PROPN
ejpam-4931	821	3	t	t	PROPN
ejpam-4931	821	4	0	0	NUM
ejpam-4931	822	1	∫	∫	PROPN
ejpam-4931	822	2	ω	ω	NUM
ejpam-4931	822	3	ξδ∇x∆	ξδ∇x∆	CCONJ
ejpam-4931	822	4	5	5	NUM
ejpam-4931	822	5	xξδφdxdydt	xξδφdxdydt	ADV
ejpam-4931	822	6	−→	−→	ADV
ejpam-4931	822	7	0	0	NUM
ejpam-4931	822	8	when	when	SCONJ
ejpam-4931	822	9	δ	δ	PROPN
ejpam-4931	822	10	−→	−→	VERB
ejpam-4931	822	11	0	0	NUM
ejpam-4931	822	12	.	.	PUNCT
ejpam-4931	823	1	(	(	PUNCT
ejpam-4931	823	2	114	114	NUM
ejpam-4931	823	3	)	)	PUNCT
ejpam-4931	824	1	so	so	ADV
ejpam-4931	824	2	,	,	PUNCT
ejpam-4931	824	3	we	we	PRON
ejpam-4931	824	4	can	can	AUX
ejpam-4931	824	5	pass	pass	VERB
ejpam-4931	824	6	to	to	ADP
ejpam-4931	824	7	the	the	DET
ejpam-4931	824	8	limit	limit	NOUN
ejpam-4931	824	9	r2	r2	NOUN
ejpam-4931	824	10	,	,	PUNCT
ejpam-4931	824	11	δ	δ	PROPN
ejpam-4931	824	12	−→	−→	NOUN
ejpam-4931	824	13	0	0	NUM
ejpam-4931	825	1	in	in	ADP
ejpam-4931	825	2	(	(	PUNCT
ejpam-4931	825	3	102	102	NUM
ejpam-4931	825	4	)	)	PUNCT
ejpam-4931	825	5	)	)	PUNCT
ejpam-4931	825	6	.	.	PUNCT
ejpam-4931	826	1	hence	hence	PROPN
ejpam-4931	826	2	∂tξ	∂tξ	PROPN
ejpam-4931	826	3	+	+	CCONJ
ejpam-4931	826	4	divx(ξu	divx(ξu	NOUN
ejpam-4931	826	5	)	)	PUNCT
ejpam-4931	826	6	+	+	SYM
ejpam-4931	826	7	∂y(ξv	∂y(ξv	NOUN
ejpam-4931	826	8	)	)	PUNCT
ejpam-4931	826	9	=	=	SYM
ejpam-4931	826	10	0	0	NUM
ejpam-4931	826	11	∂t(ξu	∂t(ξu	NOUN
ejpam-4931	826	12	)	)	PUNCT
ejpam-4931	826	13	+	+	CCONJ
ejpam-4931	826	14	divx(ξu⊗	divx(ξu⊗	NOUN
ejpam-4931	826	15	u	u	NOUN
ejpam-4931	826	16	)	)	PUNCT
ejpam-4931	826	17	+	+	CCONJ
ejpam-4931	826	18	∂y(ξuv	∂y(ξuv	X
ejpam-4931	826	19	)	)	PUNCT
ejpam-4931	827	1	+	+	X
ejpam-4931	827	2	∇xξ	∇xξ	PROPN
ejpam-4931	827	3	2	2	NUM
ejpam-4931	827	4	+	+	NUM
ejpam-4931	827	5	rξ|u|u+	rξ|u|u+	ADJ
ejpam-4931	827	6	r1u	r1u	NOUN
ejpam-4931	827	7	=	=	SYM
ejpam-4931	827	8	2divx	2divx	NUM
ejpam-4931	827	9	(	(	PUNCT
ejpam-4931	827	10	ξdx(u	ξdx(u	PROPN
ejpam-4931	827	11	)	)	PUNCT
ejpam-4931	827	12	)	)	PUNCT
ejpam-4931	828	1	+	+	CCONJ
ejpam-4931	828	2	∂y(ξ∂yu	∂y(ξ∂yu	NOUN
ejpam-4931	828	3	)	)	PUNCT
ejpam-4931	829	1	+	+	CCONJ
ejpam-4931	829	2	k1ξ∇x	k1ξ∇x	PROPN
ejpam-4931	829	3	(	(	PUNCT
ejpam-4931	829	4	∆x	∆x	PROPN
ejpam-4931	829	5	√	√	PROPN
ejpam-4931	829	6	ξ√	ξ√	PROPN
ejpam-4931	829	7	ξ	ξ	PROPN
ejpam-4931	829	8	)	)	PUNCT
ejpam-4931	829	9	∂yξ	∂yξ	PROPN
ejpam-4931	829	10	=	=	SYM
ejpam-4931	829	11	0	0	NUM
ejpam-4931	829	12	,	,	PUNCT
ejpam-4931	829	13	(	(	PUNCT
ejpam-4931	829	14	115	115	NUM
ejpam-4931	829	15	)	)	PUNCT
ejpam-4931	829	16	holds	hold	VERB
ejpam-4931	829	17	in	in	ADP
ejpam-4931	829	18	the	the	DET
ejpam-4931	829	19	sense	sense	NOUN
ejpam-4931	829	20	of	of	ADP
ejpam-4931	829	21	distribution	distribution	NOUN
ejpam-4931	829	22	on	on	ADP
ejpam-4931	829	23	[	[	X
ejpam-4931	829	24	0	0	NUM
ejpam-4931	829	25	,	,	PUNCT
ejpam-4931	829	26	t	t	X
ejpam-4931	829	27	]	]	X
ejpam-4931	829	28	×	×	PROPN
ejpam-4931	829	29	ω	ω	NOUN
ejpam-4931	829	30	.	.	PUNCT
ejpam-4931	830	1	due	due	ADP
ejpam-4931	830	2	to	to	ADP
ejpam-4931	830	3	the	the	DET
ejpam-4931	830	4	lower	low	ADJ
ejpam-4931	830	5	semi	semi	NOUN
ejpam-4931	830	6	-	-	NOUN
ejpam-4931	830	7	continuity	continuity	NOUN
ejpam-4931	830	8	of	of	ADP
ejpam-4931	830	9	convex	convex	NOUN
ejpam-4931	830	10	functions	function	NOUN
ejpam-4931	830	11	,	,	PUNCT
ejpam-4931	830	12	we	we	PRON
ejpam-4931	830	13	can	can	AUX
ejpam-4931	830	14	obtain	obtain	VERB
ejpam-4931	830	15	the	the	DET
ejpam-4931	830	16	following	follow	VERB
ejpam-4931	830	17	energy	energy	NOUN
ejpam-4931	830	18	inequality	inequality	NOUN
ejpam-4931	830	19	(	(	PUNCT
ejpam-4931	830	20	116	116	NUM
ejpam-4931	830	21	)	)	PUNCT
ejpam-4931	830	22	and	and	CCONJ
ejpam-4931	830	23	b	b	X
ejpam-4931	830	24	-	-	PUNCT
ejpam-4931	830	25	d	d	ADJ
ejpam-4931	830	26	entropy	entropy	NOUN
ejpam-4931	830	27	(	(	PUNCT
ejpam-4931	830	28	117	117	NUM
ejpam-4931	830	29	)	)	PUNCT
ejpam-4931	830	30	by	by	ADP
ejpam-4931	830	31	passing	pass	VERB
ejpam-4931	830	32	to	to	ADP
ejpam-4931	830	33	the	the	DET
ejpam-4931	830	34	limits	limit	NOUN
ejpam-4931	830	35	in	in	ADP
ejpam-4931	830	36	(	(	PUNCT
ejpam-4931	830	37	100	100	NUM
ejpam-4931	830	38	)	)	PUNCT
ejpam-4931	830	39	and	and	CCONJ
ejpam-4931	830	40	(	(	PUNCT
ejpam-4931	830	41	101	101	NUM
ejpam-4931	830	42	)	)	PUNCT
ejpam-4931	830	43	as	as	ADP
ejpam-4931	830	44	r2	r2	PROPN
ejpam-4931	830	45	,	,	PUNCT
ejpam-4931	831	1	δ	δ	PROPN
ejpam-4931	831	2	−→	−→	NOUN
ejpam-4931	831	3	0,∫	0,∫	PROPN
ejpam-4931	831	4	ω	ω	PROPN
ejpam-4931	831	5	(	(	PUNCT
ejpam-4931	831	6	1	1	NUM
ejpam-4931	831	7	2	2	NUM
ejpam-4931	831	8	ξu2	ξu2	NOUN
ejpam-4931	831	9	+	+	CCONJ
ejpam-4931	831	10	ξ2	ξ2	NOUN
ejpam-4931	831	11	+	+	CCONJ
ejpam-4931	831	12	k1|∇x	k1|∇x	PROPN
ejpam-4931	831	13	√	√	ADP
ejpam-4931	831	14	ξ|2	ξ|2	PROPN
ejpam-4931	831	15	)	)	PUNCT
ejpam-4931	831	16	dxdy	dxdy	NOUN
ejpam-4931	831	17	+	+	CCONJ
ejpam-4931	831	18	r1	r1	PROPN
ejpam-4931	831	19	∫	∫	PROPN
ejpam-4931	831	20	t	t	PROPN
ejpam-4931	831	21	0	0	NUM
ejpam-4931	831	22	∫	∫	PROPN
ejpam-4931	831	23	ω	ω	PROPN
ejpam-4931	832	1	u2dxdydt	u2dxdydt	PROPN
ejpam-4931	833	1	+	+	CCONJ
ejpam-4931	833	2	r	r	NOUN
ejpam-4931	833	3	∫	∫	PROPN
ejpam-4931	833	4	t	t	PROPN
ejpam-4931	833	5	0	0	NUM
ejpam-4931	833	6	∫	∫	PROPN
ejpam-4931	834	1	ω	ω	NUM
ejpam-4931	834	2	ξ|u|3dxdydt+	ξ|u|3dxdydt+	PROPN
ejpam-4931	834	3	∫	∫	PROPN
ejpam-4931	834	4	t	t	PROPN
ejpam-4931	834	5	0	0	NUM
ejpam-4931	835	1	∫	∫	PROPN
ejpam-4931	835	2	ω	ω	NUM
ejpam-4931	835	3	2ξ|dx(u)|2dxdydt+	2ξ|dx(u)|2dxdydt+	NUM
ejpam-4931	836	1	g	g	PROPN
ejpam-4931	836	2	∫	∫	PROPN
ejpam-4931	836	3	t	t	PROPN
ejpam-4931	836	4	0	0	NUM
ejpam-4931	836	5	∫	∫	PROPN
ejpam-4931	836	6	ω	ω	NUM
ejpam-4931	836	7	vξ	vξ	PROPN
ejpam-4931	836	8	ln	ln	ADJ
ejpam-4931	836	9	ξdxdydt	ξdxdydt	NOUN
ejpam-4931	836	10	+	+	CCONJ
ejpam-4931	837	1	∫	∫	PROPN
ejpam-4931	837	2	t	t	PROPN
ejpam-4931	837	3	0	0	NUM
ejpam-4931	837	4	∫	∫	PROPN
ejpam-4931	838	1	ω	ω	PROPN
ejpam-4931	838	2	ξ|∂yu|2dxdydt	ξ|∂yu|2dxdydt	PROPN
ejpam-4931	838	3	≤	≤	NUM
ejpam-4931	838	4	∫	∫	PROPN
ejpam-4931	838	5	ω	ω	PROPN
ejpam-4931	838	6	(	(	PUNCT
ejpam-4931	838	7	1	1	NUM
ejpam-4931	838	8	2	2	NUM
ejpam-4931	838	9	ξ0u	ξ0u	NOUN
ejpam-4931	838	10	2	2	NUM
ejpam-4931	838	11	0	0	NUM
ejpam-4931	838	12	+	+	CCONJ
ejpam-4931	838	13	ξ20	ξ20	X
ejpam-4931	838	14	+	+	CCONJ
ejpam-4931	838	15	k1|∇x	k1|∇x	PROPN
ejpam-4931	838	16	√	√	NUM
ejpam-4931	838	17	ξ0|2	ξ0|2	NOUN
ejpam-4931	838	18	)	)	PUNCT
ejpam-4931	838	19	ddxdy	ddxdy	NOUN
ejpam-4931	838	20	(	(	PUNCT
ejpam-4931	838	21	116	116	NUM
ejpam-4931	838	22	)	)	PUNCT
ejpam-4931	838	23	and∫	and∫	NOUN
ejpam-4931	838	24	ω	ω	PROPN
ejpam-4931	838	25	(	(	PUNCT
ejpam-4931	838	26	1	1	NUM
ejpam-4931	838	27	2	2	NUM
ejpam-4931	838	28	ξ|u+	ξ|u+	NOUN
ejpam-4931	838	29	2∇x	2∇x	NUM
ejpam-4931	838	30	ln	ln	PROPN
ejpam-4931	838	31	ξ|2	ξ|2	PROPN
ejpam-4931	838	32	−	−	PROPN
ejpam-4931	838	33	2r1	2r1	NUM
ejpam-4931	838	34	ln	ln	PROPN
ejpam-4931	838	35	ξ	ξ	PROPN
ejpam-4931	838	36	)	)	PUNCT
ejpam-4931	838	37	dxdy	dxdy	NOUN
ejpam-4931	838	38	+	+	CCONJ
ejpam-4931	838	39	2	2	NUM
ejpam-4931	838	40	∫	∫	NOUN
ejpam-4931	838	41	t	t	PROPN
ejpam-4931	838	42	0	0	NUM
ejpam-4931	838	43	∫	∫	PROPN
ejpam-4931	838	44	ω	ω	NUM
ejpam-4931	838	45	ξ|∂yv|2dxdydt+	ξ|∂yv|2dxdydt+	PROPN
ejpam-4931	838	46	r	r	NOUN
ejpam-4931	838	47	∫	∫	PROPN
ejpam-4931	838	48	t	t	PROPN
ejpam-4931	838	49	0	0	NUM
ejpam-4931	838	50	∫	∫	PROPN
ejpam-4931	838	51	ω	ω	NUM
ejpam-4931	838	52	ξ|u|3dxdydt	ξ|u|3dxdydt	PROPN
ejpam-4931	838	53	+	+	CCONJ
ejpam-4931	839	1	r1	r1	PROPN
ejpam-4931	839	2	∫	∫	PROPN
ejpam-4931	839	3	t	t	PROPN
ejpam-4931	839	4	0	0	NUM
ejpam-4931	839	5	∫	∫	PROPN
ejpam-4931	839	6	ω	ω	PROPN
ejpam-4931	839	7	u2dxdydt+	u2dxdydt+	PROPN
ejpam-4931	840	1	∫	∫	PROPN
ejpam-4931	840	2	t	t	PROPN
ejpam-4931	840	3	0	0	NUM
ejpam-4931	840	4	∫	∫	PROPN
ejpam-4931	840	5	ω	ω	X
ejpam-4931	840	6	ξ|∂yu|2dxdy	ξ|∂yu|2dxdy	X
ejpam-4931	841	1	+	+	CCONJ
ejpam-4931	841	2	k1	k1	PROPN
ejpam-4931	841	3	∫	∫	PROPN
ejpam-4931	841	4	t	t	PROPN
ejpam-4931	841	5	0	0	NUM
ejpam-4931	841	6	∫	∫	PROPN
ejpam-4931	841	7	ω	ω	NUM
ejpam-4931	841	8	ξ|∇2	ξ|∇2	PROPN
ejpam-4931	842	1	x	x	SYM
ejpam-4931	842	2	ln	ln	PROPN
ejpam-4931	842	3	ξ|2dxdydt	ξ|2dxdydt	PROPN
ejpam-4931	842	4	j.	j.	PROPN
ejpam-4931	842	5	ouya	ouya	PROPN
ejpam-4931	842	6	,	,	PUNCT
ejpam-4931	842	7	a.	a.	NOUN
ejpam-4931	842	8	ouédraogo	ouédraogo	PROPN
ejpam-4931	842	9	/	/	SYM
ejpam-4931	842	10	eur	eur	PROPN
ejpam-4931	842	11	.	.	PUNCT
ejpam-4931	843	1	j.	j.	PROPN
ejpam-4931	843	2	pure	pure	PROPN
ejpam-4931	843	3	appl	appl	PROPN
ejpam-4931	843	4	.	.	PROPN
ejpam-4931	843	5	math	math	PROPN
ejpam-4931	843	6	,	,	PUNCT
ejpam-4931	843	7	16	16	NUM
ejpam-4931	843	8	(	(	PUNCT
ejpam-4931	843	9	4	4	NUM
ejpam-4931	843	10	)	)	PUNCT
ejpam-4931	843	11	(	(	PUNCT
ejpam-4931	843	12	2023	2023	NUM
ejpam-4931	843	13	)	)	PUNCT
ejpam-4931	843	14	,	,	PUNCT
ejpam-4931	843	15	2247	2247	NUM
ejpam-4931	843	16	-	-	SYM
ejpam-4931	843	17	2285	2285	NUM
ejpam-4931	843	18	2278	2278	NUM
ejpam-4931	843	19	+	+	CCONJ
ejpam-4931	843	20	2	2	NUM
ejpam-4931	843	21	∫	∫	NOUN
ejpam-4931	843	22	t	t	NOUN
ejpam-4931	843	23	0	0	NUM
ejpam-4931	843	24	∫	∫	PROPN
ejpam-4931	844	1	ω	ω	NUM
ejpam-4931	844	2	ξ|ax(u)|2dxdydt+	ξ|ax(u)|2dxdydt+	NOUN
ejpam-4931	844	3	8	8	NUM
ejpam-4931	844	4	∫	∫	NOUN
ejpam-4931	844	5	t	t	PROPN
ejpam-4931	844	6	0	0	NUM
ejpam-4931	844	7	∫	∫	PROPN
ejpam-4931	844	8	ω	ω	NUM
ejpam-4931	844	9	ξ|∇x	ξ|∇x	ADJ
ejpam-4931	844	10	√	√	PROPN
ejpam-4931	844	11	ξ|2dxdydt	ξ|2dxdydt	NOUN
ejpam-4931	844	12	≤	≤	NUM
ejpam-4931	844	13	∫	∫	PROPN
ejpam-4931	844	14	ω	ω	PROPN
ejpam-4931	844	15	(	(	PUNCT
ejpam-4931	844	16	ξ0u	ξ0u	NOUN
ejpam-4931	844	17	2	2	NUM
ejpam-4931	844	18	0	0	NUM
ejpam-4931	845	1	+	+	CCONJ
ejpam-4931	845	2	10(∇x	10(∇x	NUM
ejpam-4931	845	3	√	√	ADJ
ejpam-4931	845	4	ξ0	ξ0	PROPN
ejpam-4931	845	5	)	)	PUNCT
ejpam-4931	845	6	2	2	NUM
ejpam-4931	845	7	−	−	PROPN
ejpam-4931	845	8	2r1	2r1	NUM
ejpam-4931	845	9	ln	ln	PROPN
ejpam-4931	845	10	ξ0	ξ0	PROPN
ejpam-4931	845	11	)	)	PUNCT
ejpam-4931	845	12	dxdy	dxdy	PROPN
ejpam-4931	845	13	+	+	CCONJ
ejpam-4931	845	14	e0	e0	PROPN
ejpam-4931	845	15	+	+	CCONJ
ejpam-4931	845	16	c.	c.	PROPN
ejpam-4931	845	17	(	(	PUNCT
ejpam-4931	845	18	117	117	NUM
ejpam-4931	845	19	)	)	PUNCT
ejpam-4931	845	20	we	we	PRON
ejpam-4931	845	21	obtain	obtain	VERB
ejpam-4931	845	22	the	the	DET
ejpam-4931	845	23	existence	existence	NOUN
ejpam-4931	845	24	of	of	ADP
ejpam-4931	845	25	the	the	DET
ejpam-4931	845	26	weak	weak	ADJ
ejpam-4931	845	27	solution	solution	NOUN
ejpam-4931	845	28	(	(	PUNCT
ejpam-4931	845	29	ξ	ξ	X
ejpam-4931	845	30	,	,	PUNCT
ejpam-4931	845	31	u	u	NOUN
ejpam-4931	845	32	,	,	PUNCT
ejpam-4931	845	33	v	v	NOUN
ejpam-4931	845	34	)	)	PUNCT
ejpam-4931	845	35	at	at	ADP
ejpam-4931	845	36	this	this	DET
ejpam-4931	845	37	level	level	NOUN
ejpam-4931	845	38	of	of	ADP
ejpam-4931	845	39	approximation	approximation	NOUN
ejpam-4931	845	40	given	give	VERB
ejpam-4931	845	41	in	in	ADP
ejpam-4931	845	42	the	the	DET
ejpam-4931	845	43	following	follow	VERB
ejpam-4931	845	44	proposition	proposition	NOUN
ejpam-4931	845	45	.	.	PUNCT
ejpam-4931	846	1	proposition	proposition	NOUN
ejpam-4931	846	2	5.2	5.2	NUM
ejpam-4931	846	3	.	.	PUNCT
ejpam-4931	847	1	for	for	ADP
ejpam-4931	847	2	any	any	DET
ejpam-4931	847	3	t	t	PROPN
ejpam-4931	847	4	>	>	X
ejpam-4931	847	5	0	0	PROPN
ejpam-4931	847	6	,	,	PUNCT
ejpam-4931	847	7	the	the	DET
ejpam-4931	847	8	system	system	NOUN
ejpam-4931	847	9	(	(	PUNCT
ejpam-4931	847	10	115	115	NUM
ejpam-4931	847	11	)	)	PUNCT
ejpam-4931	847	12	admits	admit	VERB
ejpam-4931	847	13	a	a	DET
ejpam-4931	847	14	weak	weak	ADJ
ejpam-4931	847	15	solution	solution	NOUN
ejpam-4931	847	16	with	with	ADP
ejpam-4931	847	17	appropriate	appropriate	ADJ
ejpam-4931	847	18	initial	initial	ADJ
ejpam-4931	847	19	data	datum	NOUN
ejpam-4931	847	20	.	.	PUNCT
ejpam-4931	848	1	in	in	ADP
ejpam-4931	848	2	particular	particular	ADJ
ejpam-4931	848	3	,	,	PUNCT
ejpam-4931	848	4	the	the	DET
ejpam-4931	848	5	weak	weak	ADJ
ejpam-4931	848	6	solution	solution	NOUN
ejpam-4931	848	7	(	(	PUNCT
ejpam-4931	848	8	ξ	ξ	X
ejpam-4931	848	9	,	,	PUNCT
ejpam-4931	848	10	u	u	NOUN
ejpam-4931	848	11	,	,	PUNCT
ejpam-4931	848	12	w	w	NOUN
ejpam-4931	848	13	)	)	PUNCT
ejpam-4931	848	14	satisfies	satisfy	VERB
ejpam-4931	848	15	the	the	DET
ejpam-4931	848	16	energy	energy	NOUN
ejpam-4931	848	17	inequality	inequality	NOUN
ejpam-4931	848	18	(	(	PUNCT
ejpam-4931	848	19	116	116	NUM
ejpam-4931	848	20	)	)	PUNCT
ejpam-4931	848	21	and	and	CCONJ
ejpam-4931	848	22	the	the	DET
ejpam-4931	848	23	b	b	PROPN
ejpam-4931	848	24	-	-	PUNCT
ejpam-4931	848	25	d	d	ADJ
ejpam-4931	848	26	entropy	entropy	NOUN
ejpam-4931	848	27	(	(	PUNCT
ejpam-4931	848	28	117	117	NUM
ejpam-4931	848	29	)	)	PUNCT
ejpam-4931	848	30	.	.	PUNCT
ejpam-4931	849	1	5.1.3	5.1.3	X
ejpam-4931	849	2	.	.	NOUN
ejpam-4931	849	3	passing	pass	VERB
ejpam-4931	849	4	to	to	ADP
ejpam-4931	849	5	the	the	DET
ejpam-4931	849	6	limits	limit	NOUN
ejpam-4931	849	7	as	as	ADP
ejpam-4931	849	8	k1	k1	NOUN
ejpam-4931	849	9	,	,	PUNCT
ejpam-4931	849	10	r1	r1	NOUN
ejpam-4931	849	11	−→	−→	NOUN
ejpam-4931	849	12	0	0	NUM
ejpam-4931	849	13	in	in	ADP
ejpam-4931	849	14	this	this	DET
ejpam-4931	849	15	step	step	NOUN
ejpam-4931	849	16	,	,	PUNCT
ejpam-4931	849	17	we	we	PRON
ejpam-4931	849	18	pass	pass	VERB
ejpam-4931	849	19	to	to	ADP
ejpam-4931	849	20	the	the	DET
ejpam-4931	849	21	limits	limit	NOUN
ejpam-4931	849	22	as	as	ADP
ejpam-4931	849	23	k1	k1	NOUN
ejpam-4931	849	24	,	,	PUNCT
ejpam-4931	849	25	r1	r1	NOUN
ejpam-4931	849	26	−→	−→	NOUN
ejpam-4931	849	27	0	0	NUM
ejpam-4931	849	28	.	.	PUNCT
ejpam-4931	850	1	we	we	PRON
ejpam-4931	850	2	denote	denote	VERB
ejpam-4931	850	3	by	by	ADP
ejpam-4931	850	4	(	(	PUNCT
ejpam-4931	850	5	ξk1,r1	ξk1,r1	INTJ
ejpam-4931	850	6	,	,	PUNCT
ejpam-4931	850	7	uk1,r1	uk1,r1	INTJ
ejpam-4931	850	8	,	,	PUNCT
ejpam-4931	850	9	vk1,r1	vk1,r1	PROPN
ejpam-4931	850	10	)	)	PUNCT
ejpam-4931	850	11	the	the	DET
ejpam-4931	850	12	weak	weak	ADJ
ejpam-4931	850	13	solution	solution	NOUN
ejpam-4931	850	14	at	at	ADP
ejpam-4931	850	15	this	this	DET
ejpam-4931	850	16	level	level	NOUN
ejpam-4931	850	17	.	.	PUNCT
ejpam-4931	851	1	here	here	ADV
ejpam-4931	851	2	,	,	PUNCT
ejpam-4931	851	3	the	the	DET
ejpam-4931	851	4	weak	weak	ADJ
ejpam-4931	851	5	solution	solution	NOUN
ejpam-4931	851	6	satisfies	satisfy	VERB
ejpam-4931	851	7	the	the	DET
ejpam-4931	851	8	energy	energy	NOUN
ejpam-4931	851	9	inequality	inequality	NOUN
ejpam-4931	851	10	(	(	PUNCT
ejpam-4931	851	11	116	116	NUM
ejpam-4931	851	12	)	)	PUNCT
ejpam-4931	851	13	and	and	CCONJ
ejpam-4931	851	14	the	the	DET
ejpam-4931	851	15	b	b	PROPN
ejpam-4931	851	16	-	-	PUNCT
ejpam-4931	851	17	d	d	ADJ
ejpam-4931	851	18	entropy	entropy	NOUN
ejpam-4931	851	19	(	(	PUNCT
ejpam-4931	851	20	117	117	NUM
ejpam-4931	851	21	)	)	PUNCT
ejpam-4931	851	22	,	,	PUNCT
ejpam-4931	851	23	then	then	ADV
ejpam-4931	851	24	,	,	PUNCT
ejpam-4931	851	25	we	we	PRON
ejpam-4931	851	26	have	have	VERB
ejpam-4931	851	27	the	the	DET
ejpam-4931	851	28	following	follow	VERB
ejpam-4931	851	29	regularities	regularities	PROPN
ejpam-4931	851	30	√	√	PROPN
ejpam-4931	851	31	ξk1,r1uk1,r1	ξk1,r1uk1,r1	PROPN
ejpam-4931	851	32	∈	∈	PROPN
ejpam-4931	851	33	l∞	l∞	NOUN
ejpam-4931	851	34	(	(	PUNCT
ejpam-4931	851	35	[	[	X
ejpam-4931	851	36	0	0	NUM
ejpam-4931	851	37	,	,	PUNCT
ejpam-4931	851	38	t	t	X
ejpam-4931	851	39	]	]	PUNCT
ejpam-4931	851	40	;	;	PUNCT
ejpam-4931	851	41	l2(ω	l2(ω	NUM
ejpam-4931	851	42	)	)	PUNCT
ejpam-4931	851	43	)	)	PUNCT
ejpam-4931	851	44	,	,	PUNCT
ejpam-4931	851	45	√	√	NUM
ejpam-4931	851	46	ξk1,r1dx(uk1,r1	ξk1,r1dx(uk1,r1	PROPN
ejpam-4931	851	47	)	)	PUNCT
ejpam-4931	851	48	∈	∈	NOUN
ejpam-4931	851	49	l2	l2	NOUN
ejpam-4931	851	50	(	(	PUNCT
ejpam-4931	851	51	[	[	X
ejpam-4931	851	52	0	0	NUM
ejpam-4931	851	53	,	,	PUNCT
ejpam-4931	851	54	t	t	X
ejpam-4931	851	55	]	]	PUNCT
ejpam-4931	851	56	;	;	PUNCT
ejpam-4931	851	57	l2(ω	l2(ω	NUM
ejpam-4931	851	58	)	)	PUNCT
ejpam-4931	851	59	)	)	PUNCT
ejpam-4931	851	60	,	,	PUNCT
ejpam-4931	851	61	∇x	∇x	NOUN
ejpam-4931	851	62	√	√	NUM
ejpam-4931	851	63	ξk1,r1	ξk1,r1	NUM
ejpam-4931	851	64	∈	∈	PROPN
ejpam-4931	851	65	l∞	l∞	NOUN
ejpam-4931	851	66	(	(	PUNCT
ejpam-4931	851	67	[	[	X
ejpam-4931	851	68	0	0	NUM
ejpam-4931	851	69	,	,	PUNCT
ejpam-4931	851	70	t	t	X
ejpam-4931	851	71	]	]	PUNCT
ejpam-4931	851	72	;	;	PUNCT
ejpam-4931	851	73	l2(ω	l2(ω	NUM
ejpam-4931	851	74	)	)	PUNCT
ejpam-4931	851	75	)	)	PUNCT
ejpam-4931	851	76	,	,	PUNCT
ejpam-4931	851	77	√	√	NUM
ejpam-4931	851	78	ξk1,r1∂yuk1,r1	ξk1,r1∂yuk1,r1	PROPN
ejpam-4931	851	79	∈	∈	PROPN
ejpam-4931	851	80	l2	l2	NOUN
ejpam-4931	851	81	(	(	PUNCT
ejpam-4931	851	82	[	[	X
ejpam-4931	851	83	0	0	NUM
ejpam-4931	851	84	,	,	PUNCT
ejpam-4931	851	85	t	t	X
ejpam-4931	851	86	]	]	PUNCT
ejpam-4931	851	87	;	;	PUNCT
ejpam-4931	851	88	l2(ω	l2(ω	NUM
ejpam-4931	851	89	)	)	PUNCT
ejpam-4931	851	90	)	)	PUNCT
ejpam-4931	851	91	,	,	PUNCT
ejpam-4931	851	92	ξ	ξ	PROPN
ejpam-4931	851	93	1	1	NUM
ejpam-4931	851	94	3	3	NUM
ejpam-4931	851	95	k1,r1	k1,r1	PROPN
ejpam-4931	851	96	uk1,r1	uk1,r1	PROPN
ejpam-4931	851	97	∈	∈	PROPN
ejpam-4931	851	98	l3	l3	X
ejpam-4931	851	99	(	(	PUNCT
ejpam-4931	851	100	[	[	X
ejpam-4931	851	101	0	0	NUM
ejpam-4931	851	102	,	,	PUNCT
ejpam-4931	851	103	t	t	X
ejpam-4931	851	104	]	]	PUNCT
ejpam-4931	851	105	;	;	PUNCT
ejpam-4931	851	106	l3(ω	l3(ω	X
ejpam-4931	851	107	)	)	PUNCT
ejpam-4931	851	108	)	)	PUNCT
ejpam-4931	851	109	,	,	PUNCT
ejpam-4931	851	110	√	√	NUM
ejpam-4931	851	111	ξk1,r1∇xuk1,r1	ξk1,r1∇xuk1,r1	PROPN
ejpam-4931	851	112	∈	∈	PROPN
ejpam-4931	851	113	l2	l2	NOUN
ejpam-4931	851	114	(	(	PUNCT
ejpam-4931	851	115	[	[	X
ejpam-4931	851	116	0	0	NUM
ejpam-4931	851	117	,	,	PUNCT
ejpam-4931	851	118	t	t	X
ejpam-4931	851	119	]	]	PUNCT
ejpam-4931	851	120	;	;	PUNCT
ejpam-4931	851	121	l2(ω	l2(ω	NUM
ejpam-4931	851	122	)	)	PUNCT
ejpam-4931	851	123	)	)	PUNCT
ejpam-4931	851	124	,	,	PUNCT
ejpam-4931	851	125	uk1,r1	uk1,r1	PROPN
ejpam-4931	851	126	∈	∈	PROPN
ejpam-4931	851	127	l2	l2	NOUN
ejpam-4931	851	128	(	(	PUNCT
ejpam-4931	851	129	[	[	X
ejpam-4931	851	130	0	0	NUM
ejpam-4931	851	131	,	,	PUNCT
ejpam-4931	851	132	t	t	X
ejpam-4931	851	133	]	]	PUNCT
ejpam-4931	851	134	;	;	PUNCT
ejpam-4931	851	135	l2(ω	l2(ω	NUM
ejpam-4931	851	136	)	)	PUNCT
ejpam-4931	851	137	)	)	PUNCT
ejpam-4931	851	138	,	,	PUNCT
ejpam-4931	851	139	r1	r1	PROPN
ejpam-4931	851	140	ln	ln	PROPN
ejpam-4931	851	141	ξk1,r1	ξk1,r1	PROPN
ejpam-4931	851	142	∈	∈	PROPN
ejpam-4931	851	143	l∞	l∞	NOUN
ejpam-4931	851	144	(	(	PUNCT
ejpam-4931	851	145	[	[	X
ejpam-4931	851	146	0	0	NUM
ejpam-4931	851	147	,	,	PUNCT
ejpam-4931	851	148	t	t	X
ejpam-4931	851	149	]	]	PUNCT
ejpam-4931	851	150	;	;	PUNCT
ejpam-4931	851	151	l1(ω	l1(ω	X
ejpam-4931	851	152	)	)	PUNCT
ejpam-4931	851	153	)	)	PUNCT
ejpam-4931	851	154	,	,	PUNCT
ejpam-4931	851	155	√	√	NUM
ejpam-4931	851	156	ξk1,r1∂yvk1,r1	ξk1,r1∂yvk1,r1	PROPN
ejpam-4931	851	157	∈	∈	PROPN
ejpam-4931	851	158	l2	l2	NOUN
ejpam-4931	851	159	(	(	PUNCT
ejpam-4931	851	160	[	[	X
ejpam-4931	851	161	0	0	NUM
ejpam-4931	851	162	,	,	PUNCT
ejpam-4931	851	163	t	t	X
ejpam-4931	851	164	]	]	PUNCT
ejpam-4931	851	165	;	;	PUNCT
ejpam-4931	851	166	l2(ω	l2(ω	NUM
ejpam-4931	851	167	)	)	PUNCT
ejpam-4931	851	168	)	)	PUNCT
ejpam-4931	851	169	,	,	PUNCT
ejpam-4931	851	170	√	√	PROPN
ejpam-4931	851	171	k1	k1	PROPN
ejpam-4931	851	172	√	√	PROPN
ejpam-4931	851	173	ξk1,r1	ξk1,r1	CCONJ
ejpam-4931	851	174	∈	∈	PROPN
ejpam-4931	851	175	l2	l2	NOUN
ejpam-4931	851	176	(	(	PUNCT
ejpam-4931	851	177	[	[	X
ejpam-4931	851	178	0	0	NUM
ejpam-4931	851	179	,	,	PUNCT
ejpam-4931	851	180	t	t	X
ejpam-4931	851	181	]	]	PUNCT
ejpam-4931	851	182	;	;	PUNCT
ejpam-4931	851	183	h2(ω	h2(ω	NUM
ejpam-4931	851	184	)	)	PUNCT
ejpam-4931	851	185	)	)	PUNCT
ejpam-4931	851	186	,	,	PUNCT
ejpam-4931	851	187	√	√	NUM
ejpam-4931	851	188	ξk1,r1∇x	ξk1,r1∇x	NOUN
ejpam-4931	851	189	√	√	NUM
ejpam-4931	851	190	ξk1,r1	ξk1,r1	CCONJ
ejpam-4931	851	191	∈	∈	PROPN
ejpam-4931	851	192	l2	l2	NOUN
ejpam-4931	851	193	(	(	PUNCT
ejpam-4931	851	194	[	[	X
ejpam-4931	851	195	0	0	NUM
ejpam-4931	851	196	,	,	PUNCT
ejpam-4931	851	197	t	t	X
ejpam-4931	851	198	]	]	PUNCT
ejpam-4931	851	199	;	;	PUNCT
ejpam-4931	851	200	l2(ω	l2(ω	NUM
ejpam-4931	851	201	)	)	PUNCT
ejpam-4931	851	202	)	)	PUNCT
ejpam-4931	851	203	,	,	PUNCT
ejpam-4931	851	204	4	4	NUM
ejpam-4931	851	205	√	√	NOUN
ejpam-4931	851	206	k1∇xξ	k1∇xξ	PROPN
ejpam-4931	851	207	1	1	NUM
ejpam-4931	851	208	4	4	NUM
ejpam-4931	851	209	k1,r1	k1,r1	PROPN
ejpam-4931	851	210	∈	∈	PROPN
ejpam-4931	851	211	l4	l4	PROPN
ejpam-4931	851	212	(	(	PUNCT
ejpam-4931	851	213	[	[	X
ejpam-4931	851	214	0	0	NUM
ejpam-4931	851	215	,	,	PUNCT
ejpam-4931	851	216	t	t	X
ejpam-4931	851	217	]	]	PUNCT
ejpam-4931	851	218	;	;	PUNCT
ejpam-4931	851	219	l4(ω	l4(ω	X
ejpam-4931	851	220	)	)	PUNCT
ejpam-4931	851	221	)	)	PUNCT
ejpam-4931	851	222	.	.	PUNCT
ejpam-4931	852	1	(	(	PUNCT
ejpam-4931	852	2	118	118	NUM
ejpam-4931	852	3	)	)	PUNCT
ejpam-4931	852	4	lemma	lemma	PROPN
ejpam-4931	852	5	15	15	NUM
ejpam-4931	852	6	.	.	PUNCT
ejpam-4931	853	1	(	(	PUNCT
ejpam-4931	853	2	convergence	convergence	NOUN
ejpam-4931	853	3	of	of	ADP
ejpam-4931	853	4	(	(	PUNCT
ejpam-4931	853	5	√	√	PROPN
ejpam-4931	853	6	ξk1,r1)k1,r1	ξk1,r1)k1,r1	NUM
ejpam-4931	853	7	)	)	PUNCT
ejpam-4931	853	8	.	.	PUNCT
ejpam-4931	854	1	for	for	ADP
ejpam-4931	854	2	√	√	PROPN
ejpam-4931	854	3	ξk1,r1	ξk1,r1	ADV
ejpam-4931	854	4	satisfying	satisfy	VERB
ejpam-4931	854	5	proposition	proposition	NOUN
ejpam-4931	854	6	5.2	5.2	NUM
ejpam-4931	854	7	,	,	PUNCT
ejpam-4931	854	8	we	we	PRON
ejpam-4931	854	9	deduce	deduce	VERB
ejpam-4931	854	10	that	that	PRON
ejpam-4931	854	11	(	(	PUNCT
ejpam-4931	854	12	√	√	INTJ
ejpam-4931	854	13	ξk1,r1)k1,r1	ξk1,r1)k1,r1	PROPN
ejpam-4931	854	14	is	be	AUX
ejpam-4931	854	15	bounded	bound	VERB
ejpam-4931	854	16	in	in	ADP
ejpam-4931	854	17	l∞	l∞	PROPN
ejpam-4931	854	18	(	(	PUNCT
ejpam-4931	854	19	[	[	X
ejpam-4931	854	20	0	0	NUM
ejpam-4931	854	21	,	,	PUNCT
ejpam-4931	854	22	t	t	X
ejpam-4931	854	23	]	]	PUNCT
ejpam-4931	854	24	;	;	PUNCT
ejpam-4931	854	25	h1(ω	h1(ω	PROPN
ejpam-4931	854	26	)	)	PUNCT
ejpam-4931	854	27	)	)	PUNCT
ejpam-4931	854	28	and	and	CCONJ
ejpam-4931	854	29	(	(	PUNCT
ejpam-4931	854	30	∂t	∂t	PROPN
ejpam-4931	854	31	√	√	PROPN
ejpam-4931	854	32	ξk1,r1)k1,r1	ξk1,r1)k1,r1	PROPN
ejpam-4931	854	33	is	be	AUX
ejpam-4931	854	34	bounded	bound	VERB
ejpam-4931	854	35	in	in	ADP
ejpam-4931	854	36	l2	l2	NOUN
ejpam-4931	854	37	(	(	PUNCT
ejpam-4931	854	38	[	[	X
ejpam-4931	854	39	0	0	NUM
ejpam-4931	854	40	,	,	PUNCT
ejpam-4931	854	41	t	t	X
ejpam-4931	854	42	]	]	PUNCT
ejpam-4931	854	43	;	;	PUNCT
ejpam-4931	854	44	h−1(ω	h−1(ω	PROPN
ejpam-4931	854	45	)	)	PUNCT
ejpam-4931	854	46	)	)	PUNCT
ejpam-4931	854	47	.	.	PUNCT
ejpam-4931	855	1	then	then	ADV
ejpam-4931	855	2	,	,	PUNCT
ejpam-4931	855	3	up	up	ADP
ejpam-4931	855	4	to	to	ADP
ejpam-4931	855	5	a	a	DET
ejpam-4931	855	6	subsequence	subsequence	NOUN
ejpam-4931	855	7	,	,	PUNCT
ejpam-4931	855	8	we	we	PRON
ejpam-4931	855	9	have√	have√	VERB
ejpam-4931	855	10	ξk1,r1	ξk1,r1	ADV
ejpam-4931	855	11	−→	−→	ADV
ejpam-4931	855	12	√	√	PRON
ejpam-4931	855	13	ξ	ξ	PROPN
ejpam-4931	855	14	a.e	a.e	PROPN
ejpam-4931	855	15	.	.	PROPN
ejpam-4931	855	16	and	and	CCONJ
ejpam-4931	855	17	strongly	strongly	ADV
ejpam-4931	855	18	in	in	ADP
ejpam-4931	855	19	l2	l2	NOUN
ejpam-4931	855	20	(	(	PUNCT
ejpam-4931	855	21	[	[	X
ejpam-4931	855	22	0	0	NUM
ejpam-4931	855	23	,	,	PUNCT
ejpam-4931	855	24	t	t	X
ejpam-4931	855	25	]	]	PUNCT
ejpam-4931	855	26	;	;	PUNCT
ejpam-4931	855	27	l2(ω	l2(ω	NUM
ejpam-4931	855	28	)	)	PUNCT
ejpam-4931	855	29	.	.	PUNCT
ejpam-4931	856	1	furthermore	furthermore	ADV
ejpam-4931	856	2	,	,	PUNCT
ejpam-4931	856	3	we	we	PRON
ejpam-4931	856	4	have	have	VERB
ejpam-4931	856	5	ξk1,r1	ξk1,r1	ADV
ejpam-4931	856	6	−→	−→	ADJ
ejpam-4931	856	7	ξ	ξ	X
ejpam-4931	856	8	a.e	a.e	PROPN
ejpam-4931	856	9	.	.	PROPN
ejpam-4931	856	10	and	and	CCONJ
ejpam-4931	856	11	strongly	strongly	ADV
ejpam-4931	856	12	in	in	ADP
ejpam-4931	856	13	c	c	PROPN
ejpam-4931	856	14	(	(	PUNCT
ejpam-4931	856	15	[	[	X
ejpam-4931	856	16	0	0	NUM
ejpam-4931	856	17	,	,	PUNCT
ejpam-4931	856	18	t	t	X
ejpam-4931	856	19	]	]	PUNCT
ejpam-4931	856	20	;	;	PUNCT
ejpam-4931	856	21	lp(ω	lp(ω	NUM
ejpam-4931	856	22	)	)	PUNCT
ejpam-4931	856	23	,	,	PUNCT
ejpam-4931	856	24	∀	∀	NOUN
ejpam-4931	856	25	1	1	NUM
ejpam-4931	856	26	≤	≤	NOUN
ejpam-4931	856	27	p	p	X
ejpam-4931	856	28	<	<	X
ejpam-4931	856	29	3	3	NUM
ejpam-4931	856	30	.	.	PUNCT
ejpam-4931	857	1	proof	proof	NOUN
ejpam-4931	857	2	.	.	PUNCT
ejpam-4931	858	1	since	since	SCONJ
ejpam-4931	858	2	∥	∥	NUM
ejpam-4931	858	3	√	√	NUM
ejpam-4931	858	4	ξk1,r1∥2l2(ω)=	ξk1,r1∥2l2(ω)=	PROPN
ejpam-4931	858	5	∥ξ0∥l1(ω	∥ξ0∥l1(ω	NOUN
ejpam-4931	858	6	)	)	PUNCT
ejpam-4931	858	7	and	and	CCONJ
ejpam-4931	858	8	∇x	∇x	NOUN
ejpam-4931	858	9	√	√	NUM
ejpam-4931	858	10	ξk1,r1	ξk1,r1	PROPN
ejpam-4931	858	11	∈	∈	PROPN
ejpam-4931	858	12	l∞	l∞	NOUN
ejpam-4931	858	13	(	(	PUNCT
ejpam-4931	858	14	[	[	X
ejpam-4931	858	15	0	0	NUM
ejpam-4931	858	16	,	,	PUNCT
ejpam-4931	858	17	t	t	X
ejpam-4931	858	18	]	]	PUNCT
ejpam-4931	858	19	;	;	PUNCT
ejpam-4931	858	20	l2(ω	l2(ω	NUM
ejpam-4931	858	21	)	)	PUNCT
ejpam-4931	858	22	,	,	PUNCT
ejpam-4931	858	23	we	we	PRON
ejpam-4931	858	24	have√	have√	VERB
ejpam-4931	858	25	ξk1,r1	ξk1,r1	PROPN
ejpam-4931	858	26	∈	∈	PROPN
ejpam-4931	858	27	l∞	l∞	PROPN
ejpam-4931	858	28	(	(	PUNCT
ejpam-4931	858	29	[	[	X
ejpam-4931	858	30	0	0	NUM
ejpam-4931	858	31	,	,	PUNCT
ejpam-4931	858	32	t	t	X
ejpam-4931	858	33	]	]	PUNCT
ejpam-4931	858	34	;	;	PUNCT
ejpam-4931	858	35	h1(ω	h1(ω	PROPN
ejpam-4931	858	36	)	)	PUNCT
ejpam-4931	858	37	.	.	PUNCT
ejpam-4931	859	1	then	then	ADV
ejpam-4931	859	2	,	,	PUNCT
ejpam-4931	859	3	we	we	PRON
ejpam-4931	859	4	claim	claim	VERB
ejpam-4931	859	5	that	that	SCONJ
ejpam-4931	859	6	∂t	∂t	PROPN
ejpam-4931	859	7	√	√	PROPN
ejpam-4931	859	8	ξk1,r1	ξk1,r1	PROPN
ejpam-4931	860	1	=	=	SYM
ejpam-4931	860	2	−1	−1	NOUN
ejpam-4931	860	3	2	2	NUM
ejpam-4931	860	4	√	√	NUM
ejpam-4931	860	5	ξk1,r1divx(uk1,r1)−	ξk1,r1divx(uk1,r1)−	NOUN
ejpam-4931	860	6	uk1,r1	uk1,r1	PROPN
ejpam-4931	860	7	.∇x	.∇x	PUNCT
ejpam-4931	861	1	√	√	PROPN
ejpam-4931	861	2	ξk1,r1	ξk1,r1	INTJ
ejpam-4931	862	1	−	−	NUM
ejpam-4931	862	2	1	1	NUM
ejpam-4931	862	3	2	2	NUM
ejpam-4931	862	4	√	√	PROPN
ejpam-4931	862	5	ξk1,r1∂yvk1,r1	ξk1,r1∂yvk1,r1	PROPN
ejpam-4931	862	6	j.	j.	PROPN
ejpam-4931	862	7	ouya	ouya	PROPN
ejpam-4931	862	8	,	,	PUNCT
ejpam-4931	862	9	a.	a.	NOUN
ejpam-4931	862	10	ouédraogo	ouédraogo	PROPN
ejpam-4931	862	11	/	/	SYM
ejpam-4931	862	12	eur	eur	PROPN
ejpam-4931	862	13	.	.	PUNCT
ejpam-4931	863	1	j.	j.	PROPN
ejpam-4931	863	2	pure	pure	PROPN
ejpam-4931	863	3	appl	appl	PROPN
ejpam-4931	863	4	.	.	PROPN
ejpam-4931	863	5	math	math	PROPN
ejpam-4931	863	6	,	,	PUNCT
ejpam-4931	863	7	16	16	NUM
ejpam-4931	863	8	(	(	PUNCT
ejpam-4931	863	9	4	4	NUM
ejpam-4931	863	10	)	)	PUNCT
ejpam-4931	863	11	(	(	PUNCT
ejpam-4931	863	12	2023	2023	NUM
ejpam-4931	863	13	)	)	PUNCT
ejpam-4931	863	14	,	,	PUNCT
ejpam-4931	863	15	2247	2247	NUM
ejpam-4931	863	16	-	-	SYM
ejpam-4931	863	17	2285	2285	NUM
ejpam-4931	863	18	2279	2279	NUM
ejpam-4931	863	19	=	=	SYM
ejpam-4931	863	20	1	1	NUM
ejpam-4931	863	21	2	2	NUM
ejpam-4931	863	22	√	√	NUM
ejpam-4931	863	23	ξk1,r1divx(uk1,r1)−	ξk1,r1divx(uk1,r1)−	PROPN
ejpam-4931	863	24	divx	divx	PROPN
ejpam-4931	863	25	(	(	PUNCT
ejpam-4931	863	26	√	√	PROPN
ejpam-4931	863	27	ξk1,r1uk1,r1)−	ξk1,r1uk1,r1)−	NOUN
ejpam-4931	863	28	1	1	NUM
ejpam-4931	863	29	2	2	NUM
ejpam-4931	863	30	√	√	NOUN
ejpam-4931	863	31	ξk1,r1∂yvk1,r1	ξk1,r1∂yvk1,r1	PROPN
ejpam-4931	863	32	.	.	PUNCT
ejpam-4931	864	1	(	(	PUNCT
ejpam-4931	864	2	119	119	NUM
ejpam-4931	864	3	)	)	PUNCT
ejpam-4931	864	4	indeed	indeed	ADV
ejpam-4931	864	5	,	,	PUNCT
ejpam-4931	864	6	we	we	PRON
ejpam-4931	864	7	have	have	VERB
ejpam-4931	864	8	∂tξk1,r1	∂tξk1,r1	PROPN
ejpam-4931	864	9	+	+	CCONJ
ejpam-4931	864	10	∂y(ξk1,r1vk1,r1	∂y(ξk1,r1vk1,r1	PROPN
ejpam-4931	864	11	)	)	PUNCT
ejpam-4931	864	12	=	=	SYM
ejpam-4931	865	1	−divx(ξk1,r1uk1,r1	−divx(ξk1,r1uk1,r1	NOUN
ejpam-4931	865	2	)	)	PUNCT
ejpam-4931	865	3	.	.	PUNCT
ejpam-4931	866	1	furthermore	furthermore	ADV
ejpam-4931	866	2	,	,	PUNCT
ejpam-4931	866	3	∂t	∂t	PROPN
ejpam-4931	866	4	√	√	PROPN
ejpam-4931	866	5	ξk1,r1	ξk1,r1	NOUN
ejpam-4931	866	6	=	=	SYM
ejpam-4931	866	7	1	1	NUM
ejpam-4931	866	8	2	2	NUM
ejpam-4931	866	9	1√	1√	NUM
ejpam-4931	866	10	ξk1,r1	ξk1,r1	NOUN
ejpam-4931	866	11	∂tξk1,r1	∂tξk1,r1	PROPN
ejpam-4931	866	12	,	,	PUNCT
ejpam-4931	866	13	hence	hence	ADV
ejpam-4931	866	14	∂t	∂t	PROPN
ejpam-4931	866	15	√	√	PROPN
ejpam-4931	866	16	ξk1,r1	ξk1,r1	NOUN
ejpam-4931	866	17	=	=	SYM
ejpam-4931	866	18	−1	−1	NOUN
ejpam-4931	866	19	2	2	NUM
ejpam-4931	866	20	1√	1√	PROPN
ejpam-4931	866	21	ξk1,r1	ξk1,r1	NOUN
ejpam-4931	866	22	(	(	PUNCT
ejpam-4931	866	23	divx(ξk1,r1uk1,r1	divx(ξk1,r1uk1,r1	PROPN
ejpam-4931	866	24	)	)	PUNCT
ejpam-4931	867	1	+	+	CCONJ
ejpam-4931	867	2	∂y(ξk1,r1vk1,r1	∂y(ξk1,r1vk1,r1	PROPN
ejpam-4931	867	3	)	)	PUNCT
ejpam-4931	867	4	)	)	PUNCT
ejpam-4931	867	5	.	.	PUNCT
ejpam-4931	868	1	by	by	ADP
ejpam-4931	868	2	developing	develop	VERB
ejpam-4931	868	3	the	the	DET
ejpam-4931	868	4	divergence	divergence	NOUN
ejpam-4931	868	5	part	part	NOUN
ejpam-4931	868	6	and	and	CCONJ
ejpam-4931	868	7	replacing	replace	VERB
ejpam-4931	868	8	ξk1,r1	ξk1,r1	INTJ
ejpam-4931	868	9	by	by	ADP
ejpam-4931	868	10	√	√	PROPN
ejpam-4931	869	1	ξk1,r1	ξk1,r1	INTJ
ejpam-4931	869	2	.	.	PUNCT
ejpam-4931	870	1	√	√	PROPN
ejpam-4931	871	1	ξk1,r1	ξk1,r1	INTJ
ejpam-4931	871	2	,	,	PUNCT
ejpam-4931	871	3	we	we	PRON
ejpam-4931	871	4	obtain	obtain	VERB
ejpam-4931	871	5	∂t	∂t	PROPN
ejpam-4931	871	6	√	√	PROPN
ejpam-4931	871	7	ξk1,r1	ξk1,r1	NOUN
ejpam-4931	872	1	=	=	SYM
ejpam-4931	872	2	−1	−1	NOUN
ejpam-4931	872	3	2	2	NUM
ejpam-4931	872	4	√	√	NUM
ejpam-4931	872	5	ξk1,r1divx(uk1,r1)−	ξk1,r1divx(uk1,r1)−	VERB
ejpam-4931	872	6	uk1,r1∇x	uk1,r1∇x	PROPN
ejpam-4931	872	7	√	√	PROPN
ejpam-4931	873	1	ξk1,r1	ξk1,r1	INTJ
ejpam-4931	874	1	−	−	PROPN
ejpam-4931	874	2	1	1	NUM
ejpam-4931	874	3	2	2	NUM
ejpam-4931	874	4	√	√	NOUN
ejpam-4931	874	5	ξk1,r1∂yvk1,r1	ξk1,r1∂yvk1,r1	NOUN
ejpam-4931	874	6	.	.	PUNCT
ejpam-4931	875	1	adding	add	VERB
ejpam-4931	875	2	and	and	CCONJ
ejpam-4931	875	3	deducting	deduct	VERB
ejpam-4931	875	4	√	√	NUM
ejpam-4931	875	5	ξk1,r1divx(uk1,r1	ξk1,r1divx(uk1,r1	PROPN
ejpam-4931	875	6	)	)	PUNCT
ejpam-4931	875	7	in	in	ADP
ejpam-4931	875	8	the	the	DET
ejpam-4931	875	9	above	above	ADJ
ejpam-4931	875	10	equality	equality	NOUN
ejpam-4931	875	11	,	,	PUNCT
ejpam-4931	875	12	we	we	PRON
ejpam-4931	875	13	obtain	obtain	VERB
ejpam-4931	875	14	(	(	PUNCT
ejpam-4931	875	15	119	119	NUM
ejpam-4931	875	16	)	)	PUNCT
ejpam-4931	875	17	.	.	PUNCT
ejpam-4931	876	1	this	this	PRON
ejpam-4931	876	2	gives	give	VERB
ejpam-4931	876	3	∂t	∂t	PROPN
ejpam-4931	876	4	√	√	PROPN
ejpam-4931	876	5	ξk1,r1	ξk1,r1	PROPN
ejpam-4931	876	6	∈	∈	PROPN
ejpam-4931	876	7	l2	l2	NOUN
ejpam-4931	876	8	(	(	PUNCT
ejpam-4931	876	9	[	[	X
ejpam-4931	876	10	0	0	NUM
ejpam-4931	876	11	,	,	PUNCT
ejpam-4931	876	12	t	t	X
ejpam-4931	876	13	]	]	PUNCT
ejpam-4931	876	14	;	;	PUNCT
ejpam-4931	876	15	h−1(ω	h−1(ω	PROPN
ejpam-4931	876	16	)	)	PUNCT
ejpam-4931	876	17	)	)	PUNCT
ejpam-4931	876	18	.	.	PUNCT
ejpam-4931	877	1	using	use	VERB
ejpam-4931	877	2	lemma	lemma	PROPN
ejpam-4931	877	3	1	1	NUM
ejpam-4931	877	4	we	we	PRON
ejpam-4931	877	5	have	have	VERB
ejpam-4931	877	6	√	√	NUM
ejpam-4931	877	7	ξk1,r1	ξk1,r1	ADV
ejpam-4931	878	1	−→	−→	ADJ
ejpam-4931	878	2	√	√	PROPN
ejpam-4931	878	3	ξ	ξ	ADP
ejpam-4931	878	4	strongly	strongly	ADV
ejpam-4931	878	5	in	in	ADP
ejpam-4931	878	6	l2	l2	NOUN
ejpam-4931	878	7	(	(	PUNCT
ejpam-4931	878	8	[	[	X
ejpam-4931	878	9	0	0	NUM
ejpam-4931	878	10	,	,	PUNCT
ejpam-4931	878	11	t	t	X
ejpam-4931	878	12	]	]	PUNCT
ejpam-4931	878	13	;	;	PUNCT
ejpam-4931	878	14	h1(ω	h1(ω	PROPN
ejpam-4931	878	15	)	)	PUNCT
ejpam-4931	878	16	)	)	PUNCT
ejpam-4931	878	17	,	,	PUNCT
ejpam-4931	878	18	thus	thus	ADV
ejpam-4931	878	19	in	in	ADP
ejpam-4931	878	20	l2	l2	NOUN
ejpam-4931	878	21	(	(	PUNCT
ejpam-4931	878	22	[	[	X
ejpam-4931	878	23	0	0	NUM
ejpam-4931	878	24	,	,	PUNCT
ejpam-4931	878	25	t	t	X
ejpam-4931	878	26	]	]	PUNCT
ejpam-4931	878	27	;	;	PUNCT
ejpam-4931	878	28	l2(ω	l2(ω	NUM
ejpam-4931	878	29	)	)	PUNCT
ejpam-4931	878	30	)	)	PUNCT
ejpam-4931	879	1	and	and	CCONJ
ejpam-4931	879	2	this	this	PRON
ejpam-4931	879	3	gives	give	VERB
ejpam-4931	879	4	that	that	PRON
ejpam-4931	879	5	√	√	NOUN
ejpam-4931	879	6	ξk1,r1	ξk1,r1	ADV
ejpam-4931	879	7	−→	−→	ADJ
ejpam-4931	879	8	√	√	PRON
ejpam-4931	879	9	ξ	ξ	PRON
ejpam-4931	879	10	a.e	a.e	PROPN
ejpam-4931	879	11	.	.	PROPN
ejpam-4931	879	12	using	use	VERB
ejpam-4931	879	13	the	the	DET
ejpam-4931	879	14	sobolev	sobolev	NOUN
ejpam-4931	879	15	injection	injection	NOUN
ejpam-4931	879	16	theorem	theorem	NOUN
ejpam-4931	879	17	,	,	PUNCT
ejpam-4931	879	18	we	we	PRON
ejpam-4931	879	19	deduce	deduce	VERB
ejpam-4931	879	20	that	that	DET
ejpam-4931	879	21	√	√	PROPN
ejpam-4931	879	22	ξk1,r1	ξk1,r1	PROPN
ejpam-4931	879	23	is	be	AUX
ejpam-4931	879	24	bounded	bound	VERB
ejpam-4931	879	25	in	in	ADP
ejpam-4931	879	26	l∞	l∞	PROPN
ejpam-4931	879	27	(	(	PUNCT
ejpam-4931	879	28	[	[	X
ejpam-4931	879	29	0	0	NUM
ejpam-4931	879	30	,	,	PUNCT
ejpam-4931	879	31	t	t	X
ejpam-4931	879	32	]	]	PUNCT
ejpam-4931	879	33	;	;	PUNCT
ejpam-4931	879	34	l6(ω	l6(ω	PROPN
ejpam-4931	879	35	)	)	PUNCT
ejpam-4931	879	36	)	)	PUNCT
ejpam-4931	879	37	,	,	PUNCT
ejpam-4931	879	38	so	so	CCONJ
ejpam-4931	879	39	ξk1,r1	ξk1,r1	PROPN
ejpam-4931	879	40	∈	∈	PROPN
ejpam-4931	879	41	l∞	l∞	PROPN
ejpam-4931	879	42	(	(	PUNCT
ejpam-4931	879	43	[	[	X
ejpam-4931	879	44	0	0	NUM
ejpam-4931	879	45	,	,	PUNCT
ejpam-4931	879	46	t	t	X
ejpam-4931	879	47	]	]	PUNCT
ejpam-4931	879	48	;	;	PUNCT
ejpam-4931	879	49	l3(ω	l3(ω	X
ejpam-4931	879	50	)	)	PUNCT
ejpam-4931	879	51	)	)	PUNCT
ejpam-4931	879	52	.	.	PUNCT
ejpam-4931	880	1	then	then	ADV
ejpam-4931	880	2	,	,	PUNCT
ejpam-4931	880	3	we	we	PRON
ejpam-4931	880	4	deduce	deduce	VERB
ejpam-4931	880	5	by	by	ADP
ejpam-4931	880	6	using	use	VERB
ejpam-4931	880	7	the	the	DET
ejpam-4931	880	8	hölder	hölder	NOUN
ejpam-4931	880	9	inequality	inequality	NOUN
ejpam-4931	880	10	that	that	SCONJ
ejpam-4931	880	11	ξk1,r1uk1,r1	ξk1,r1uk1,r1	PROPN
ejpam-4931	880	12	=	=	PUNCT
ejpam-4931	881	1	√	√	PROPN
ejpam-4931	881	2	ξk1,r1	ξk1,r1	NUM
ejpam-4931	881	3	√	√	INTJ
ejpam-4931	881	4	ξk1,r1uk1,r1	ξk1,r1uk1,r1	PROPN
ejpam-4931	881	5	∈	∈	PROPN
ejpam-4931	881	6	l∞	l∞	NOUN
ejpam-4931	881	7	(	(	PUNCT
ejpam-4931	881	8	[	[	X
ejpam-4931	881	9	0	0	NUM
ejpam-4931	881	10	,	,	PUNCT
ejpam-4931	881	11	t	t	X
ejpam-4931	881	12	]	]	PUNCT
ejpam-4931	881	13	;	;	PUNCT
ejpam-4931	881	14	l	l	NOUN
ejpam-4931	881	15	3	3	NUM
ejpam-4931	881	16	2	2	NUM
ejpam-4931	881	17	(	(	PUNCT
ejpam-4931	881	18	ω	ω	NOUN
ejpam-4931	881	19	)	)	PUNCT
ejpam-4931	881	20	)	)	PUNCT
ejpam-4931	881	21	.	.	PUNCT
ejpam-4931	882	1	(	(	PUNCT
ejpam-4931	882	2	120	120	NUM
ejpam-4931	882	3	)	)	PUNCT
ejpam-4931	882	4	this	this	PRON
ejpam-4931	882	5	gives	give	VERB
ejpam-4931	882	6	divx(ξk1,r1uk1,r1	divx(ξk1,r1uk1,r1	PROPN
ejpam-4931	882	7	)	)	PUNCT
ejpam-4931	882	8	∈	∈	PROPN
ejpam-4931	882	9	l∞	l∞	NOUN
ejpam-4931	882	10	(	(	PUNCT
ejpam-4931	882	11	[	[	X
ejpam-4931	882	12	0	0	NUM
ejpam-4931	882	13	,	,	PUNCT
ejpam-4931	882	14	t	t	X
ejpam-4931	882	15	]	]	PUNCT
ejpam-4931	882	16	;	;	PUNCT
ejpam-4931	882	17	w−1	w−1	PROPN
ejpam-4931	882	18	,	,	PUNCT
ejpam-4931	882	19	3	3	NUM
ejpam-4931	882	20	2	2	NUM
ejpam-4931	882	21	(	(	PUNCT
ejpam-4931	882	22	ω	ω	NOUN
ejpam-4931	882	23	)	)	PUNCT
ejpam-4931	882	24	)	)	PUNCT
ejpam-4931	882	25	.	.	PUNCT
ejpam-4931	883	1	this	this	DET
ejpam-4931	883	2	last	last	ADJ
ejpam-4931	883	3	result	result	NOUN
ejpam-4931	883	4	,	,	PUNCT
ejpam-4931	883	5	combined	combined	ADJ
ejpam-4931	883	6	with√	with√	PROPN
ejpam-4931	883	7	ξk1,r1∂yvk1,r1	ξk1,r1∂yvk1,r1	PROPN
ejpam-4931	883	8	∈	∈	PROPN
ejpam-4931	883	9	l2	l2	NOUN
ejpam-4931	883	10	(	(	PUNCT
ejpam-4931	883	11	[	[	X
ejpam-4931	883	12	0	0	NUM
ejpam-4931	883	13	,	,	PUNCT
ejpam-4931	883	14	t	t	X
ejpam-4931	883	15	]	]	PUNCT
ejpam-4931	883	16	;	;	PUNCT
ejpam-4931	883	17	l2(ω	l2(ω	NUM
ejpam-4931	883	18	)	)	PUNCT
ejpam-4931	883	19	)	)	PUNCT
ejpam-4931	883	20	and	and	CCONJ
ejpam-4931	883	21	the	the	DET
ejpam-4931	883	22	continuity	continuity	NOUN
ejpam-4931	883	23	equation	equation	NOUN
ejpam-4931	883	24	,	,	PUNCT
ejpam-4931	883	25	give	give	VERB
ejpam-4931	883	26	∂t	∂t	PROPN
ejpam-4931	883	27	√	√	PROPN
ejpam-4931	883	28	ξk1,r1	ξk1,r1	PROPN
ejpam-4931	883	29	∈	∈	PROPN
ejpam-4931	883	30	l2	l2	NOUN
ejpam-4931	883	31	(	(	PUNCT
ejpam-4931	883	32	[	[	X
ejpam-4931	883	33	0	0	NUM
ejpam-4931	883	34	,	,	PUNCT
ejpam-4931	883	35	t	t	X
ejpam-4931	883	36	]	]	PUNCT
ejpam-4931	883	37	;	;	PUNCT
ejpam-4931	883	38	w−1	w−1	PROPN
ejpam-4931	883	39	,	,	PUNCT
ejpam-4931	883	40	3	3	NUM
ejpam-4931	883	41	2	2	NUM
ejpam-4931	883	42	(	(	PUNCT
ejpam-4931	883	43	ω	ω	NOUN
ejpam-4931	883	44	)	)	PUNCT
ejpam-4931	883	45	)	)	PUNCT
ejpam-4931	883	46	.	.	PUNCT
ejpam-4931	884	1	moreover	moreover	ADV
ejpam-4931	884	2	,	,	PUNCT
ejpam-4931	884	3	we	we	PRON
ejpam-4931	884	4	have	have	VERB
ejpam-4931	884	5	∇xξk1,r1	∇xξk1,r1	VERB
ejpam-4931	884	6	=	=	SYM
ejpam-4931	884	7	2	2	NUM
ejpam-4931	884	8	√	√	NUM
ejpam-4931	884	9	ξk1,r1∇x	ξk1,r1∇x	NOUN
ejpam-4931	884	10	√	√	NUM
ejpam-4931	884	11	ξk1,r1	ξk1,r1	CCONJ
ejpam-4931	884	12	∈	∈	PROPN
ejpam-4931	884	13	l∞	l∞	NOUN
ejpam-4931	884	14	(	(	PUNCT
ejpam-4931	884	15	[	[	X
ejpam-4931	884	16	0	0	NUM
ejpam-4931	884	17	,	,	PUNCT
ejpam-4931	884	18	t	t	X
ejpam-4931	884	19	]	]	PUNCT
ejpam-4931	884	20	;	;	PUNCT
ejpam-4931	884	21	l	l	NOUN
ejpam-4931	884	22	3	3	NUM
ejpam-4931	884	23	2	2	NUM
ejpam-4931	884	24	(	(	PUNCT
ejpam-4931	884	25	ω	ω	NOUN
ejpam-4931	884	26	)	)	PUNCT
ejpam-4931	884	27	)	)	PUNCT
ejpam-4931	884	28	.	.	PUNCT
ejpam-4931	885	1	(	(	PUNCT
ejpam-4931	885	2	121	121	NUM
ejpam-4931	885	3	)	)	PUNCT
ejpam-4931	885	4	then	then	ADV
ejpam-4931	885	5	,	,	PUNCT
ejpam-4931	885	6	we	we	PRON
ejpam-4931	885	7	conclude	conclude	VERB
ejpam-4931	885	8	that	that	SCONJ
ejpam-4931	885	9	ξk1,r1	ξk1,r1	PROPN
ejpam-4931	885	10	is	be	AUX
ejpam-4931	885	11	bounded	bound	VERB
ejpam-4931	885	12	in	in	ADP
ejpam-4931	885	13	l∞	l∞	PROPN
ejpam-4931	885	14	(	(	PUNCT
ejpam-4931	885	15	[	[	X
ejpam-4931	885	16	0	0	NUM
ejpam-4931	885	17	,	,	PUNCT
ejpam-4931	885	18	t	t	X
ejpam-4931	885	19	]	]	PUNCT
ejpam-4931	885	20	;	;	PUNCT
ejpam-4931	885	21	w	w	PROPN
ejpam-4931	885	22	1	1	NUM
ejpam-4931	885	23	,	,	PUNCT
ejpam-4931	885	24	3	3	NUM
ejpam-4931	885	25	2	2	NUM
ejpam-4931	885	26	(	(	PUNCT
ejpam-4931	885	27	ω	ω	NOUN
ejpam-4931	885	28	)	)	PUNCT
ejpam-4931	885	29	)	)	PUNCT
ejpam-4931	885	30	.	.	PUNCT
ejpam-4931	886	1	now	now	ADV
ejpam-4931	886	2	,	,	PUNCT
ejpam-4931	886	3	we	we	PRON
ejpam-4931	886	4	use	use	VERB
ejpam-4931	886	5	lemma	lemma	PROPN
ejpam-4931	886	6	1	1	NUM
ejpam-4931	886	7	to	to	PART
ejpam-4931	886	8	get	get	VERB
ejpam-4931	886	9	ξk1,r1	ξk1,r1	ADV
ejpam-4931	886	10	−→	−→	NOUN
ejpam-4931	886	11	ξ	ξ	X
ejpam-4931	886	12	strongly	strongly	ADV
ejpam-4931	886	13	in	in	ADP
ejpam-4931	886	14	c	c	PROPN
ejpam-4931	886	15	(	(	PUNCT
ejpam-4931	886	16	[	[	X
ejpam-4931	886	17	0	0	NUM
ejpam-4931	886	18	,	,	PUNCT
ejpam-4931	886	19	t	t	X
ejpam-4931	886	20	]	]	PUNCT
ejpam-4931	886	21	;	;	PUNCT
ejpam-4931	886	22	lp(ω	lp(ω	X
ejpam-4931	886	23	)	)	PUNCT
ejpam-4931	886	24	)	)	PUNCT
ejpam-4931	886	25	,	,	PUNCT
ejpam-4931	886	26	∀1	∀1	VERB
ejpam-4931	886	27	≤	≤	PUNCT
ejpam-4931	887	1	p	p	X
ejpam-4931	887	2	<	<	X
ejpam-4931	887	3	3	3	NUM
ejpam-4931	887	4	.	.	PUNCT
ejpam-4931	887	5	(	(	PUNCT
ejpam-4931	887	6	122	122	NUM
ejpam-4931	887	7	)	)	PUNCT
ejpam-4931	887	8	therefore	therefore	ADV
ejpam-4931	887	9	,	,	PUNCT
ejpam-4931	887	10	we	we	PRON
ejpam-4931	887	11	get	get	VERB
ejpam-4931	887	12	ξk1,r1	ξk1,r1	ADV
ejpam-4931	888	1	−→	−→	ADJ
ejpam-4931	888	2	ξ	ξ	PROPN
ejpam-4931	888	3	a.e	a.e	PROPN
ejpam-4931	888	4	.	.	PROPN
ejpam-4931	888	5	lemma	lemma	PROPN
ejpam-4931	889	1	16	16	NUM
ejpam-4931	889	2	.	.	PUNCT
ejpam-4931	890	1	(	(	PUNCT
ejpam-4931	890	2	convergence	convergence	NOUN
ejpam-4931	890	3	of	of	ADP
ejpam-4931	890	4	the	the	DET
ejpam-4931	890	5	momentum	momentum	NOUN
ejpam-4931	890	6	)	)	PUNCT
ejpam-4931	890	7	.	.	PUNCT
ejpam-4931	891	1	up	up	ADP
ejpam-4931	891	2	to	to	ADP
ejpam-4931	891	3	a	a	DET
ejpam-4931	891	4	subsequence	subsequence	NOUN
ejpam-4931	891	5	,	,	PUNCT
ejpam-4931	891	6	the	the	DET
ejpam-4931	891	7	momentum	momentum	NOUN
ejpam-4931	891	8	mk1,r1	mk1,r1	NOUN
ejpam-4931	891	9	=	=	SYM
ejpam-4931	891	10	ξk1,r1uk1,r1	ξk1,r1uk1,r1	ADJ
ejpam-4931	891	11	satisfies	satisfie	NOUN
ejpam-4931	891	12	mk1,r1	mk1,r1	VERB
ejpam-4931	891	13	−→	−→	ADV
ejpam-4931	891	14	m	m	VERB
ejpam-4931	891	15	strongly	strongly	ADV
ejpam-4931	891	16	in	in	ADP
ejpam-4931	891	17	l2	l2	NOUN
ejpam-4931	891	18	(	(	PUNCT
ejpam-4931	891	19	[	[	X
ejpam-4931	891	20	0	0	NUM
ejpam-4931	891	21	,	,	PUNCT
ejpam-4931	891	22	t	t	X
ejpam-4931	891	23	]	]	PUNCT
ejpam-4931	891	24	;	;	PUNCT
ejpam-4931	891	25	lq(ω	lq(ω	X
ejpam-4931	891	26	)	)	PUNCT
ejpam-4931	891	27	)	)	PUNCT
ejpam-4931	891	28	,	,	PUNCT
ejpam-4931	891	29	∀1	∀1	VERB
ejpam-4931	891	30	≤	≤	PUNCT
ejpam-4931	891	31	q	q	NOUN
ejpam-4931	891	32	<	<	X
ejpam-4931	891	33	3	3	NUM
ejpam-4931	891	34	2	2	NUM
ejpam-4931	891	35	.	.	PUNCT
ejpam-4931	892	1	in	in	ADP
ejpam-4931	892	2	particular	particular	ADJ
ejpam-4931	892	3	,	,	PUNCT
ejpam-4931	892	4	mk1,r1	mk1,r1	VERB
ejpam-4931	892	5	−→	−→	ADJ
ejpam-4931	892	6	m	m	NOUN
ejpam-4931	892	7	for	for	ADP
ejpam-4931	892	8	(	(	PUNCT
ejpam-4931	892	9	t	t	PROPN
ejpam-4931	892	10	,	,	PUNCT
ejpam-4931	892	11	x	x	NOUN
ejpam-4931	892	12	)	)	PUNCT
ejpam-4931	892	13	∈	∈	PROPN
ejpam-4931	893	1	[	[	X
ejpam-4931	893	2	0	0	NUM
ejpam-4931	893	3	,	,	PUNCT
ejpam-4931	893	4	t	t	X
ejpam-4931	893	5	]	]	X
ejpam-4931	893	6	×	×	PROPN
ejpam-4931	893	7	ω	ω	PROPN
ejpam-4931	893	8	.	.	PUNCT
ejpam-4931	894	1	j.	j.	PROPN
ejpam-4931	894	2	ouya	ouya	PROPN
ejpam-4931	894	3	,	,	PUNCT
ejpam-4931	894	4	a.	a.	NOUN
ejpam-4931	894	5	ouédraogo	ouédraogo	PROPN
ejpam-4931	894	6	/	/	SYM
ejpam-4931	894	7	eur	eur	PROPN
ejpam-4931	894	8	.	.	PUNCT
ejpam-4931	895	1	j.	j.	PROPN
ejpam-4931	895	2	pure	pure	PROPN
ejpam-4931	895	3	appl	appl	PROPN
ejpam-4931	895	4	.	.	PROPN
ejpam-4931	895	5	math	math	PROPN
ejpam-4931	895	6	,	,	PUNCT
ejpam-4931	895	7	16	16	NUM
ejpam-4931	895	8	(	(	PUNCT
ejpam-4931	895	9	4	4	NUM
ejpam-4931	895	10	)	)	PUNCT
ejpam-4931	895	11	(	(	PUNCT
ejpam-4931	895	12	2023	2023	NUM
ejpam-4931	895	13	)	)	PUNCT
ejpam-4931	895	14	,	,	PUNCT
ejpam-4931	895	15	2247	2247	NUM
ejpam-4931	895	16	-	-	SYM
ejpam-4931	895	17	2285	2285	NUM
ejpam-4931	895	18	2280	2280	NUM
ejpam-4931	895	19	proof	proof	NOUN
ejpam-4931	895	20	.	.	PUNCT
ejpam-4931	896	1	since	since	SCONJ
ejpam-4931	896	2	∇x(ξk1,r1uk1,r1	∇x(ξk1,r1uk1,r1	PROPN
ejpam-4931	896	3	)	)	PUNCT
ejpam-4931	896	4	=	=	SYM
ejpam-4931	896	5	∇xξk1,r1	∇xξk1,r1	PROPN
ejpam-4931	896	6	⊗	⊗	PROPN
ejpam-4931	896	7	uk1,r1	uk1,r1	PROPN
ejpam-4931	897	1	+	+	CCONJ
ejpam-4931	897	2	ξk1,r1∇xuk1,r1	ξk1,r1∇xuk1,r1	PROPN
ejpam-4931	897	3	=	=	NOUN
ejpam-4931	897	4	2∇x	2∇x	NUM
ejpam-4931	897	5	√	√	PROPN
ejpam-4931	897	6	ξk1,r1	ξk1,r1	PROPN
ejpam-4931	898	1	⊗	⊗	PROPN
ejpam-4931	899	1	√	√	INTJ
ejpam-4931	900	1	ξk1,r1uk1,r1	ξk1,r1uk1,r1	PROPN
ejpam-4931	900	2	+	+	CCONJ
ejpam-4931	900	3	√	√	PROPN
ejpam-4931	900	4	ξk1,r1	ξk1,r1	NUM
ejpam-4931	900	5	√	√	ADP
ejpam-4931	900	6	ξk1,r1∇xuk1,r1	ξk1,r1∇xuk1,r1	PROPN
ejpam-4931	900	7	∈	∈	PROPN
ejpam-4931	900	8	l2	l2	NOUN
ejpam-4931	900	9	(	(	PUNCT
ejpam-4931	900	10	[	[	X
ejpam-4931	900	11	0	0	NUM
ejpam-4931	900	12	,	,	PUNCT
ejpam-4931	900	13	t	t	X
ejpam-4931	900	14	]	]	PUNCT
ejpam-4931	900	15	;	;	PUNCT
ejpam-4931	900	16	l1(ω	l1(ω	X
ejpam-4931	900	17	)	)	PUNCT
ejpam-4931	900	18	)	)	PUNCT
ejpam-4931	900	19	and	and	CCONJ
ejpam-4931	900	20	∂y(ξk1,r1uk1,r1	∂y(ξk1,r1uk1,r1	PROPN
ejpam-4931	900	21	)	)	PUNCT
ejpam-4931	900	22	=	=	PUNCT
ejpam-4931	901	1	√	√	PROPN
ejpam-4931	901	2	ξk1,r1	ξk1,r1	NUM
ejpam-4931	901	3	√	√	VERB
ejpam-4931	901	4	ξk1,r1∂yuk1,r1	ξk1,r1∂yuk1,r1	PROPN
ejpam-4931	901	5	∈	∈	PROPN
ejpam-4931	901	6	l2	l2	NOUN
ejpam-4931	901	7	(	(	PUNCT
ejpam-4931	901	8	[	[	X
ejpam-4931	901	9	0	0	NUM
ejpam-4931	901	10	,	,	PUNCT
ejpam-4931	901	11	t	t	X
ejpam-4931	901	12	]	]	PUNCT
ejpam-4931	901	13	;	;	PUNCT
ejpam-4931	901	14	l	l	NOUN
ejpam-4931	901	15	3	3	NUM
ejpam-4931	901	16	2	2	NUM
ejpam-4931	901	17	(	(	PUNCT
ejpam-4931	901	18	ω	ω	NOUN
ejpam-4931	901	19	)	)	PUNCT
ejpam-4931	901	20	)	)	PUNCT
ejpam-4931	901	21	,	,	PUNCT
ejpam-4931	901	22	we	we	PRON
ejpam-4931	901	23	use	use	VERB
ejpam-4931	901	24	(	(	PUNCT
ejpam-4931	901	25	120	120	NUM
ejpam-4931	901	26	)	)	PUNCT
ejpam-4931	901	27	to	to	PART
ejpam-4931	901	28	deduce	deduce	VERB
ejpam-4931	901	29	that	that	SCONJ
ejpam-4931	901	30	ξk1,r1uk1,r1	ξk1,r1uk1,r1	PROPN
ejpam-4931	901	31	∈	∈	PROPN
ejpam-4931	901	32	l2	l2	NOUN
ejpam-4931	901	33	(	(	PUNCT
ejpam-4931	901	34	[	[	X
ejpam-4931	901	35	0	0	NUM
ejpam-4931	901	36	,	,	PUNCT
ejpam-4931	901	37	t	t	X
ejpam-4931	901	38	]	]	PUNCT
ejpam-4931	901	39	;	;	PUNCT
ejpam-4931	901	40	w	w	PROPN
ejpam-4931	901	41	1,1(ω	1,1(ω	NUM
ejpam-4931	901	42	)	)	PUNCT
ejpam-4931	901	43	)	)	PUNCT
ejpam-4931	901	44	.	.	PUNCT
ejpam-4931	902	1	now	now	ADV
ejpam-4931	902	2	,	,	PUNCT
ejpam-4931	902	3	we	we	PRON
ejpam-4931	902	4	claim	claim	VERB
ejpam-4931	902	5	that	that	SCONJ
ejpam-4931	902	6	∂y(ξk1,r1uk1,r1	∂y(ξk1,r1uk1,r1	PROPN
ejpam-4931	902	7	)	)	PUNCT
ejpam-4931	902	8	is	be	AUX
ejpam-4931	902	9	bounded	bound	VERB
ejpam-4931	902	10	in	in	ADP
ejpam-4931	902	11	l2	l2	NOUN
ejpam-4931	902	12	(	(	PUNCT
ejpam-4931	902	13	[	[	X
ejpam-4931	902	14	0	0	NUM
ejpam-4931	902	15	,	,	PUNCT
ejpam-4931	902	16	t	t	X
ejpam-4931	902	17	]	]	PUNCT
ejpam-4931	902	18	;	;	PUNCT
ejpam-4931	902	19	h−s(ω	h−s(ω	NOUN
ejpam-4931	902	20	)	)	PUNCT
ejpam-4931	902	21	)	)	PUNCT
ejpam-4931	902	22	for	for	ADP
ejpam-4931	902	23	some	some	DET
ejpam-4931	902	24	constant	constant	ADJ
ejpam-4931	902	25	s	s	X
ejpam-4931	902	26	>	>	X
ejpam-4931	902	27	0	0	NUM
ejpam-4931	902	28	.	.	PUNCT
ejpam-4931	903	1	indeed	indeed	ADV
ejpam-4931	903	2	,	,	PUNCT
ejpam-4931	903	3	∂y(ξk1,r1uk1,r1	∂y(ξk1,r1uk1,r1	PROPN
ejpam-4931	903	4	)	)	PUNCT
ejpam-4931	903	5	=	=	PUNCT
ejpam-4931	904	1	2divx	2divx	NUM
ejpam-4931	904	2	(	(	PUNCT
ejpam-4931	904	3	ξk1,r1dx(uk1,r1	ξk1,r1dx(uk1,r1	PROPN
ejpam-4931	904	4	)	)	PUNCT
ejpam-4931	904	5	)	)	PUNCT
ejpam-4931	905	1	+	+	CCONJ
ejpam-4931	905	2	∂y(ξk1,r1∂yuk1,r1	∂y(ξk1,r1∂yuk1,r1	PROPN
ejpam-4931	905	3	)	)	PUNCT
ejpam-4931	906	1	+	+	CCONJ
ejpam-4931	906	2	k1ξk1,r1∇x	k1ξk1,r1∇x	PROPN
ejpam-4931	906	3	(	(	PUNCT
ejpam-4931	906	4	∆x	∆x	PROPN
ejpam-4931	906	5	√	√	PROPN
ejpam-4931	906	6	ξk1,r1√	ξk1,r1√	PROPN
ejpam-4931	906	7	ξk1,r1	ξk1,r1	ADJ
ejpam-4931	906	8	)	)	PUNCT
ejpam-4931	907	1	+	+	CCONJ
ejpam-4931	908	1	δξk1,r1∇x∆	δξk1,r1∇x∆	X
ejpam-4931	908	2	5	5	NUM
ejpam-4931	908	3	xξk1,r1	xξk1,r1	PROPN
ejpam-4931	908	4	−	−	PROPN
ejpam-4931	909	1	divx(ξk1,r1uk1,r1	divx(ξk1,r1uk1,r1	PROPN
ejpam-4931	910	1	⊗	⊗	PROPN
ejpam-4931	910	2	uk1,r1	uk1,r1	PROPN
ejpam-4931	910	3	)	)	PUNCT
ejpam-4931	911	1	−	−	PROPN
ejpam-4931	912	1	∂y(ξk1,r1uk1,r1vk1,r1)−∇xξ	∂y(ξk1,r1uk1,r1vk1,r1)−∇xξ	PROPN
ejpam-4931	912	2	2	2	NUM
ejpam-4931	913	1	k1,r1	k1,r1	PROPN
ejpam-4931	913	2	−	−	PROPN
ejpam-4931	913	3	r1uk1,r1	r1uk1,r1	NUM
ejpam-4931	913	4	−	−	PROPN
ejpam-4931	913	5	rξk1,r1uk1,r1	rξk1,r1uk1,r1	PROPN
ejpam-4931	913	6	|uk1,r1	|uk1,r1	NOUN
ejpam-4931	913	7	|	|	ADV
ejpam-4931	913	8	.	.	PUNCT
ejpam-4931	914	1	(	(	PUNCT
ejpam-4931	914	2	123	123	NUM
ejpam-4931	914	3	)	)	PUNCT
ejpam-4931	914	4	with	with	ADP
ejpam-4931	914	5	the	the	DET
ejpam-4931	914	6	estimates	estimate	NOUN
ejpam-4931	914	7	of	of	ADP
ejpam-4931	914	8	(	(	PUNCT
ejpam-4931	914	9	118	118	NUM
ejpam-4931	914	10	)	)	PUNCT
ejpam-4931	914	11	,	,	PUNCT
ejpam-4931	914	12	we	we	PRON
ejpam-4931	914	13	deduce	deduce	VERB
ejpam-4931	914	14	that	that	SCONJ
ejpam-4931	914	15	ξk1,r1uk1,r1	ξk1,r1uk1,r1	PROPN
ejpam-4931	914	16	⊗	⊗	PROPN
ejpam-4931	914	17	uk1,r1	uk1,r1	PROPN
ejpam-4931	915	1	∈	∈	PROPN
ejpam-4931	915	2	l∞	l∞	PROPN
ejpam-4931	915	3	(	(	PUNCT
ejpam-4931	915	4	[	[	X
ejpam-4931	915	5	0	0	NUM
ejpam-4931	915	6	,	,	PUNCT
ejpam-4931	915	7	t	t	X
ejpam-4931	915	8	]	]	PUNCT
ejpam-4931	915	9	;	;	PUNCT
ejpam-4931	915	10	l1(ω	l1(ω	X
ejpam-4931	915	11	)	)	PUNCT
ejpam-4931	915	12	)	)	PUNCT
ejpam-4931	915	13	,	,	PUNCT
ejpam-4931	915	14	ξk1,r1uk1,r1vk1,r1	ξk1,r1uk1,r1vk1,r1	PROPN
ejpam-4931	915	15	∈	∈	NOUN
ejpam-4931	915	16	l2	l2	NOUN
ejpam-4931	915	17	(	(	PUNCT
ejpam-4931	915	18	[	[	X
ejpam-4931	915	19	0	0	NUM
ejpam-4931	915	20	,	,	PUNCT
ejpam-4931	915	21	t	t	X
ejpam-4931	915	22	]	]	PUNCT
ejpam-4931	915	23	;	;	PUNCT
ejpam-4931	915	24	l1(ω	l1(ω	X
ejpam-4931	915	25	)	)	PUNCT
ejpam-4931	915	26	)	)	PUNCT
ejpam-4931	915	27	and	and	CCONJ
ejpam-4931	915	28	ξk1,r1∂yuk1,r1	ξk1,r1∂yuk1,r1	PROPN
ejpam-4931	915	29	∈	∈	PROPN
ejpam-4931	915	30	l2	l2	NOUN
ejpam-4931	915	31	(	(	PUNCT
ejpam-4931	916	1	[	[	X
ejpam-4931	916	2	0	0	NUM
ejpam-4931	916	3	,	,	PUNCT
ejpam-4931	916	4	t	t	X
ejpam-4931	916	5	]	]	PUNCT
ejpam-4931	916	6	;	;	PUNCT
ejpam-4931	916	7	l	l	NOUN
ejpam-4931	916	8	3	3	NUM
ejpam-4931	916	9	2	2	NUM
ejpam-4931	916	10	(	(	PUNCT
ejpam-4931	916	11	ω	ω	NOUN
ejpam-4931	916	12	)	)	PUNCT
ejpam-4931	916	13	)	)	PUNCT
ejpam-4931	916	14	,	,	PUNCT
ejpam-4931	916	15	ξk1,r1dx(uk1,r1	ξk1,r1dx(uk1,r1	PROPN
ejpam-4931	916	16	)	)	PUNCT
ejpam-4931	916	17	∈	∈	NOUN
ejpam-4931	916	18	l2	l2	NOUN
ejpam-4931	916	19	(	(	PUNCT
ejpam-4931	916	20	[	[	X
ejpam-4931	916	21	0	0	NUM
ejpam-4931	916	22	,	,	PUNCT
ejpam-4931	916	23	t	t	X
ejpam-4931	916	24	]	]	PUNCT
ejpam-4931	916	25	;	;	PUNCT
ejpam-4931	916	26	l	l	NOUN
ejpam-4931	916	27	3	3	NUM
ejpam-4931	916	28	2	2	NUM
ejpam-4931	916	29	(	(	PUNCT
ejpam-4931	916	30	ω	ω	NOUN
ejpam-4931	916	31	)	)	PUNCT
ejpam-4931	916	32	)	)	PUNCT
ejpam-4931	916	33	.	.	PUNCT
ejpam-4931	917	1	in	in	ADP
ejpam-4931	917	2	particular	particular	ADJ
ejpam-4931	917	3	,	,	PUNCT
ejpam-4931	917	4	thanks	thank	NOUN
ejpam-4931	917	5	to	to	ADP
ejpam-4931	917	6	the	the	DET
ejpam-4931	917	7	sobolev	sobolev	PROPN
ejpam-4931	917	8	injection	injection	NOUN
ejpam-4931	917	9	theorem	theorem	NOUN
ejpam-4931	917	10	,	,	PUNCT
ejpam-4931	917	11	we	we	PRON
ejpam-4931	917	12	have	have	PROPN
ejpam-4931	917	13	divx(ξk1,r1uk1,r1	divx(ξk1,r1uk1,r1	PROPN
ejpam-4931	917	14	⊗	⊗	PROPN
ejpam-4931	917	15	uk1,r1	uk1,r1	PROPN
ejpam-4931	917	16	)	)	PUNCT
ejpam-4931	917	17	∈	∈	PROPN
ejpam-4931	917	18	l∞	l∞	NOUN
ejpam-4931	917	19	(	(	PUNCT
ejpam-4931	917	20	[	[	X
ejpam-4931	917	21	0	0	NUM
ejpam-4931	917	22	,	,	PUNCT
ejpam-4931	917	23	t	t	X
ejpam-4931	917	24	]	]	PUNCT
ejpam-4931	917	25	;	;	PUNCT
ejpam-4931	917	26	w−2,2(ω	w−2,2(ω	ADV
ejpam-4931	917	27	)	)	PUNCT
ejpam-4931	917	28	)	)	PUNCT
ejpam-4931	917	29	,	,	PUNCT
ejpam-4931	917	30	∂y(ξk1,r1uk1,r1vk1,r1	∂y(ξk1,r1uk1,r1vk1,r1	PROPN
ejpam-4931	917	31	)	)	PUNCT
ejpam-4931	917	32	∈	∈	NOUN
ejpam-4931	917	33	l2	l2	NOUN
ejpam-4931	917	34	(	(	PUNCT
ejpam-4931	917	35	[	[	X
ejpam-4931	917	36	0	0	NUM
ejpam-4931	917	37	,	,	PUNCT
ejpam-4931	917	38	t	t	X
ejpam-4931	917	39	]	]	PUNCT
ejpam-4931	917	40	;	;	PUNCT
ejpam-4931	917	41	w−2,2(ω	w−2,2(ω	ADV
ejpam-4931	917	42	)	)	PUNCT
ejpam-4931	917	43	)	)	PUNCT
ejpam-4931	917	44	,	,	PUNCT
ejpam-4931	917	45	∂y(ξk1,r1∂yuk1,r1	∂y(ξk1,r1∂yuk1,r1	PROPN
ejpam-4931	917	46	)	)	PUNCT
ejpam-4931	917	47	∈	∈	PROPN
ejpam-4931	917	48	l2	l2	NOUN
ejpam-4931	917	49	(	(	PUNCT
ejpam-4931	917	50	[	[	X
ejpam-4931	917	51	0	0	NUM
ejpam-4931	917	52	,	,	PUNCT
ejpam-4931	917	53	t	t	X
ejpam-4931	917	54	]	]	PUNCT
ejpam-4931	917	55	;	;	PUNCT
ejpam-4931	917	56	w−2,2(ω	w−2,2(ω	ADV
ejpam-4931	917	57	)	)	PUNCT
ejpam-4931	917	58	)	)	PUNCT
ejpam-4931	917	59	,	,	PUNCT
ejpam-4931	917	60	divx(ξk1,r1dx(uk1,r1	divx(ξk1,r1dx(uk1,r1	PROPN
ejpam-4931	917	61	)	)	PUNCT
ejpam-4931	917	62	)	)	PUNCT
ejpam-4931	917	63	∈	∈	NOUN
ejpam-4931	917	64	l2	l2	NOUN
ejpam-4931	917	65	(	(	PUNCT
ejpam-4931	917	66	[	[	X
ejpam-4931	917	67	0	0	NUM
ejpam-4931	917	68	,	,	PUNCT
ejpam-4931	917	69	t	t	X
ejpam-4931	917	70	]	]	PUNCT
ejpam-4931	917	71	;	;	PUNCT
ejpam-4931	917	72	w−2,2(ω	w−2,2(ω	ADV
ejpam-4931	917	73	)	)	PUNCT
ejpam-4931	917	74	)	)	PUNCT
ejpam-4931	917	75	,	,	PUNCT
ejpam-4931	917	76	k1ξk1,r1∇x	k1ξk1,r1∇x	PROPN
ejpam-4931	917	77	(	(	PUNCT
ejpam-4931	917	78	∆x	∆x	PROPN
ejpam-4931	917	79	√	√	PROPN
ejpam-4931	917	80	ξk1,r1√	ξk1,r1√	PROPN
ejpam-4931	917	81	ξk1,r1	ξk1,r1	ADJ
ejpam-4931	917	82	)	)	PUNCT
ejpam-4931	918	1	=	=	SYM
ejpam-4931	918	2	k1∇x	k1∇x	PROPN
ejpam-4931	918	3	(	(	PUNCT
ejpam-4931	918	4	√	√	ADP
ejpam-4931	918	5	ξk1,r1∆x	ξk1,r1∆x	PROPN
ejpam-4931	918	6	√	√	NUM
ejpam-4931	918	7	ξk1,r1)−	ξk1,r1)−	NOUN
ejpam-4931	918	8	2k1∆x	2k1∆x	NUM
ejpam-4931	918	9	√	√	PROPN
ejpam-4931	919	1	ξk1,r1∇x	ξk1,r1∇x	NOUN
ejpam-4931	919	2	√	√	NUM
ejpam-4931	919	3	ξk1,r1	ξk1,r1	CCONJ
ejpam-4931	919	4	∈	∈	PROPN
ejpam-4931	919	5	l2	l2	NOUN
ejpam-4931	919	6	(	(	PUNCT
ejpam-4931	919	7	[	[	X
ejpam-4931	919	8	0	0	NUM
ejpam-4931	919	9	,	,	PUNCT
ejpam-4931	919	10	t	t	X
ejpam-4931	919	11	]	]	PUNCT
ejpam-4931	919	12	;	;	PUNCT
ejpam-4931	919	13	w−3,2(ω	w−3,2(ω	X
ejpam-4931	919	14	)	)	PUNCT
ejpam-4931	919	15	)	)	PUNCT
ejpam-4931	919	16	.	.	PUNCT
ejpam-4931	920	1	then	then	ADV
ejpam-4931	920	2	,	,	PUNCT
ejpam-4931	920	3	we	we	PRON
ejpam-4931	920	4	obtain	obtain	VERB
ejpam-4931	920	5	the	the	DET
ejpam-4931	920	6	boundedness	boundedness	NOUN
ejpam-4931	920	7	of	of	ADP
ejpam-4931	920	8	∂t(ξk1,r1uk1,r1	∂t(ξk1,r1uk1,r1	PROPN
ejpam-4931	920	9	)	)	PUNCT
ejpam-4931	920	10	in	in	ADP
ejpam-4931	920	11	l	l	NOUN
ejpam-4931	920	12	2	2	NUM
ejpam-4931	920	13	(	(	PUNCT
ejpam-4931	920	14	[	[	X
ejpam-4931	920	15	0	0	NUM
ejpam-4931	920	16	,	,	PUNCT
ejpam-4931	920	17	t	t	X
ejpam-4931	920	18	]	]	PUNCT
ejpam-4931	920	19	;	;	PUNCT
ejpam-4931	920	20	h−5(ω	h−5(ω	PROPN
ejpam-4931	920	21	)	)	PUNCT
ejpam-4931	920	22	)	)	PUNCT
ejpam-4931	920	23	.	.	PUNCT
ejpam-4931	921	1	therefore	therefore	ADV
ejpam-4931	921	2	,	,	PUNCT
ejpam-4931	921	3	we	we	PRON
ejpam-4931	921	4	use	use	VERB
ejpam-4931	921	5	lemma	lemma	PROPN
ejpam-4931	921	6	1	1	NUM
ejpam-4931	921	7	to	to	PART
ejpam-4931	921	8	conclude	conclude	VERB
ejpam-4931	921	9	the	the	DET
ejpam-4931	921	10	proof	proof	NOUN
ejpam-4931	921	11	of	of	ADP
ejpam-4931	921	12	lemma	lemma	PROPN
ejpam-4931	921	13	16	16	NUM
ejpam-4931	921	14	.	.	PUNCT
ejpam-4931	922	1	remark	remark	PROPN
ejpam-4931	922	2	1	1	NUM
ejpam-4931	922	3	.	.	PUNCT
ejpam-4931	923	1	we	we	PRON
ejpam-4931	923	2	can	can	AUX
ejpam-4931	923	3	define	define	VERB
ejpam-4931	923	4	u(t	u(t	NOUN
ejpam-4931	923	5	,	,	PUNCT
ejpam-4931	923	6	x	x	NOUN
ejpam-4931	923	7	,	,	PUNCT
ejpam-4931	923	8	y	y	NOUN
ejpam-4931	923	9	)	)	PUNCT
ejpam-4931	923	10	=	=	SYM
ejpam-4931	923	11	m(t	m(t	NOUN
ejpam-4931	923	12	,	,	PUNCT
ejpam-4931	923	13	x	x	X
ejpam-4931	923	14	,	,	PUNCT
ejpam-4931	923	15	y	y	NOUN
ejpam-4931	923	16	)	)	PUNCT
ejpam-4931	923	17	ξ(t	ξ(t	NOUN
ejpam-4931	923	18	,	,	PUNCT
ejpam-4931	923	19	x	x	NOUN
ejpam-4931	923	20	,	,	PUNCT
ejpam-4931	923	21	y	y	PROPN
ejpam-4931	923	22	)	)	PUNCT
ejpam-4931	923	23	outside	outside	ADP
ejpam-4931	923	24	the	the	DET
ejpam-4931	923	25	vacuum	vacuum	NOUN
ejpam-4931	923	26	set	set	PROPN
ejpam-4931	923	27	{	{	PUNCT
ejpam-4931	923	28	x|ξ(t	x|ξ(t	PROPN
ejpam-4931	923	29	,	,	PUNCT
ejpam-4931	923	30	x	x	NOUN
ejpam-4931	923	31	)	)	PUNCT
ejpam-4931	923	32	=	=	SYM
ejpam-4931	923	33	0	0	NUM
ejpam-4931	923	34	}	}	PUNCT
ejpam-4931	923	35	.	.	PUNCT
ejpam-4931	924	1	then	then	ADV
ejpam-4931	924	2	,	,	PUNCT
ejpam-4931	924	3	we	we	PRON
ejpam-4931	924	4	obtain	obtain	VERB
ejpam-4931	924	5	ξk1,r1uk1,r1	ξk1,r1uk1,r1	PROPN
ejpam-4931	924	6	−→	−→	NOUN
ejpam-4931	924	7	ξu	ξu	X
ejpam-4931	924	8	strongly	strongly	ADV
ejpam-4931	924	9	in	in	ADP
ejpam-4931	924	10	l2	l2	NOUN
ejpam-4931	924	11	(	(	PUNCT
ejpam-4931	924	12	[	[	X
ejpam-4931	924	13	0	0	NUM
ejpam-4931	924	14	,	,	PUNCT
ejpam-4931	924	15	t	t	X
ejpam-4931	924	16	]	]	PUNCT
ejpam-4931	924	17	;	;	PUNCT
ejpam-4931	924	18	lq(ω	lq(ω	X
ejpam-4931	924	19	)	)	PUNCT
ejpam-4931	924	20	)	)	PUNCT
ejpam-4931	924	21	,	,	PUNCT
ejpam-4931	924	22	∀1	∀1	VERB
ejpam-4931	924	23	≤	≤	PUNCT
ejpam-4931	924	24	q	q	NOUN
ejpam-4931	924	25	<	<	X
ejpam-4931	924	26	1.5	1.5	NUM
ejpam-4931	924	27	.	.	PUNCT
ejpam-4931	925	1	j.	j.	PROPN
ejpam-4931	925	2	ouya	ouya	PROPN
ejpam-4931	925	3	,	,	PUNCT
ejpam-4931	925	4	a.	a.	NOUN
ejpam-4931	925	5	ouédraogo	ouédraogo	PROPN
ejpam-4931	925	6	/	/	SYM
ejpam-4931	925	7	eur	eur	PROPN
ejpam-4931	925	8	.	.	PUNCT
ejpam-4931	926	1	j.	j.	PROPN
ejpam-4931	926	2	pure	pure	PROPN
ejpam-4931	926	3	appl	appl	PROPN
ejpam-4931	926	4	.	.	PROPN
ejpam-4931	926	5	math	math	PROPN
ejpam-4931	926	6	,	,	PUNCT
ejpam-4931	926	7	16	16	NUM
ejpam-4931	926	8	(	(	PUNCT
ejpam-4931	926	9	4	4	NUM
ejpam-4931	926	10	)	)	PUNCT
ejpam-4931	926	11	(	(	PUNCT
ejpam-4931	926	12	2023	2023	NUM
ejpam-4931	926	13	)	)	PUNCT
ejpam-4931	926	14	,	,	PUNCT
ejpam-4931	926	15	2247	2247	NUM
ejpam-4931	926	16	-	-	SYM
ejpam-4931	926	17	2285	2285	NUM
ejpam-4931	926	18	2281	2281	NUM
ejpam-4931	926	19	with	with	ADP
ejpam-4931	926	20	lemmas	lemmas	PROPN
ejpam-4931	926	21	14	14	NUM
ejpam-4931	926	22	and	and	CCONJ
ejpam-4931	926	23	16	16	NUM
ejpam-4931	926	24	,	,	PUNCT
ejpam-4931	926	25	in	in	ADP
ejpam-4931	926	26	a	a	DET
ejpam-4931	926	27	similar	similar	ADJ
ejpam-4931	926	28	way	way	NOUN
ejpam-4931	926	29	to	to	ADP
ejpam-4931	926	30	the	the	DET
ejpam-4931	926	31	proof	proof	NOUN
ejpam-4931	926	32	of	of	ADP
ejpam-4931	926	33	lemma	lemma	PROPN
ejpam-4931	926	34	8	8	NUM
ejpam-4931	926	35	,	,	PUNCT
ejpam-4931	926	36	we	we	PRON
ejpam-4931	926	37	can	can	AUX
ejpam-4931	926	38	deduce	deduce	VERB
ejpam-4931	926	39	that	that	SCONJ
ejpam-4931	926	40	when	when	SCONJ
ejpam-4931	926	41	k1	k1	NOUN
ejpam-4931	926	42	,	,	PUNCT
ejpam-4931	926	43	r1	r1	NOUN
ejpam-4931	926	44	−→	−→	NOUN
ejpam-4931	926	45	0,√	0,√	PUNCT
ejpam-4931	927	1	ξk1,r1uk1,r1	ξk1,r1uk1,r1	ADJ
ejpam-4931	927	2	−→	−→	NOUN
ejpam-4931	927	3	√	√	NUM
ejpam-4931	927	4	ξu	ξu	VERB
ejpam-4931	927	5	strongly	strongly	ADV
ejpam-4931	927	6	in	in	ADP
ejpam-4931	927	7	l2	l2	NOUN
ejpam-4931	927	8	(	(	PUNCT
ejpam-4931	927	9	[	[	X
ejpam-4931	927	10	0	0	NUM
ejpam-4931	927	11	,	,	PUNCT
ejpam-4931	927	12	t	t	X
ejpam-4931	927	13	]	]	PUNCT
ejpam-4931	927	14	;	;	PUNCT
ejpam-4931	927	15	l2(ω	l2(ω	NUM
ejpam-4931	927	16	)	)	PUNCT
ejpam-4931	927	17	)	)	PUNCT
ejpam-4931	927	18	.	.	PUNCT
ejpam-4931	928	1	(	(	PUNCT
ejpam-4931	928	2	124	124	NUM
ejpam-4931	928	3	)	)	PUNCT
ejpam-4931	928	4	lemma	lemma	PROPN
ejpam-4931	928	5	17	17	NUM
ejpam-4931	928	6	.	.	PUNCT
ejpam-4931	929	1	(	(	PUNCT
ejpam-4931	929	2	convergence	convergence	NOUN
ejpam-4931	929	3	of	of	ADP
ejpam-4931	929	4	terms	term	NOUN
ejpam-4931	929	5	divx(ξk1,r1dx(uk1,r1	divx(ξk1,r1dx(uk1,r1	PROPN
ejpam-4931	929	6	)	)	PUNCT
ejpam-4931	929	7	)	)	PUNCT
ejpam-4931	929	8	,	,	PUNCT
ejpam-4931	929	9	k1ξk1,r1∇x	k1ξk1,r1∇x	PROPN
ejpam-4931	929	10	(	(	PUNCT
ejpam-4931	929	11	∆x	∆x	PROPN
ejpam-4931	929	12	√	√	PROPN
ejpam-4931	929	13	ξk1,r1√	ξk1,r1√	PROPN
ejpam-4931	929	14	ξk1,r1	ξk1,r1	ADJ
ejpam-4931	929	15	)	)	PUNCT
ejpam-4931	929	16	and	and	CCONJ
ejpam-4931	929	17	r1uk1,r1	r1uk1,r1	NOUN
ejpam-4931	929	18	)	)	PUNCT
ejpam-4931	929	19	.	.	PUNCT
ejpam-4931	930	1	for	for	ADP
ejpam-4931	930	2	any	any	DET
ejpam-4931	930	3	test	test	NOUN
ejpam-4931	930	4	function	function	NOUN
ejpam-4931	930	5	φ	φ	PROPN
ejpam-4931	930	6	∈	∈	PROPN
ejpam-4931	930	7	c∞	c∞	PROPN
ejpam-4931	930	8	c	c	NOUN
ejpam-4931	930	9	(	(	PUNCT
ejpam-4931	930	10	[	[	X
ejpam-4931	930	11	0	0	NUM
ejpam-4931	930	12	,	,	PUNCT
ejpam-4931	930	13	t	t	X
ejpam-4931	930	14	]	]	PUNCT
ejpam-4931	930	15	;	;	PUNCT
ejpam-4931	930	16	ω	ω	X
ejpam-4931	930	17	)	)	PUNCT
ejpam-4931	930	18	,	,	PUNCT
ejpam-4931	930	19	we	we	PRON
ejpam-4931	930	20	have	have	VERB
ejpam-4931	930	21	r1	r1	PROPN
ejpam-4931	930	22	∫	∫	PROPN
ejpam-4931	930	23	t	t	PROPN
ejpam-4931	930	24	0	0	NUM
ejpam-4931	931	1	∫	∫	PROPN
ejpam-4931	931	2	ω	ω	PROPN
ejpam-4931	931	3	uk1,r1φdxdydt	uk1,r1φdxdydt	NOUN
ejpam-4931	931	4	−→	−→	NOUN
ejpam-4931	931	5	0	0	PUNCT
ejpam-4931	931	6	as	as	ADP
ejpam-4931	931	7	r1	r1	PROPN
ejpam-4931	931	8	−→	−→	NOUN
ejpam-4931	931	9	0	0	NUM
ejpam-4931	931	10	,	,	PUNCT
ejpam-4931	931	11	(	(	PUNCT
ejpam-4931	931	12	125)∫	125)∫	PROPN
ejpam-4931	931	13	t	t	NOUN
ejpam-4931	931	14	0	0	NUM
ejpam-4931	931	15	∫	∫	PROPN
ejpam-4931	932	1	ω	ω	NUM
ejpam-4931	932	2	divx(ξk1,r1dx(uk1,r1))φdxdydt	divx(ξk1,r1dx(uk1,r1))φdxdydt	PROPN
ejpam-4931	932	3	−→	−→	PROPN
ejpam-4931	932	4	∫	∫	PROPN
ejpam-4931	932	5	t	t	PROPN
ejpam-4931	932	6	0	0	NUM
ejpam-4931	932	7	∫	∫	PROPN
ejpam-4931	933	1	ω	ω	PROPN
ejpam-4931	933	2	divx(ξdx(u))φdxdydt	divx(ξdx(u))φdxdydt	PROPN
ejpam-4931	933	3	as	as	ADP
ejpam-4931	933	4	r1	r1	NOUN
ejpam-4931	933	5	,	,	PUNCT
ejpam-4931	933	6	k1	k1	ADJ
ejpam-4931	933	7	−→	−→	NOUN
ejpam-4931	933	8	0,(126	0,(126	NOUN
ejpam-4931	933	9	)	)	PUNCT
ejpam-4931	933	10	k1	k1	PROPN
ejpam-4931	933	11	∫	∫	PROPN
ejpam-4931	933	12	t	t	PROPN
ejpam-4931	933	13	0	0	NUM
ejpam-4931	933	14	∫	∫	PROPN
ejpam-4931	934	1	ω	ω	NUM
ejpam-4931	934	2	ξk1,r1∇x	ξk1,r1∇x	PROPN
ejpam-4931	934	3	(	(	PUNCT
ejpam-4931	934	4	∆x	∆x	PROPN
ejpam-4931	934	5	√	√	PROPN
ejpam-4931	934	6	ξk1,r1√	ξk1,r1√	PROPN
ejpam-4931	934	7	ξk1,r1	ξk1,r1	ADJ
ejpam-4931	934	8	)	)	PUNCT
ejpam-4931	935	1	φdxdydt	φdxdydt	ADV
ejpam-4931	935	2	−→	−→	NOUN
ejpam-4931	935	3	0	0	NUM
ejpam-4931	935	4	as	as	ADP
ejpam-4931	935	5	k1	k1	NOUN
ejpam-4931	935	6	−→	−→	NOUN
ejpam-4931	935	7	0	0	NUM
ejpam-4931	935	8	.	.	PUNCT
ejpam-4931	936	1	(	(	PUNCT
ejpam-4931	936	2	127	127	NUM
ejpam-4931	936	3	)	)	PUNCT
ejpam-4931	936	4	proof	proof	NOUN
ejpam-4931	936	5	.	.	PUNCT
ejpam-4931	937	1	we	we	PRON
ejpam-4931	937	2	take	take	VERB
ejpam-4931	937	3	φ	φ	PROPN
ejpam-4931	937	4	∈	∈	PROPN
ejpam-4931	937	5	c∞	c∞	PROPN
ejpam-4931	937	6	c	c	NOUN
ejpam-4931	937	7	(	(	PUNCT
ejpam-4931	937	8	[	[	X
ejpam-4931	937	9	0	0	NUM
ejpam-4931	937	10	,	,	PUNCT
ejpam-4931	937	11	t	t	X
ejpam-4931	937	12	]	]	PUNCT
ejpam-4931	937	13	;	;	PUNCT
ejpam-4931	937	14	ω	ω	X
ejpam-4931	937	15	)	)	PUNCT
ejpam-4931	937	16	as	as	ADP
ejpam-4931	937	17	a	a	DET
ejpam-4931	937	18	test	test	NOUN
ejpam-4931	937	19	function	function	NOUN
ejpam-4931	937	20	.	.	PUNCT
ejpam-4931	938	1	firstly	firstly	ADV
ejpam-4931	938	2	,	,	PUNCT
ejpam-4931	938	3	we	we	PRON
ejpam-4931	938	4	prove	prove	VERB
ejpam-4931	938	5	(	(	PUNCT
ejpam-4931	938	6	125	125	NUM
ejpam-4931	938	7	)	)	PUNCT
ejpam-4931	938	8	.	.	PUNCT
ejpam-4931	939	1	using	use	VERB
ejpam-4931	939	2	hölder	hölder	PROPN
ejpam-4931	939	3	’s	’s	PART
ejpam-4931	939	4	inequality	inequality	NOUN
ejpam-4931	939	5	,	,	PUNCT
ejpam-4931	939	6	we	we	PRON
ejpam-4931	939	7	get	get	VERB
ejpam-4931	940	1	r1	r1	PROPN
ejpam-4931	940	2	∫	∫	PROPN
ejpam-4931	940	3	t	t	PROPN
ejpam-4931	940	4	0	0	NUM
ejpam-4931	940	5	∫	∫	PROPN
ejpam-4931	940	6	ω	ω	PROPN
ejpam-4931	940	7	uk1,r1φdxdydt	uk1,r1φdxdydt	PROPN
ejpam-4931	940	8	≤	≤	PROPN
ejpam-4931	940	9	√	√	NUM
ejpam-4931	940	10	r1∥	r1∥	NOUN
ejpam-4931	940	11	√	√	VERB
ejpam-4931	940	12	r1uk1,r1∥l2	r1uk1,r1∥l2	NOUN
ejpam-4931	940	13	(	(	PUNCT
ejpam-4931	940	14	[	[	X
ejpam-4931	940	15	0,t	0,t	X
ejpam-4931	940	16	]	]	X
ejpam-4931	940	17	;	;	PUNCT
ejpam-4931	940	18	l2(ω	l2(ω	NUM
ejpam-4931	940	19	)	)	PUNCT
ejpam-4931	940	20	)	)	PUNCT
ejpam-4931	940	21	∥φ∥	∥φ∥	NOUN
ejpam-4931	940	22	l2	l2	NOUN
ejpam-4931	940	23	(	(	PUNCT
ejpam-4931	940	24	[	[	X
ejpam-4931	940	25	0,t	0,t	X
ejpam-4931	940	26	]	]	X
ejpam-4931	940	27	;	;	PUNCT
ejpam-4931	940	28	l2(ω	l2(ω	NUM
ejpam-4931	940	29	)	)	PUNCT
ejpam-4931	940	30	)	)	PUNCT
ejpam-4931	941	1	−→	−→	ADV
ejpam-4931	941	2	r1→0	r1→0	NOUN
ejpam-4931	941	3	0	0	NUM
ejpam-4931	941	4	.	.	PUNCT
ejpam-4931	942	1	secondly	secondly	ADV
ejpam-4931	942	2	,	,	PUNCT
ejpam-4931	942	3	we	we	PRON
ejpam-4931	942	4	deal	deal	VERB
ejpam-4931	942	5	with	with	ADP
ejpam-4931	942	6	(	(	PUNCT
ejpam-4931	942	7	126	126	NUM
ejpam-4931	942	8	)	)	PUNCT
ejpam-4931	942	9	.	.	PUNCT
ejpam-4931	943	1	recalling	recall	VERB
ejpam-4931	943	2	(	(	PUNCT
ejpam-4931	943	3	57	57	NUM
ejpam-4931	943	4	)	)	PUNCT
ejpam-4931	943	5	,	,	PUNCT
ejpam-4931	943	6	we	we	PRON
ejpam-4931	943	7	have∫	have∫	VERB
ejpam-4931	943	8	t	t	PROPN
ejpam-4931	943	9	0	0	NUM
ejpam-4931	943	10	∫	∫	PROPN
ejpam-4931	944	1	ω	ω	NUM
ejpam-4931	944	2	divx(ξk1,r1dx(uk1,r1))φdxdydt	divx(ξk1,r1dx(uk1,r1))φdxdydt	PROPN
ejpam-4931	944	3	=	=	SYM
ejpam-4931	944	4	1	1	NUM
ejpam-4931	944	5	2	2	NUM
ejpam-4931	944	6	∫	∫	NOUN
ejpam-4931	944	7	t	t	PROPN
ejpam-4931	944	8	0	0	NUM
ejpam-4931	944	9	∫	∫	PROPN
ejpam-4931	944	10	ω	ω	PROPN
ejpam-4931	944	11	(	(	PUNCT
ejpam-4931	944	12	ξk1,r1uk1,r1	ξk1,r1uk1,r1	PROPN
ejpam-4931	944	13	·	·	PUNCT
ejpam-4931	944	14	∆xφ+	∆xφ+	NOUN
ejpam-4931	944	15	2∇xφ	2∇xφ	NOUN
ejpam-4931	944	16	·	·	PUNCT
ejpam-4931	944	17	∇x	∇x	NOUN
ejpam-4931	944	18	√	√	NUM
ejpam-4931	944	19	ξk1,r1	ξk1,r1	NUM
ejpam-4931	944	20	·	·	PUNCT
ejpam-4931	944	21	√	√	NUM
ejpam-4931	944	22	ξk1,r1uk1,r1	ξk1,r1uk1,r1	ADJ
ejpam-4931	944	23	)	)	PUNCT
ejpam-4931	944	24	dxdydt	dxdydt	NOUN
ejpam-4931	944	25	+	+	CCONJ
ejpam-4931	944	26	1	1	NUM
ejpam-4931	944	27	2	2	NUM
ejpam-4931	944	28	∫	∫	NOUN
ejpam-4931	944	29	t	t	PROPN
ejpam-4931	944	30	0	0	NUM
ejpam-4931	944	31	∫	∫	PROPN
ejpam-4931	945	1	ω	ω	PROPN
ejpam-4931	945	2	(	(	PUNCT
ejpam-4931	945	3	ξk1,r1uk1,r1	ξk1,r1uk1,r1	PROPN
ejpam-4931	945	4	·	·	PUNCT
ejpam-4931	945	5	divx(∇t	divx(∇t	ADP
ejpam-4931	946	1	xφ	xφ	NOUN
ejpam-4931	946	2	)	)	PUNCT
ejpam-4931	947	1	+	+	CCONJ
ejpam-4931	947	2	2∇t	2∇t	NUM
ejpam-4931	947	3	xφ	xφ	NUM
ejpam-4931	947	4	·	·	PUNCT
ejpam-4931	947	5	∇x	∇x	NOUN
ejpam-4931	947	6	√	√	NUM
ejpam-4931	947	7	ξk1,r1	ξk1,r1	NUM
ejpam-4931	947	8	·	·	PUNCT
ejpam-4931	947	9	√	√	NUM
ejpam-4931	947	10	ξk1,r1uk1,r1	ξk1,r1uk1,r1	ADJ
ejpam-4931	947	11	)	)	PUNCT
ejpam-4931	947	12	dxdydt	dxdydt	NOUN
ejpam-4931	947	13	.	.	PUNCT
ejpam-4931	948	1	since	since	SCONJ
ejpam-4931	948	2	∇x	∇x	NOUN
ejpam-4931	948	3	√	√	NUM
ejpam-4931	948	4	ξk1,r1	ξk1,r1	NUM
ejpam-4931	948	5	∈	∈	PROPN
ejpam-4931	948	6	l∞	l∞	NOUN
ejpam-4931	948	7	(	(	PUNCT
ejpam-4931	948	8	[	[	X
ejpam-4931	948	9	0	0	NUM
ejpam-4931	948	10	,	,	PUNCT
ejpam-4931	948	11	t	t	X
ejpam-4931	948	12	]	]	PUNCT
ejpam-4931	948	13	;	;	PUNCT
ejpam-4931	948	14	l2(ω	l2(ω	NUM
ejpam-4931	948	15	)	)	PUNCT
ejpam-4931	948	16	)	)	PUNCT
ejpam-4931	948	17	,	,	PUNCT
ejpam-4931	948	18	then	then	ADV
ejpam-4931	948	19	the	the	DET
ejpam-4931	948	20	sequence	sequence	NOUN
ejpam-4931	948	21	∇x	∇x	NOUN
ejpam-4931	948	22	√	√	NUM
ejpam-4931	948	23	ξk1,r1	ξk1,r1	PROPN
ejpam-4931	948	24	is	be	AUX
ejpam-4931	948	25	weakly	weakly	ADJ
ejpam-4931	948	26	converges	converge	NOUN
ejpam-4931	948	27	.	.	PUNCT
ejpam-4931	949	1	now	now	ADV
ejpam-4931	949	2	,	,	PUNCT
ejpam-4931	949	3	using	use	VERB
ejpam-4931	949	4	lemmas	lemmas	PROPN
ejpam-4931	949	5	14	14	NUM
ejpam-4931	949	6	and	and	CCONJ
ejpam-4931	949	7	16	16	NUM
ejpam-4931	949	8	,	,	PUNCT
ejpam-4931	949	9	and	and	CCONJ
ejpam-4931	949	10	the	the	DET
ejpam-4931	949	11	fact	fact	NOUN
ejpam-4931	949	12	that	that	SCONJ
ejpam-4931	949	13	√	√	INTJ
ejpam-4931	949	14	ξk1,r1uk1,r1	ξk1,r1uk1,r1	ADJ
ejpam-4931	949	15	−→	−→	NOUN
ejpam-4931	949	16	√	√	NUM
ejpam-4931	949	17	ξu	ξu	VERB
ejpam-4931	949	18	strongly	strongly	ADV
ejpam-4931	949	19	in	in	ADP
ejpam-4931	949	20	l2	l2	NOUN
ejpam-4931	949	21	(	(	PUNCT
ejpam-4931	949	22	[	[	X
ejpam-4931	949	23	0	0	NUM
ejpam-4931	949	24	,	,	PUNCT
ejpam-4931	949	25	t	t	X
ejpam-4931	949	26	]	]	PUNCT
ejpam-4931	949	27	;	;	PUNCT
ejpam-4931	949	28	l2(ω	l2(ω	NUM
ejpam-4931	949	29	)	)	PUNCT
ejpam-4931	949	30	)	)	PUNCT
ejpam-4931	949	31	,	,	PUNCT
ejpam-4931	949	32	we	we	PRON
ejpam-4931	949	33	obtain	obtain	VERB
ejpam-4931	949	34	1	1	NUM
ejpam-4931	949	35	2	2	NUM
ejpam-4931	949	36	∫	∫	NOUN
ejpam-4931	949	37	t	t	PROPN
ejpam-4931	949	38	0	0	NUM
ejpam-4931	949	39	∫	∫	PROPN
ejpam-4931	950	1	ω	ω	PROPN
ejpam-4931	950	2	(	(	PUNCT
ejpam-4931	950	3	ξk1,r1uk1,r1	ξk1,r1uk1,r1	PROPN
ejpam-4931	950	4	·	·	PUNCT
ejpam-4931	950	5	∆xφ+	∆xφ+	NOUN
ejpam-4931	950	6	2∇xφ	2∇xφ	NOUN
ejpam-4931	950	7	·	·	PUNCT
ejpam-4931	950	8	∇x	∇x	NOUN
ejpam-4931	950	9	√	√	NUM
ejpam-4931	950	10	ξk1,r1	ξk1,r1	NUM
ejpam-4931	950	11	·	·	PUNCT
ejpam-4931	950	12	√	√	NUM
ejpam-4931	950	13	ξk1,r1uk1,r1	ξk1,r1uk1,r1	ADJ
ejpam-4931	950	14	)	)	PUNCT
ejpam-4931	950	15	dxdydt	dxdydt	NOUN
ejpam-4931	950	16	+	+	CCONJ
ejpam-4931	950	17	1	1	NUM
ejpam-4931	950	18	2	2	NUM
ejpam-4931	950	19	∫	∫	NOUN
ejpam-4931	950	20	t	t	PROPN
ejpam-4931	950	21	0	0	NUM
ejpam-4931	950	22	∫	∫	PROPN
ejpam-4931	950	23	ω	ω	PROPN
ejpam-4931	950	24	(	(	PUNCT
ejpam-4931	950	25	ξk1,r1uk1,r1	ξk1,r1uk1,r1	PROPN
ejpam-4931	950	26	·	·	PUNCT
ejpam-4931	951	1	divx(∇t	divx(∇t	ADP
ejpam-4931	952	1	xφ	xφ	NOUN
ejpam-4931	952	2	)	)	PUNCT
ejpam-4931	953	1	+	+	CCONJ
ejpam-4931	953	2	2∇t	2∇t	NUM
ejpam-4931	953	3	xφ	xφ	NUM
ejpam-4931	953	4	·	·	PUNCT
ejpam-4931	953	5	∇x	∇x	NOUN
ejpam-4931	953	6	√	√	NUM
ejpam-4931	953	7	ξk1,r1	ξk1,r1	NUM
ejpam-4931	953	8	·	·	PUNCT
ejpam-4931	953	9	√	√	NUM
ejpam-4931	953	10	ξk1,r1uk1,r1	ξk1,r1uk1,r1	ADJ
ejpam-4931	953	11	)	)	PUNCT
ejpam-4931	953	12	dxdydt	dxdydt	NOUN
ejpam-4931	953	13	−→	−→	NOUN
ejpam-4931	953	14	k1,r1−→0	k1,r1−→0	PROPN
ejpam-4931	953	15	1	1	NUM
ejpam-4931	953	16	2	2	NUM
ejpam-4931	953	17	∫	∫	NOUN
ejpam-4931	953	18	t	t	PROPN
ejpam-4931	953	19	0	0	NUM
ejpam-4931	954	1	∫	∫	PROPN
ejpam-4931	955	1	ω	ω	PROPN
ejpam-4931	955	2	(	(	PUNCT
ejpam-4931	955	3	ξu	ξu	PROPN
ejpam-4931	955	4	·	·	PUNCT
ejpam-4931	955	5	∆xφ+	∆xφ+	NOUN
ejpam-4931	955	6	2∇xφ	2∇xφ	NOUN
ejpam-4931	955	7	·	·	PUNCT
ejpam-4931	955	8	∇x	∇x	NOUN
ejpam-4931	955	9	√	√	SYM
ejpam-4931	955	10	ξ	ξ	PROPN
ejpam-4931	955	11	·	·	PUNCT
ejpam-4931	955	12	√	√	NUM
ejpam-4931	955	13	ξu	ξu	NOUN
ejpam-4931	955	14	)	)	PUNCT
ejpam-4931	955	15	dxdydt	dxdydt	NOUN
ejpam-4931	955	16	+	+	CCONJ
ejpam-4931	955	17	1	1	NUM
ejpam-4931	955	18	2	2	NUM
ejpam-4931	955	19	∫	∫	NOUN
ejpam-4931	955	20	t	t	PROPN
ejpam-4931	955	21	0	0	NUM
ejpam-4931	955	22	∫	∫	PROPN
ejpam-4931	955	23	ω	ω	PROPN
ejpam-4931	955	24	(	(	PUNCT
ejpam-4931	955	25	ξu	ξu	PROPN
ejpam-4931	955	26	·	·	PUNCT
ejpam-4931	955	27	divx(∇t	divx(∇t	NOUN
ejpam-4931	955	28	xφ	xφ	NOUN
ejpam-4931	955	29	)	)	PUNCT
ejpam-4931	956	1	+	+	CCONJ
ejpam-4931	956	2	2∇t	2∇t	NUM
ejpam-4931	956	3	xφ	xφ	NUM
ejpam-4931	956	4	·	·	PUNCT
ejpam-4931	956	5	∇x	∇x	NOUN
ejpam-4931	956	6	√	√	NUM
ejpam-4931	956	7	ξ	ξ	PROPN
ejpam-4931	956	8	·	·	PUNCT
ejpam-4931	956	9	√	√	NUM
ejpam-4931	956	10	ξu	ξu	PROPN
ejpam-4931	956	11	)	)	PUNCT
ejpam-4931	956	12	dxdydt	dxdydt	PROPN
ejpam-4931	956	13	,	,	PUNCT
ejpam-4931	956	14	j.	j.	PROPN
ejpam-4931	956	15	ouya	ouya	PROPN
ejpam-4931	956	16	,	,	PUNCT
ejpam-4931	956	17	a.	a.	NOUN
ejpam-4931	956	18	ouédraogo	ouédraogo	PROPN
ejpam-4931	956	19	/	/	SYM
ejpam-4931	956	20	eur	eur	PROPN
ejpam-4931	956	21	.	.	PUNCT
ejpam-4931	957	1	j.	j.	PROPN
ejpam-4931	957	2	pure	pure	PROPN
ejpam-4931	957	3	appl	appl	PROPN
ejpam-4931	957	4	.	.	PROPN
ejpam-4931	957	5	math	math	PROPN
ejpam-4931	957	6	,	,	PUNCT
ejpam-4931	957	7	16	16	NUM
ejpam-4931	957	8	(	(	PUNCT
ejpam-4931	957	9	4	4	NUM
ejpam-4931	957	10	)	)	PUNCT
ejpam-4931	957	11	(	(	PUNCT
ejpam-4931	957	12	2023	2023	NUM
ejpam-4931	957	13	)	)	PUNCT
ejpam-4931	957	14	,	,	PUNCT
ejpam-4931	957	15	2247	2247	NUM
ejpam-4931	957	16	-	-	SYM
ejpam-4931	957	17	2285	2285	NUM
ejpam-4931	957	18	2282	2282	NUM
ejpam-4931	957	19	which	which	PRON
ejpam-4931	957	20	implies	imply	VERB
ejpam-4931	957	21	that∫	that∫	PROPN
ejpam-4931	957	22	t	t	PROPN
ejpam-4931	957	23	0	0	NUM
ejpam-4931	957	24	∫	∫	PROPN
ejpam-4931	958	1	ω	ω	NUM
ejpam-4931	958	2	divx(ξk1,r1dx(uk1,r1))φdxdydt	divx(ξk1,r1dx(uk1,r1))φdxdydt	PROPN
ejpam-4931	958	3	−→	−→	NOUN
ejpam-4931	958	4	k1,r1−→0	k1,r1−→0	PROPN
ejpam-4931	958	5	∫	∫	PROPN
ejpam-4931	958	6	t	t	PROPN
ejpam-4931	958	7	0	0	NUM
ejpam-4931	958	8	∫	∫	PROPN
ejpam-4931	958	9	ω	ω	PROPN
ejpam-4931	958	10	divx(ξdx(u))φdxdydt	divx(ξdx(u))φdxdydt	PROPN
ejpam-4931	958	11	.	.	PROPN
ejpam-4931	959	1	at	at	ADP
ejpam-4931	959	2	last	last	ADV
ejpam-4931	959	3	,	,	PUNCT
ejpam-4931	959	4	we	we	PRON
ejpam-4931	959	5	prove	prove	VERB
ejpam-4931	959	6	(	(	PUNCT
ejpam-4931	959	7	127	127	NUM
ejpam-4931	959	8	)	)	PUNCT
ejpam-4931	959	9	.	.	PUNCT
ejpam-4931	960	1	recalling	recall	VERB
ejpam-4931	960	2	(	(	PUNCT
ejpam-4931	960	3	118	118	NUM
ejpam-4931	960	4	)	)	PUNCT
ejpam-4931	960	5	,	,	PUNCT
ejpam-4931	960	6	we	we	PRON
ejpam-4931	960	7	have	have	VERB
ejpam-4931	960	8	k1	k1	PROPN
ejpam-4931	960	9	∫	∫	PROPN
ejpam-4931	960	10	t	t	PROPN
ejpam-4931	960	11	0	0	NUM
ejpam-4931	960	12	∫	∫	PROPN
ejpam-4931	961	1	ω	ω	NUM
ejpam-4931	961	2	ξk1,r1∇x	ξk1,r1∇x	PROPN
ejpam-4931	961	3	(	(	PUNCT
ejpam-4931	961	4	∆x	∆x	PROPN
ejpam-4931	961	5	√	√	PROPN
ejpam-4931	961	6	ξk1,r1√	ξk1,r1√	PROPN
ejpam-4931	961	7	ξk1,r1	ξk1,r1	ADJ
ejpam-4931	961	8	)	)	PUNCT
ejpam-4931	962	1	φdxdydt	φdxdydt	NOUN
ejpam-4931	962	2	=	=	SYM
ejpam-4931	962	3	−2k1	−2k1	NUM
ejpam-4931	963	1	∫	∫	PROPN
ejpam-4931	963	2	t	t	PROPN
ejpam-4931	963	3	0	0	NUM
ejpam-4931	963	4	∫	∫	PROPN
ejpam-4931	963	5	ω	ω	PROPN
ejpam-4931	963	6	∆x	∆x	PROPN
ejpam-4931	963	7	√	√	PROPN
ejpam-4931	963	8	ξk1,r1∇x	ξk1,r1∇x	NOUN
ejpam-4931	963	9	√	√	PROPN
ejpam-4931	963	10	ξk1,r1φdxdydt−	ξk1,r1φdxdydt−	ADJ
ejpam-4931	963	11	k1	k1	PROPN
ejpam-4931	963	12	∫	∫	PROPN
ejpam-4931	963	13	t	t	PROPN
ejpam-4931	963	14	0	0	NUM
ejpam-4931	963	15	∫	∫	PROPN
ejpam-4931	964	1	ω	ω	PROPN
ejpam-4931	964	2	∆x	∆x	PROPN
ejpam-4931	964	3	√	√	PROPN
ejpam-4931	964	4	ξk1,r1	ξk1,r1	ADJ
ejpam-4931	964	5	√	√	PROPN
ejpam-4931	964	6	ξk1,r1divxφdxdydt	ξk1,r1divxφdxdydt	ADJ
ejpam-4931	964	7	≤	≤	NUM
ejpam-4931	964	8	2	2	NUM
ejpam-4931	964	9	√	√	NOUN
ejpam-4931	964	10	k1∥	k1∥	ADJ
ejpam-4931	964	11	√	√	VERB
ejpam-4931	964	12	k1∆x	k1∆x	ADJ
ejpam-4931	964	13	√	√	PROPN
ejpam-4931	964	14	ξk1,r1∥l2	ξk1,r1∥l2	NOUN
ejpam-4931	964	15	(	(	PUNCT
ejpam-4931	964	16	[	[	X
ejpam-4931	964	17	0,t	0,t	X
ejpam-4931	964	18	]	]	X
ejpam-4931	964	19	;	;	PUNCT
ejpam-4931	964	20	l2(ω	l2(ω	NUM
ejpam-4931	964	21	)	)	PUNCT
ejpam-4931	964	22	)	)	PUNCT
ejpam-4931	964	23	∥∇x	∥∇x	NOUN
ejpam-4931	964	24	√	√	VERB
ejpam-4931	964	25	ξk1,r1∥l2	ξk1,r1∥l2	NOUN
ejpam-4931	964	26	(	(	PUNCT
ejpam-4931	964	27	[	[	X
ejpam-4931	964	28	0,t	0,t	X
ejpam-4931	964	29	]	]	X
ejpam-4931	964	30	;	;	PUNCT
ejpam-4931	964	31	l2(ω	l2(ω	NUM
ejpam-4931	964	32	)	)	PUNCT
ejpam-4931	964	33	)	)	PUNCT
ejpam-4931	964	34	∥φ∥	∥φ∥	VERB
ejpam-4931	964	35	l∞	l∞	NOUN
ejpam-4931	964	36	(	(	PUNCT
ejpam-4931	964	37	[	[	X
ejpam-4931	964	38	0,t	0,t	X
ejpam-4931	964	39	]	]	X
ejpam-4931	964	40	;	;	PUNCT
ejpam-4931	964	41	l∞(ω	l∞(ω	X
ejpam-4931	964	42	)	)	PUNCT
ejpam-4931	964	43	)	)	PUNCT
ejpam-4931	965	1	+	+	CCONJ
ejpam-4931	965	2	√	√	INTJ
ejpam-4931	965	3	k1∥	k1∥	ADJ
ejpam-4931	965	4	√	√	VERB
ejpam-4931	965	5	k1∆x	k1∆x	ADJ
ejpam-4931	965	6	√	√	PROPN
ejpam-4931	965	7	ξk1,r1∥l2	ξk1,r1∥l2	NOUN
ejpam-4931	965	8	(	(	PUNCT
ejpam-4931	965	9	[	[	X
ejpam-4931	965	10	0,t	0,t	X
ejpam-4931	965	11	]	]	X
ejpam-4931	965	12	;	;	PUNCT
ejpam-4931	965	13	l2(ω	l2(ω	NUM
ejpam-4931	965	14	)	)	PUNCT
ejpam-4931	965	15	)	)	PUNCT
ejpam-4931	966	1	∥√ξk1,r1∥l2	∥√ξk1,r1∥l2	PROPN
ejpam-4931	966	2	(	(	PUNCT
ejpam-4931	966	3	[	[	X
ejpam-4931	966	4	0,t	0,t	X
ejpam-4931	966	5	]	]	X
ejpam-4931	966	6	;	;	PUNCT
ejpam-4931	966	7	l2(ω	l2(ω	NUM
ejpam-4931	966	8	)	)	PUNCT
ejpam-4931	966	9	)	)	PUNCT
ejpam-4931	966	10	∥divxφ∥l∞	∥divxφ∥l∞	NUM
ejpam-4931	967	1	(	(	PUNCT
ejpam-4931	967	2	[	[	X
ejpam-4931	967	3	0,t	0,t	X
ejpam-4931	967	4	]	]	X
ejpam-4931	967	5	;	;	PUNCT
ejpam-4931	967	6	l∞(ω	l∞(ω	X
ejpam-4931	967	7	)	)	PUNCT
ejpam-4931	967	8	)	)	PUNCT
ejpam-4931	968	1	−→	−→	NOUN
ejpam-4931	968	2	0	0	PUNCT
ejpam-4931	968	3	as	as	ADP
ejpam-4931	968	4	k1	k1	NOUN
ejpam-4931	968	5	−→	−→	NOUN
ejpam-4931	968	6	0	0	NUM
ejpam-4931	968	7	.	.	PUNCT
ejpam-4931	969	1	passing	pass	VERB
ejpam-4931	969	2	to	to	ADP
ejpam-4931	969	3	the	the	DET
ejpam-4931	969	4	limits	limit	NOUN
ejpam-4931	969	5	in	in	ADP
ejpam-4931	969	6	(	(	PUNCT
ejpam-4931	969	7	116	116	NUM
ejpam-4931	969	8	)	)	PUNCT
ejpam-4931	969	9	and	and	CCONJ
ejpam-4931	969	10	(	(	PUNCT
ejpam-4931	969	11	117	117	NUM
ejpam-4931	969	12	)	)	PUNCT
ejpam-4931	969	13	the	the	DET
ejpam-4931	969	14	energy	energy	NOUN
ejpam-4931	969	15	inequality	inequality	NOUN
ejpam-4931	969	16	and	and	CCONJ
ejpam-4931	969	17	the	the	DET
ejpam-4931	969	18	b	b	PROPN
ejpam-4931	969	19	-	-	PUNCT
ejpam-4931	969	20	d	d	NOUN
ejpam-4931	969	21	entropy	entropy	NOUN
ejpam-4931	969	22	give	give	VERB
ejpam-4931	969	23	respectively∫	respectively∫	NOUN
ejpam-4931	969	24	ω	ω	NOUN
ejpam-4931	969	25	(	(	PUNCT
ejpam-4931	970	1	1	1	NUM
ejpam-4931	970	2	2	2	NUM
ejpam-4931	970	3	ξu2	ξu2	NOUN
ejpam-4931	970	4	+	+	CCONJ
ejpam-4931	970	5	ξ2	ξ2	NOUN
ejpam-4931	970	6	)	)	PUNCT
ejpam-4931	970	7	dxdy	dxdy	NOUN
ejpam-4931	970	8	+	+	CCONJ
ejpam-4931	971	1	r	r	NOUN
ejpam-4931	971	2	∫	∫	PROPN
ejpam-4931	971	3	t	t	PROPN
ejpam-4931	971	4	0	0	NUM
ejpam-4931	971	5	∫	∫	PROPN
ejpam-4931	972	1	ω	ω	NUM
ejpam-4931	972	2	ξ|u|3dxdydt+	ξ|u|3dxdydt+	PROPN
ejpam-4931	972	3	∫	∫	PROPN
ejpam-4931	972	4	t	t	PROPN
ejpam-4931	972	5	0	0	NUM
ejpam-4931	973	1	∫	∫	PROPN
ejpam-4931	973	2	ω	ω	NUM
ejpam-4931	973	3	ξ|∂yu|2dxdydt	ξ|∂yu|2dxdydt	PROPN
ejpam-4931	973	4	+	+	CCONJ
ejpam-4931	974	1	∫	∫	PROPN
ejpam-4931	974	2	t	t	PROPN
ejpam-4931	974	3	0	0	NUM
ejpam-4931	974	4	∫	∫	PROPN
ejpam-4931	975	1	ω	ω	NUM
ejpam-4931	975	2	2ξ|dx(u)|2dxdydt	2ξ|dx(u)|2dxdydt	PROPN
ejpam-4931	975	3	≤	≤	NUM
ejpam-4931	975	4	∫	∫	PROPN
ejpam-4931	976	1	ω	ω	PROPN
ejpam-4931	976	2	(	(	PUNCT
ejpam-4931	976	3	1	1	NUM
ejpam-4931	976	4	2	2	NUM
ejpam-4931	976	5	ξ0u	ξ0u	NOUN
ejpam-4931	976	6	2	2	NUM
ejpam-4931	976	7	0	0	NUM
ejpam-4931	976	8	+	+	CCONJ
ejpam-4931	976	9	ξ20	ξ20	X
ejpam-4931	976	10	)	)	PUNCT
ejpam-4931	976	11	dxdy	dxdy	NOUN
ejpam-4931	976	12	(	(	PUNCT
ejpam-4931	976	13	128	128	NUM
ejpam-4931	976	14	)	)	PUNCT
ejpam-4931	976	15	and	and	CCONJ
ejpam-4931	976	16	∫	∫	PROPN
ejpam-4931	976	17	ω	ω	PROPN
ejpam-4931	976	18	(	(	PUNCT
ejpam-4931	976	19	1	1	NUM
ejpam-4931	976	20	2	2	NUM
ejpam-4931	976	21	ξ|u+	ξ|u+	NOUN
ejpam-4931	976	22	2∇x	2∇x	NUM
ejpam-4931	976	23	ln	ln	PROPN
ejpam-4931	976	24	ξ|2	ξ|2	PROPN
ejpam-4931	976	25	)	)	PUNCT
ejpam-4931	976	26	dxdy	dxdy	NOUN
ejpam-4931	976	27	+	+	CCONJ
ejpam-4931	976	28	2	2	NUM
ejpam-4931	976	29	∫	∫	NOUN
ejpam-4931	976	30	t	t	PROPN
ejpam-4931	976	31	0	0	NUM
ejpam-4931	976	32	∫	∫	PROPN
ejpam-4931	976	33	ω	ω	NUM
ejpam-4931	976	34	ξ|∂yv|2dxdydt+	ξ|∂yv|2dxdydt+	PROPN
ejpam-4931	976	35	r	r	NOUN
ejpam-4931	976	36	∫	∫	PROPN
ejpam-4931	976	37	t	t	PROPN
ejpam-4931	976	38	0	0	NUM
ejpam-4931	976	39	∫	∫	PROPN
ejpam-4931	976	40	ω	ω	NUM
ejpam-4931	976	41	ξ|u|3dxdydt	ξ|u|3dxdydt	PROPN
ejpam-4931	976	42	+	+	CCONJ
ejpam-4931	976	43	∫	∫	PROPN
ejpam-4931	976	44	t	t	PROPN
ejpam-4931	976	45	0	0	NUM
ejpam-4931	976	46	∫	∫	PROPN
ejpam-4931	976	47	ω	ω	X
ejpam-4931	976	48	ξ|∂yu|2dxdy	ξ|∂yu|2dxdy	X
ejpam-4931	976	49	+	+	CCONJ
ejpam-4931	976	50	2	2	NUM
ejpam-4931	976	51	∫	∫	NOUN
ejpam-4931	976	52	t	t	PROPN
ejpam-4931	976	53	0	0	NUM
ejpam-4931	976	54	∫	∫	PROPN
ejpam-4931	976	55	ω	ω	NUM
ejpam-4931	976	56	ξ|ax(u)|2dxdydt+	ξ|ax(u)|2dxdydt+	NOUN
ejpam-4931	976	57	8	8	NUM
ejpam-4931	976	58	∫	∫	NOUN
ejpam-4931	976	59	t	t	PROPN
ejpam-4931	976	60	0	0	NUM
ejpam-4931	976	61	∫	∫	PROPN
ejpam-4931	976	62	ω	ω	NUM
ejpam-4931	976	63	ξ|∇x	ξ|∇x	ADJ
ejpam-4931	976	64	√	√	PROPN
ejpam-4931	976	65	ξ|2dxdydt	ξ|2dxdydt	NOUN
ejpam-4931	976	66	≤	≤	NUM
ejpam-4931	976	67	∫	∫	PROPN
ejpam-4931	976	68	ω	ω	PROPN
ejpam-4931	976	69	(	(	PUNCT
ejpam-4931	976	70	ξ0u	ξ0u	NOUN
ejpam-4931	976	71	2	2	NUM
ejpam-4931	976	72	0	0	NUM
ejpam-4931	976	73	+	+	CCONJ
ejpam-4931	976	74	10(∇x	10(∇x	NUM
ejpam-4931	976	75	√	√	ADP
ejpam-4931	976	76	ξ0	ξ0	PROPN
ejpam-4931	976	77	)	)	PUNCT
ejpam-4931	976	78	2	2	NUM
ejpam-4931	976	79	)	)	PUNCT
ejpam-4931	976	80	dxdy	dxdy	NOUN
ejpam-4931	976	81	+	+	CCONJ
ejpam-4931	976	82	∫	∫	PROPN
ejpam-4931	976	83	ω	ω	PROPN
ejpam-4931	976	84	(	(	PUNCT
ejpam-4931	976	85	1	1	NUM
ejpam-4931	976	86	2	2	NUM
ejpam-4931	976	87	ξ0u	ξ0u	NOUN
ejpam-4931	976	88	2	2	NUM
ejpam-4931	976	89	0	0	NUM
ejpam-4931	976	90	+	+	CCONJ
ejpam-4931	976	91	ξ20	ξ20	X
ejpam-4931	976	92	)	)	PUNCT
ejpam-4931	976	93	dxdy	dxdy	PROPN
ejpam-4931	976	94	+	+	CCONJ
ejpam-4931	976	95	c.	c.	PROPN
ejpam-4931	976	96	(	(	PUNCT
ejpam-4931	976	97	129	129	NUM
ejpam-4931	976	98	)	)	PUNCT
ejpam-4931	976	99	passing	pass	VERB
ejpam-4931	976	100	to	to	ADP
ejpam-4931	976	101	the	the	DET
ejpam-4931	976	102	limits	limit	NOUN
ejpam-4931	976	103	in	in	ADP
ejpam-4931	976	104	(	(	PUNCT
ejpam-4931	976	105	115	115	NUM
ejpam-4931	976	106	)	)	PUNCT
ejpam-4931	976	107	when	when	SCONJ
ejpam-4931	976	108	k1	k1	NOUN
ejpam-4931	976	109	−→	−→	NOUN
ejpam-4931	976	110	0	0	NUM
ejpam-4931	976	111	and	and	CCONJ
ejpam-4931	976	112	r1	r1	VERB
ejpam-4931	976	113	−→	−→	NOUN
ejpam-4931	976	114	0	0	NUM
ejpam-4931	976	115	,	,	PUNCT
ejpam-4931	976	116	the	the	DET
ejpam-4931	976	117	system	system	PROPN
ejpam-4931	976	118	∂tξ	∂tξ	VERB
ejpam-4931	976	119	+	+	CCONJ
ejpam-4931	976	120	divx(ξu	divx(ξu	NOUN
ejpam-4931	976	121	)	)	PUNCT
ejpam-4931	976	122	+	+	SYM
ejpam-4931	976	123	∂y(ξv	∂y(ξv	NOUN
ejpam-4931	976	124	)	)	PUNCT
ejpam-4931	976	125	=	=	SYM
ejpam-4931	976	126	0	0	NUM
ejpam-4931	976	127	∂t(ξu	∂t(ξu	NOUN
ejpam-4931	976	128	)	)	PUNCT
ejpam-4931	977	1	+	+	CCONJ
ejpam-4931	977	2	divx(ξu⊗	divx(ξu⊗	NOUN
ejpam-4931	977	3	u	u	NOUN
ejpam-4931	977	4	)	)	PUNCT
ejpam-4931	977	5	+	+	CCONJ
ejpam-4931	977	6	∂y(ξuv	∂y(ξuv	X
ejpam-4931	977	7	)	)	PUNCT
ejpam-4931	978	1	+	+	X
ejpam-4931	978	2	∇xξ	∇xξ	PROPN
ejpam-4931	978	3	2	2	NUM
ejpam-4931	978	4	+	+	CCONJ
ejpam-4931	978	5	rξ|u|u	rξ|u|u	NOUN
ejpam-4931	978	6	=	=	SYM
ejpam-4931	978	7	2divx	2divx	NUM
ejpam-4931	978	8	(	(	PUNCT
ejpam-4931	978	9	ξdx(u	ξdx(u	PROPN
ejpam-4931	978	10	)	)	PUNCT
ejpam-4931	978	11	)	)	PUNCT
ejpam-4931	979	1	+	+	CCONJ
ejpam-4931	979	2	∂y(ξ∂yu	∂y(ξ∂yu	PROPN
ejpam-4931	979	3	)	)	PUNCT
ejpam-4931	979	4	∂yξ	∂yξ	PROPN
ejpam-4931	979	5	=	=	SYM
ejpam-4931	979	6	0	0	NUM
ejpam-4931	979	7	(	(	PUNCT
ejpam-4931	979	8	130	130	NUM
ejpam-4931	979	9	)	)	PUNCT
ejpam-4931	979	10	holds	hold	VERB
ejpam-4931	979	11	in	in	ADP
ejpam-4931	979	12	the	the	DET
ejpam-4931	979	13	sense	sense	NOUN
ejpam-4931	979	14	of	of	ADP
ejpam-4931	979	15	distribution	distribution	NOUN
ejpam-4931	979	16	on[0	on[0	NOUN
ejpam-4931	979	17	,	,	PUNCT
ejpam-4931	979	18	t	t	X
ejpam-4931	979	19	]	]	X
ejpam-4931	979	20	×	×	PROPN
ejpam-4931	979	21	ω	ω	X
ejpam-4931	979	22	.	.	PUNCT
ejpam-4931	979	23	therefore	therefore	ADV
ejpam-4931	979	24	theorem	theorem	VERB
ejpam-4931	979	25	1	1	NUM
ejpam-4931	979	26	is	be	AUX
ejpam-4931	979	27	proved	prove	VERB
ejpam-4931	979	28	.	.	PUNCT
ejpam-4931	980	1	j.	j.	PROPN
ejpam-4931	980	2	ouya	ouya	PROPN
ejpam-4931	980	3	,	,	PUNCT
ejpam-4931	980	4	a.	a.	NOUN
ejpam-4931	980	5	ouédraogo	ouédraogo	PROPN
ejpam-4931	980	6	/	/	SYM
ejpam-4931	980	7	eur	eur	PROPN
ejpam-4931	980	8	.	.	PUNCT
ejpam-4931	981	1	j.	j.	PROPN
ejpam-4931	981	2	pure	pure	PROPN
ejpam-4931	981	3	appl	appl	PROPN
ejpam-4931	981	4	.	.	PROPN
ejpam-4931	981	5	math	math	PROPN
ejpam-4931	981	6	,	,	PUNCT
ejpam-4931	981	7	16	16	NUM
ejpam-4931	981	8	(	(	PUNCT
ejpam-4931	981	9	4	4	NUM
ejpam-4931	981	10	)	)	PUNCT
ejpam-4931	981	11	(	(	PUNCT
ejpam-4931	981	12	2023	2023	NUM
ejpam-4931	981	13	)	)	PUNCT
ejpam-4931	981	14	,	,	PUNCT
ejpam-4931	981	15	2247	2247	NUM
ejpam-4931	981	16	-	-	SYM
ejpam-4931	981	17	2285	2285	NUM
ejpam-4931	981	18	2283	2283	NUM
ejpam-4931	981	19	5.2	5.2	NUM
ejpam-4931	981	20	.	.	PUNCT
ejpam-4931	982	1	proof	proof	NOUN
ejpam-4931	982	2	of	of	ADP
ejpam-4931	982	3	theorem	theorem	ADJ
ejpam-4931	982	4	2	2	NUM
ejpam-4931	982	5	let	let	VERB
ejpam-4931	982	6	us	we	PRON
ejpam-4931	982	7	now	now	ADV
ejpam-4931	982	8	consider	consider	VERB
ejpam-4931	982	9	the	the	DET
ejpam-4931	982	10	weak	weak	ADJ
ejpam-4931	982	11	solution	solution	NOUN
ejpam-4931	982	12	(	(	PUNCT
ejpam-4931	982	13	ξ	ξ	X
ejpam-4931	982	14	,	,	PUNCT
ejpam-4931	982	15	u	u	NOUN
ejpam-4931	982	16	,	,	PUNCT
ejpam-4931	982	17	v	v	NOUN
ejpam-4931	982	18	)	)	PUNCT
ejpam-4931	982	19	of	of	ADP
ejpam-4931	982	20	the	the	DET
ejpam-4931	982	21	system	system	NOUN
ejpam-4931	982	22	(	(	PUNCT
ejpam-4931	982	23	7	7	NUM
ejpam-4931	982	24	)	)	PUNCT
ejpam-4931	982	25	.	.	PUNCT
ejpam-4931	983	1	from	from	ADP
ejpam-4931	983	2	theorem	theorem	NOUN
ejpam-4931	983	3	1	1	NUM
ejpam-4931	983	4	,	,	PUNCT
ejpam-4931	983	5	we	we	PRON
ejpam-4931	983	6	have	have	VERB
ejpam-4931	983	7	the	the	DET
ejpam-4931	983	8	following	follow	VERB
ejpam-4931	983	9	regularities:	regularities:	NOUN
ejpam-4931	983	10	ξ	ξ	PROPN
ejpam-4931	983	11	∈	∈	PROPN
ejpam-4931	983	12	l∞	l∞	NOUN
ejpam-4931	983	13	(	(	PUNCT
ejpam-4931	983	14	[	[	X
ejpam-4931	983	15	0	0	NUM
ejpam-4931	983	16	,	,	PUNCT
ejpam-4931	983	17	t	t	X
ejpam-4931	983	18	]	]	PUNCT
ejpam-4931	983	19	;	;	PUNCT
ejpam-4931	983	20	h1(ω	h1(ω	PROPN
ejpam-4931	983	21	)	)	PUNCT
ejpam-4931	983	22	)	)	PUNCT
ejpam-4931	983	23	,	,	PUNCT
ejpam-4931	983	24	√	√	NUM
ejpam-4931	983	25	ξu	ξu	ADP
ejpam-4931	983	26	∈	∈	PROPN
ejpam-4931	983	27	l∞	l∞	PROPN
ejpam-4931	983	28	(	(	PUNCT
ejpam-4931	983	29	[	[	X
ejpam-4931	983	30	0	0	NUM
ejpam-4931	983	31	,	,	PUNCT
ejpam-4931	983	32	t	t	X
ejpam-4931	983	33	]	]	PUNCT
ejpam-4931	983	34	;	;	PUNCT
ejpam-4931	983	35	l2(ω	l2(ω	NUM
ejpam-4931	983	36	)	)	PUNCT
ejpam-4931	983	37	)	)	PUNCT
ejpam-4931	983	38	,	,	PUNCT
ejpam-4931	983	39	ξ∇xu	ξ∇xu	PROPN
ejpam-4931	983	40	∈	∈	NOUN
ejpam-4931	983	41	l2	l2	NOUN
ejpam-4931	983	42	(	(	PUNCT
ejpam-4931	983	43	[	[	X
ejpam-4931	983	44	0	0	NUM
ejpam-4931	983	45	,	,	PUNCT
ejpam-4931	983	46	t	t	X
ejpam-4931	983	47	]	]	PUNCT
ejpam-4931	983	48	;	;	PUNCT
ejpam-4931	983	49	l2(ω	l2(ω	NUM
ejpam-4931	983	50	)	)	PUNCT
ejpam-4931	983	51	)	)	PUNCT
ejpam-4931	983	52	,	,	PUNCT
ejpam-4931	983	53	ξ(∇xu	ξ(∇xu	NUM
ejpam-4931	983	54	)	)	PUNCT
ejpam-4931	983	55	t	t	PROPN
ejpam-4931	983	56	∈	∈	NOUN
ejpam-4931	983	57	l2	l2	NOUN
ejpam-4931	983	58	(	(	PUNCT
ejpam-4931	983	59	[	[	X
ejpam-4931	983	60	0	0	NUM
ejpam-4931	983	61	,	,	PUNCT
ejpam-4931	983	62	t	t	X
ejpam-4931	983	63	]	]	PUNCT
ejpam-4931	983	64	;	;	PUNCT
ejpam-4931	983	65	l2(ω	l2(ω	NUM
ejpam-4931	983	66	)	)	PUNCT
ejpam-4931	983	67	)	)	PUNCT
ejpam-4931	983	68	,	,	PUNCT
ejpam-4931	983	69	√	√	NUM
ejpam-4931	983	70	ξ∂yv	ξ∂yv	PROPN
ejpam-4931	983	71	∈	∈	NOUN
ejpam-4931	983	72	l2	l2	NOUN
ejpam-4931	983	73	(	(	PUNCT
ejpam-4931	983	74	[	[	X
ejpam-4931	983	75	0	0	NUM
ejpam-4931	983	76	,	,	PUNCT
ejpam-4931	983	77	t	t	X
ejpam-4931	983	78	]	]	PUNCT
ejpam-4931	983	79	;	;	PUNCT
ejpam-4931	983	80	l2(ω	l2(ω	NUM
ejpam-4931	983	81	)	)	PUNCT
ejpam-4931	983	82	)	)	PUNCT
ejpam-4931	983	83	,	,	PUNCT
ejpam-4931	983	84	√	√	CCONJ
ejpam-4931	983	85	ξ∂yu	ξ∂yu	NOUN
ejpam-4931	983	86	∈	∈	NOUN
ejpam-4931	983	87	l2	l2	NOUN
ejpam-4931	983	88	(	(	PUNCT
ejpam-4931	983	89	[	[	X
ejpam-4931	983	90	0	0	NUM
ejpam-4931	983	91	,	,	PUNCT
ejpam-4931	983	92	t	t	X
ejpam-4931	983	93	]	]	PUNCT
ejpam-4931	983	94	;	;	PUNCT
ejpam-4931	983	95	l2(ω	l2(ω	NUM
ejpam-4931	983	96	)	)	PUNCT
ejpam-4931	983	97	)	)	PUNCT
ejpam-4931	983	98	,	,	PUNCT
ejpam-4931	983	99	ξ	ξ	X
ejpam-4931	983	100	1	1	NUM
ejpam-4931	983	101	3u	3u	NUM
ejpam-4931	983	102	∈	∈	PROPN
ejpam-4931	983	103	l3	l3	NOUN
ejpam-4931	983	104	(	(	PUNCT
ejpam-4931	983	105	[	[	X
ejpam-4931	983	106	0	0	NUM
ejpam-4931	983	107	,	,	PUNCT
ejpam-4931	983	108	t	t	X
ejpam-4931	983	109	]	]	PUNCT
ejpam-4931	983	110	;	;	PUNCT
ejpam-4931	983	111	l3(ω	l3(ω	X
ejpam-4931	983	112	)	)	PUNCT
ejpam-4931	983	113	)	)	PUNCT
ejpam-4931	983	114	,	,	PUNCT
ejpam-4931	983	115	√	√	VERB
ejpam-4931	983	116	ξv	ξv	DET
ejpam-4931	983	117	∈	∈	NOUN
ejpam-4931	983	118	l2	l2	NOUN
ejpam-4931	983	119	(	(	PUNCT
ejpam-4931	983	120	[	[	X
ejpam-4931	983	121	0	0	NUM
ejpam-4931	983	122	,	,	PUNCT
ejpam-4931	983	123	t	t	X
ejpam-4931	983	124	]	]	PUNCT
ejpam-4931	983	125	;	;	PUNCT
ejpam-4931	983	126	l2(ω	l2(ω	NUM
ejpam-4931	983	127	)	)	PUNCT
ejpam-4931	983	128	)	)	PUNCT
ejpam-4931	983	129	.	.	PUNCT
ejpam-4931	984	1	(	(	PUNCT
ejpam-4931	984	2	131	131	X
ejpam-4931	984	3	)	)	PUNCT
ejpam-4931	984	4	recall	recall	NOUN
ejpam-4931	984	5	that	that	DET
ejpam-4931	984	6	ρ(t	ρ(t	PROPN
ejpam-4931	984	7	,	,	PUNCT
ejpam-4931	984	8	x	x	NOUN
ejpam-4931	984	9	,	,	PUNCT
ejpam-4931	984	10	y	y	NOUN
ejpam-4931	984	11	)	)	PUNCT
ejpam-4931	984	12	=	=	SYM
ejpam-4931	984	13	ξ(t	ξ(t	NOUN
ejpam-4931	984	14	,	,	PUNCT
ejpam-4931	984	15	x	x	PRON
ejpam-4931	984	16	)	)	PUNCT
ejpam-4931	984	17	+	+	CCONJ
ejpam-4931	985	1	ϕ(y	ϕ(y	PROPN
ejpam-4931	985	2	)	)	PUNCT
ejpam-4931	985	3	,	,	PUNCT
ejpam-4931	985	4	so	so	SCONJ
ejpam-4931	985	5	we	we	PRON
ejpam-4931	985	6	obtain	obtain	VERB
ejpam-4931	985	7	the	the	DET
ejpam-4931	985	8	following	follow	VERB
ejpam-4931	985	9	properties:	properties:	PROPN
ejpam-4931	985	10	∥√ρ∥	∥√ρ∥	NOUN
ejpam-4931	985	11	l∞	l∞	NOUN
ejpam-4931	985	12	(	(	PUNCT
ejpam-4931	985	13	[	[	X
ejpam-4931	985	14	0,t	0,t	X
ejpam-4931	985	15	]	]	X
ejpam-4931	985	16	;	;	PUNCT
ejpam-4931	985	17	h1(ω	h1(ω	PROPN
ejpam-4931	985	18	)	)	PUNCT
ejpam-4931	985	19	)	)	PUNCT
ejpam-4931	985	20	≥	≥	NOUN
ejpam-4931	985	21	∥	∥	NUM
ejpam-4931	985	22	√	√	NUM
ejpam-4931	985	23	ξ∥	ξ∥	PROPN
ejpam-4931	985	24	l∞	l∞	NOUN
ejpam-4931	985	25	(	(	PUNCT
ejpam-4931	985	26	[	[	X
ejpam-4931	985	27	0,t	0,t	X
ejpam-4931	985	28	]	]	X
ejpam-4931	985	29	;	;	PUNCT
ejpam-4931	985	30	h1(ω	h1(ω	PROPN
ejpam-4931	985	31	)	)	PUNCT
ejpam-4931	985	32	)	)	PUNCT
ejpam-4931	985	33	,	,	PUNCT
ejpam-4931	985	34	∥√ρu∥	∥√ρu∥	PROPN
ejpam-4931	985	35	l∞	l∞	NOUN
ejpam-4931	985	36	(	(	PUNCT
ejpam-4931	985	37	[	[	X
ejpam-4931	985	38	0,t	0,t	X
ejpam-4931	985	39	]	]	X
ejpam-4931	985	40	;	;	PUNCT
ejpam-4931	985	41	l2(ω	l2(ω	NUM
ejpam-4931	985	42	)	)	PUNCT
ejpam-4931	985	43	)	)	PUNCT
ejpam-4931	985	44	≥	≥	NOUN
ejpam-4931	985	45	∥	∥	NUM
ejpam-4931	985	46	√	√	NUM
ejpam-4931	985	47	ξu∥	ξu∥	NOUN
ejpam-4931	985	48	l∞	l∞	NOUN
ejpam-4931	985	49	(	(	PUNCT
ejpam-4931	985	50	[	[	X
ejpam-4931	985	51	0,t	0,t	X
ejpam-4931	985	52	]	]	X
ejpam-4931	985	53	;	;	PUNCT
ejpam-4931	985	54	l2(ω	l2(ω	NUM
ejpam-4931	985	55	)	)	PUNCT
ejpam-4931	985	56	)	)	PUNCT
ejpam-4931	985	57	,	,	PUNCT
ejpam-4931	985	58	∥	∥	PROPN
ejpam-4931	985	59	3	3	NUM
ejpam-4931	985	60	√	√	NUM
ejpam-4931	985	61	ρu∥	ρu∥	NOUN
ejpam-4931	985	62	l3	l3	NOUN
ejpam-4931	985	63	(	(	PUNCT
ejpam-4931	985	64	[	[	X
ejpam-4931	985	65	0,t	0,t	X
ejpam-4931	985	66	]	]	X
ejpam-4931	985	67	;	;	PUNCT
ejpam-4931	985	68	l3(ω	l3(ω	X
ejpam-4931	985	69	)	)	PUNCT
ejpam-4931	985	70	)	)	PUNCT
ejpam-4931	985	71	≥	≥	NOUN
ejpam-4931	985	72	∥	∥	NUM
ejpam-4931	985	73	3	3	NUM
ejpam-4931	985	74	√	√	PROPN
ejpam-4931	985	75	ξu∥	ξu∥	PROPN
ejpam-4931	985	76	l3	l3	NOUN
ejpam-4931	985	77	(	(	PUNCT
ejpam-4931	985	78	[	[	X
ejpam-4931	985	79	0,t	0,t	X
ejpam-4931	985	80	]	]	X
ejpam-4931	985	81	;	;	PUNCT
ejpam-4931	985	82	l3(ω	l3(ω	X
ejpam-4931	985	83	)	)	PUNCT
ejpam-4931	985	84	)	)	PUNCT
ejpam-4931	985	85	,	,	PUNCT
ejpam-4931	985	86	∥ρdxu∥l2	∥ρdxu∥l2	NOUN
ejpam-4931	985	87	(	(	PUNCT
ejpam-4931	985	88	[	[	X
ejpam-4931	985	89	0,t	0,t	X
ejpam-4931	985	90	]	]	X
ejpam-4931	985	91	;	;	PUNCT
ejpam-4931	985	92	l2(ω	l2(ω	NUM
ejpam-4931	985	93	)	)	PUNCT
ejpam-4931	985	94	)	)	PUNCT
ejpam-4931	985	95	≥	≥	X
ejpam-4931	985	96	∥ξdxu∥l2	∥ξdxu∥l2	PROPN
ejpam-4931	985	97	(	(	PUNCT
ejpam-4931	985	98	[	[	X
ejpam-4931	985	99	0,t	0,t	X
ejpam-4931	985	100	]	]	X
ejpam-4931	985	101	;	;	PUNCT
ejpam-4931	985	102	l2(ω	l2(ω	NUM
ejpam-4931	985	103	)	)	PUNCT
ejpam-4931	985	104	)	)	PUNCT
ejpam-4931	985	105	,	,	PUNCT
ejpam-4931	985	106	∥√ρ∂yu∥l2	∥√ρ∂yu∥l2	NOUN
ejpam-4931	985	107	(	(	PUNCT
ejpam-4931	985	108	[	[	X
ejpam-4931	985	109	0,t	0,t	X
ejpam-4931	985	110	]	]	X
ejpam-4931	985	111	;	;	PUNCT
ejpam-4931	985	112	l2(ω	l2(ω	NUM
ejpam-4931	985	113	)	)	PUNCT
ejpam-4931	985	114	)	)	PUNCT
ejpam-4931	985	115	≥	≥	NOUN
ejpam-4931	985	116	∥	∥	NUM
ejpam-4931	985	117	√	√	ADP
ejpam-4931	985	118	ξ∂yu∥l2	ξ∂yu∥l2	PROPN
ejpam-4931	985	119	(	(	PUNCT
ejpam-4931	985	120	[	[	X
ejpam-4931	985	121	0,t	0,t	X
ejpam-4931	985	122	]	]	X
ejpam-4931	985	123	;	;	PUNCT
ejpam-4931	985	124	l2(ω	l2(ω	NUM
ejpam-4931	985	125	)	)	PUNCT
ejpam-4931	985	126	)	)	PUNCT
ejpam-4931	985	127	,	,	PUNCT
ejpam-4931	985	128	∥∂yρ∥l∞	∥∂yρ∥l∞	PROPN
ejpam-4931	985	129	(	(	PUNCT
ejpam-4931	985	130	[	[	X
ejpam-4931	985	131	0,t	0,t	X
ejpam-4931	985	132	]	]	X
ejpam-4931	985	133	;	;	PUNCT
ejpam-4931	985	134	l2(ω	l2(ω	NUM
ejpam-4931	985	135	)	)	PUNCT
ejpam-4931	985	136	)	)	PUNCT
ejpam-4931	985	137	=	=	SYM
ejpam-4931	985	138	1	1	NUM
ejpam-4931	985	139	2	2	NUM
ejpam-4931	985	140	g|ωx|	g|ωx|	NOUN
ejpam-4931	985	141	.	.	PUNCT
ejpam-4931	986	1	(	(	PUNCT
ejpam-4931	986	2	132	132	NUM
ejpam-4931	986	3	)	)	PUNCT
ejpam-4931	986	4	in	in	ADP
ejpam-4931	986	5	addition	addition	NOUN
ejpam-4931	986	6	,	,	PUNCT
ejpam-4931	986	7	∥√ρv∥2	∥√ρv∥2	X
ejpam-4931	986	8	l2	l2	NOUN
ejpam-4931	986	9	(	(	PUNCT
ejpam-4931	986	10	[	[	X
ejpam-4931	986	11	0,t	0,t	X
ejpam-4931	986	12	]	]	X
ejpam-4931	986	13	;	;	PUNCT
ejpam-4931	986	14	l2(ω	l2(ω	NUM
ejpam-4931	986	15	)	)	PUNCT
ejpam-4931	986	16	)	)	PUNCT
ejpam-4931	987	1	=	=	SYM
ejpam-4931	988	1	∫	∫	PROPN
ejpam-4931	988	2	t	t	PROPN
ejpam-4931	988	3	0	0	NUM
ejpam-4931	989	1	∫	∫	PROPN
ejpam-4931	989	2	1	1	NUM
ejpam-4931	989	3	0	0	NUM
ejpam-4931	989	4	∫	∫	PROPN
ejpam-4931	989	5	ωx	ωx	PROPN
ejpam-4931	989	6	|√ρv|2dxdydt	|√ρv|2dxdydt	PUNCT
ejpam-4931	989	7	=	=	SYM
ejpam-4931	989	8	∫	∫	PROPN
ejpam-4931	989	9	t	t	PROPN
ejpam-4931	989	10	0	0	NUM
ejpam-4931	990	1	∫	∫	PROPN
ejpam-4931	990	2	1	1	NUM
ejpam-4931	990	3	0	0	NUM
ejpam-4931	990	4	∫	∫	PROPN
ejpam-4931	990	5	ωx	ωx	PROPN
ejpam-4931	990	6	(	(	PUNCT
ejpam-4931	990	7	ξv2	ξv2	NOUN
ejpam-4931	990	8	+	+	CCONJ
ejpam-4931	990	9	ϕv2	ϕv2	ADJ
ejpam-4931	990	10	)	)	PUNCT
ejpam-4931	990	11	dxdydt	dxdydt	NOUN
ejpam-4931	990	12	≤	≤	NUM
ejpam-4931	990	13	2	2	NUM
ejpam-4931	990	14	∫	∫	NOUN
ejpam-4931	990	15	t	t	PROPN
ejpam-4931	990	16	0	0	NUM
ejpam-4931	991	1	∫	∫	PROPN
ejpam-4931	991	2	1	1	NUM
ejpam-4931	991	3	0	0	NUM
ejpam-4931	991	4	∫	∫	PROPN
ejpam-4931	991	5	ωx	ωx	PROPN
ejpam-4931	991	6	ξv2dxdydt+	ξv2dxdydt+	NUM
ejpam-4931	991	7	g	g	PROPN
ejpam-4931	991	8	∫	∫	PROPN
ejpam-4931	991	9	t	t	PROPN
ejpam-4931	991	10	0	0	NUM
ejpam-4931	991	11	∫	∫	PROPN
ejpam-4931	992	1	1	1	NUM
ejpam-4931	992	2	0	0	NUM
ejpam-4931	992	3	∫	∫	PROPN
ejpam-4931	992	4	ωx	ωx	PROPN
ejpam-4931	992	5	v2dxdydt	v2dxdydt	NOUN
ejpam-4931	992	6	(	(	PUNCT
ejpam-4931	992	7	133	133	NUM
ejpam-4931	992	8	)	)	PUNCT
ejpam-4931	992	9	and	and	CCONJ
ejpam-4931	992	10	∥√ρ∂yv∥2	∥√ρ∂yv∥2	PROPN
ejpam-4931	992	11	l2	l2	NOUN
ejpam-4931	992	12	(	(	PUNCT
ejpam-4931	992	13	[	[	X
ejpam-4931	992	14	0,t	0,t	X
ejpam-4931	992	15	]	]	X
ejpam-4931	992	16	;	;	PUNCT
ejpam-4931	992	17	l2(ω	l2(ω	NUM
ejpam-4931	992	18	)	)	PUNCT
ejpam-4931	992	19	)	)	PUNCT
ejpam-4931	993	1	=	=	SYM
ejpam-4931	994	1	∫	∫	PROPN
ejpam-4931	994	2	t	t	PROPN
ejpam-4931	994	3	0	0	NUM
ejpam-4931	995	1	∫	∫	PROPN
ejpam-4931	995	2	1	1	NUM
ejpam-4931	995	3	0	0	NUM
ejpam-4931	995	4	∫	∫	PROPN
ejpam-4931	995	5	ωx	ωx	PROPN
ejpam-4931	995	6	|√ρ∂yv|2dxdydt	|√ρ∂yv|2dxdydt	PROPN
ejpam-4931	995	7	≤	≤	NUM
ejpam-4931	995	8	2	2	NUM
ejpam-4931	995	9	∫	∫	NOUN
ejpam-4931	995	10	t	t	PROPN
ejpam-4931	995	11	0	0	NUM
ejpam-4931	995	12	∫	∫	PROPN
ejpam-4931	995	13	1	1	NUM
ejpam-4931	995	14	0	0	NUM
ejpam-4931	995	15	∫	∫	PROPN
ejpam-4931	995	16	ωx	ωx	PROPN
ejpam-4931	995	17	(	(	PUNCT
ejpam-4931	995	18	ξ(∂yv	ξ(∂yv	PROPN
ejpam-4931	995	19	)	)	PUNCT
ejpam-4931	995	20	2	2	NUM
ejpam-4931	995	21	+	+	CCONJ
ejpam-4931	995	22	ϕ(∂yv	ϕ(∂yv	CCONJ
ejpam-4931	995	23	)	)	PUNCT
ejpam-4931	995	24	2	2	X
ejpam-4931	995	25	)	)	PUNCT
ejpam-4931	995	26	dxdydt	dxdydt	NOUN
ejpam-4931	995	27	≤	≤	NUM
ejpam-4931	996	1	c	c	PROPN
ejpam-4931	996	2	∫	∫	PROPN
ejpam-4931	996	3	t	t	PROPN
ejpam-4931	996	4	0	0	NUM
ejpam-4931	996	5	∫	∫	PROPN
ejpam-4931	996	6	1	1	NUM
ejpam-4931	996	7	0	0	NUM
ejpam-4931	996	8	∫	∫	PROPN
ejpam-4931	996	9	ωx	ωx	PROPN
ejpam-4931	996	10	(	(	PUNCT
ejpam-4931	996	11	√	√	NUM
ejpam-4931	996	12	ξ∂yv	ξ∂yv	NOUN
ejpam-4931	996	13	)	)	PUNCT
ejpam-4931	996	14	2dxdydt+	2dxdydt+	NOUN
ejpam-4931	996	15	g	g	NOUN
ejpam-4931	996	16	∫	∫	PROPN
ejpam-4931	996	17	t	t	PROPN
ejpam-4931	996	18	0	0	NUM
ejpam-4931	997	1	∫	∫	PROPN
ejpam-4931	997	2	1	1	NUM
ejpam-4931	997	3	0	0	NUM
ejpam-4931	997	4	∫	∫	PROPN
ejpam-4931	997	5	ωx	ωx	PROPN
ejpam-4931	997	6	(	(	PUNCT
ejpam-4931	997	7	∂yv	∂yv	PROPN
ejpam-4931	997	8	)	)	PUNCT
ejpam-4931	997	9	2dxdydt	2dxdydt	NOUN
ejpam-4931	997	10	.	.	PUNCT
ejpam-4931	998	1	(	(	PUNCT
ejpam-4931	998	2	134	134	NUM
ejpam-4931	998	3	)	)	PUNCT
ejpam-4931	998	4	references	reference	NOUN
ejpam-4931	998	5	2284	2284	NUM
ejpam-4931	998	6	with	with	ADP
ejpam-4931	998	7	all	all	PRON
ejpam-4931	998	8	of	of	ADP
ejpam-4931	998	9	the	the	DET
ejpam-4931	998	10	above	above	ADJ
ejpam-4931	998	11	estimates	estimate	NOUN
ejpam-4931	998	12	,	,	PUNCT
ejpam-4931	998	13	the	the	DET
ejpam-4931	998	14	theorem	theorem	NOUN
ejpam-4931	998	15	2	2	NUM
ejpam-4931	998	16	is	be	AUX
ejpam-4931	998	17	proved	prove	VERB
ejpam-4931	998	18	,	,	PUNCT
ejpam-4931	998	19	since	since	SCONJ
ejpam-4931	998	20	(	(	PUNCT
ejpam-4931	998	21	ρ	ρ	PROPN
ejpam-4931	998	22	,	,	PUNCT
ejpam-4931	998	23	u	u	NOUN
ejpam-4931	998	24	,	,	PUNCT
ejpam-4931	998	25	v	v	NOUN
ejpam-4931	998	26	)	)	PUNCT
ejpam-4931	998	27	satisfies	satisfy	VERB
ejpam-4931	998	28	the	the	DET
ejpam-4931	998	29	conditions	condition	NOUN
ejpam-4931	998	30	of	of	ADP
ejpam-4931	998	31	definition	definition	NOUN
ejpam-4931	998	32	2.1	2.1	NUM
ejpam-4931	998	33	.	.	PUNCT
ejpam-4931	999	1	thus	thus	ADV
ejpam-4931	999	2	our	our	PRON
ejpam-4931	999	3	initial	initial	ADJ
ejpam-4931	999	4	system	system	NOUN
ejpam-4931	999	5	(	(	PUNCT
ejpam-4931	999	6	1	1	X
ejpam-4931	999	7	)	)	PUNCT
ejpam-4931	999	8	admits	admit	VERB
ejpam-4931	999	9	a	a	DET
ejpam-4931	999	10	global	global	ADJ
ejpam-4931	999	11	weak	weak	ADJ
ejpam-4931	999	12	solution	solution	NOUN
ejpam-4931	999	13	.	.	PUNCT
ejpam-4931	1000	1	6	6	X
ejpam-4931	1000	2	.	.	X
ejpam-4931	1000	3	conclusion	conclusion	NOUN
ejpam-4931	1000	4	in	in	ADP
ejpam-4931	1000	5	this	this	DET
ejpam-4931	1000	6	paper	paper	NOUN
ejpam-4931	1000	7	,	,	PUNCT
ejpam-4931	1000	8	we	we	PRON
ejpam-4931	1000	9	discussed	discuss	VERB
ejpam-4931	1000	10	in	in	ADP
ejpam-4931	1000	11	dimension	dimension	NOUN
ejpam-4931	1000	12	d	d	PROPN
ejpam-4931	1000	13	=	=	SYM
ejpam-4931	1000	14	3	3	NUM
ejpam-4931	1000	15	,	,	PUNCT
ejpam-4931	1000	16	the	the	DET
ejpam-4931	1000	17	existence	existence	NOUN
ejpam-4931	1000	18	of	of	ADP
ejpam-4931	1000	19	global	global	ADJ
ejpam-4931	1000	20	weak	weak	ADJ
ejpam-4931	1000	21	solutions	solution	NOUN
ejpam-4931	1000	22	to	to	ADP
ejpam-4931	1000	23	the	the	DET
ejpam-4931	1000	24	three	three	NUM
ejpam-4931	1000	25	-	-	PUNCT
ejpam-4931	1000	26	dimensional	dimensional	ADJ
ejpam-4931	1000	27	compressible	compressible	ADJ
ejpam-4931	1000	28	primitive	primitive	ADJ
ejpam-4931	1000	29	equations	equation	NOUN
ejpam-4931	1000	30	of	of	ADP
ejpam-4931	1000	31	atmospheric	atmospheric	ADJ
ejpam-4931	1000	32	dynamics	dynamic	NOUN
ejpam-4931	1000	33	with	with	ADP
ejpam-4931	1000	34	degenerate	degenerate	ADJ
ejpam-4931	1000	35	viscosity	viscosity	NOUN
ejpam-4931	1000	36	density	density	NOUN
ejpam-4931	1000	37	-	-	PUNCT
ejpam-4931	1000	38	dependent	dependent	ADJ
ejpam-4931	1000	39	for	for	ADP
ejpam-4931	1000	40	large	large	ADJ
ejpam-4931	1000	41	initial	initial	ADJ
ejpam-4931	1000	42	data	datum	NOUN
ejpam-4931	1000	43	.	.	PUNCT
ejpam-4931	1001	1	we	we	PRON
ejpam-4931	1001	2	have	have	AUX
ejpam-4931	1001	3	proven	prove	VERB
ejpam-4931	1001	4	that	that	SCONJ
ejpam-4931	1001	5	the	the	DET
ejpam-4931	1001	6	weak	weak	ADJ
ejpam-4931	1001	7	solutions	solution	NOUN
ejpam-4931	1001	8	satisfy	satisfy	VERB
ejpam-4931	1001	9	the	the	DET
ejpam-4931	1001	10	basic	basic	ADJ
ejpam-4931	1001	11	energy	energy	NOUN
ejpam-4931	1001	12	inequality	inequality	NOUN
ejpam-4931	1001	13	and	and	CCONJ
ejpam-4931	1001	14	the	the	DET
ejpam-4931	1001	15	bresch	bresch	NOUN
ejpam-4931	1001	16	-	-	PUNCT
ejpam-4931	1001	17	desjardins	desjardins	PROPN
ejpam-4931	1001	18	entropy	entropy	NOUN
ejpam-4931	1001	19	inequality	inequality	NOUN
ejpam-4931	1001	20	.	.	PUNCT
ejpam-4931	1002	1	we	we	PRON
ejpam-4931	1002	2	have	have	AUX
ejpam-4931	1002	3	obtained	obtain	VERB
ejpam-4931	1002	4	the	the	DET
ejpam-4931	1002	5	global	global	ADJ
ejpam-4931	1002	6	existence	existence	NOUN
ejpam-4931	1002	7	of	of	ADP
ejpam-4931	1002	8	weak	weak	ADJ
ejpam-4931	1002	9	solutions	solution	NOUN
ejpam-4931	1002	10	of	of	ADP
ejpam-4931	1002	11	(	(	PUNCT
ejpam-4931	1002	12	1	1	NUM
ejpam-4931	1002	13	)	)	PUNCT
ejpam-4931	1002	14	by	by	ADP
ejpam-4931	1002	15	vanishing	vanish	VERB
ejpam-4931	1002	16	the	the	DET
ejpam-4931	1002	17	parameters	parameter	NOUN
ejpam-4931	1002	18	in	in	ADP
ejpam-4931	1002	19	our	our	PRON
ejpam-4931	1002	20	approximate	approximate	ADJ
ejpam-4931	1002	21	system	system	NOUN
ejpam-4931	1002	22	step	step	NOUN
ejpam-4931	1002	23	by	by	ADP
ejpam-4931	1002	24	step	step	NOUN
ejpam-4931	1002	25	.	.	PUNCT
ejpam-4931	1003	1	references	reference	NOUN
ejpam-4931	1003	2	[	[	X
ejpam-4931	1003	3	1	1	NUM
ejpam-4931	1003	4	]	]	PUNCT
ejpam-4931	1003	5	didier	didier	NOUN
ejpam-4931	1003	6	bresch	bresch	PROPN
ejpam-4931	1003	7	and	and	CCONJ
ejpam-4931	1003	8	benôıt	benôıt	PROPN
ejpam-4931	1003	9	desjardins	desjardin	VERB
ejpam-4931	1003	10	.	.	PUNCT
ejpam-4931	1004	1	on	on	ADP
ejpam-4931	1004	2	the	the	DET
ejpam-4931	1004	3	construction	construction	NOUN
ejpam-4931	1004	4	of	of	ADP
ejpam-4931	1004	5	approximate	approximate	ADJ
ejpam-4931	1004	6	solutions	solution	NOUN
ejpam-4931	1004	7	for	for	ADP
ejpam-4931	1004	8	the	the	DET
ejpam-4931	1004	9	2d	2d	NUM
ejpam-4931	1004	10	viscous	viscous	ADJ
ejpam-4931	1004	11	shallow	shallow	ADJ
ejpam-4931	1004	12	water	water	NOUN
ejpam-4931	1004	13	model	model	NOUN
ejpam-4931	1004	14	and	and	CCONJ
ejpam-4931	1004	15	for	for	ADP
ejpam-4931	1004	16	compressible	compressible	ADJ
ejpam-4931	1004	17	navier	navier	NOUN
ejpam-4931	1004	18	-	-	PUNCT
ejpam-4931	1004	19	stokes	stoke	NOUN
ejpam-4931	1004	20	models	model	NOUN
ejpam-4931	1004	21	.	.	PUNCT
ejpam-4931	1005	1	j.	j.	PROPN
ejpam-4931	1005	2	math	math	PROPN
ejpam-4931	1005	3	.	.	PUNCT
ejpam-4931	1006	1	pures	pure	NOUN
ejpam-4931	1006	2	appl	appl	PROPN
ejpam-4931	1006	3	.	.	PUNCT
ejpam-4931	1007	1	(	(	PUNCT
ejpam-4931	1007	2	9	9	NUM
ejpam-4931	1007	3	)	)	PUNCT
ejpam-4931	1007	4	,	,	PUNCT
ejpam-4931	1007	5	86(4):362–368	86(4):362–368	PROPN
ejpam-4931	1007	6	,	,	PUNCT
ejpam-4931	1007	7	2006	2006	NUM
ejpam-4931	1007	8	.	.	PUNCT
ejpam-4931	1008	1	[	[	X
ejpam-4931	1008	2	2	2	NUM
ejpam-4931	1008	3	]	]	PUNCT
ejpam-4931	1008	4	didier	didier	NOUN
ejpam-4931	1008	5	bresch	bresch	PROPN
ejpam-4931	1008	6	,	,	PUNCT
ejpam-4931	1008	7	benôıt	benôıt	PROPN
ejpam-4931	1008	8	desjardins	desjardin	VERB
ejpam-4931	1008	9	,	,	PUNCT
ejpam-4931	1008	10	and	and	CCONJ
ejpam-4931	1008	11	chi	chi	ADJ
ejpam-4931	1008	12	-	-	PUNCT
ejpam-4931	1008	13	kun	kun	NOUN
ejpam-4931	1008	14	lin	lin	PROPN
ejpam-4931	1008	15	.	.	PUNCT
ejpam-4931	1009	1	on	on	ADP
ejpam-4931	1009	2	some	some	DET
ejpam-4931	1009	3	compressible	compressible	ADJ
ejpam-4931	1009	4	fluid	fluid	NOUN
ejpam-4931	1009	5	models	model	NOUN
ejpam-4931	1009	6	:	:	PUNCT
ejpam-4931	1009	7	korteweg	korteweg	NOUN
ejpam-4931	1009	8	,	,	PUNCT
ejpam-4931	1009	9	lubrication	lubrication	NOUN
ejpam-4931	1009	10	,	,	PUNCT
ejpam-4931	1009	11	and	and	CCONJ
ejpam-4931	1009	12	shallow	shallow	ADJ
ejpam-4931	1009	13	water	water	NOUN
ejpam-4931	1009	14	systems	system	NOUN
ejpam-4931	1009	15	.	.	PUNCT
ejpam-4931	1010	1	commun	commun	PROPN
ejpam-4931	1010	2	.	.	PUNCT
ejpam-4931	1011	1	partial	partial	ADJ
ejpam-4931	1011	2	differ	differ	VERB
ejpam-4931	1011	3	.	.	PUNCT
ejpam-4931	1012	1	equations	equation	NOUN
ejpam-4931	1012	2	,	,	PUNCT
ejpam-4931	1012	3	28(3	28(3	NUM
ejpam-4931	1012	4	-	-	SYM
ejpam-4931	1012	5	4):843–868	4):843–868	NUM
ejpam-4931	1012	6	,	,	PUNCT
ejpam-4931	1012	7	2003	2003	NUM
ejpam-4931	1012	8	.	.	PUNCT
ejpam-4931	1013	1	[	[	X
ejpam-4931	1013	2	3	3	X
ejpam-4931	1013	3	]	]	X
ejpam-4931	1013	4	mehmet	mehmet	PROPN
ejpam-4931	1013	5	ersoy	ersoy	PROPN
ejpam-4931	1013	6	,	,	PUNCT
ejpam-4931	1013	7	timack	timack	VERB
ejpam-4931	1013	8	ngom	ngom	ADV
ejpam-4931	1013	9	,	,	PUNCT
ejpam-4931	1013	10	and	and	CCONJ
ejpam-4931	1013	11	mamadou	mamadou	PROPN
ejpam-4931	1013	12	sy	sy	PROPN
ejpam-4931	1013	13	.	.	PROPN
ejpam-4931	1013	14	compressible	compressible	ADJ
ejpam-4931	1013	15	primitive	primitive	ADJ
ejpam-4931	1013	16	equations	equation	NOUN
ejpam-4931	1013	17	:	:	PUNCT
ejpam-4931	1013	18	formal	formal	ADJ
ejpam-4931	1013	19	derivation	derivation	NOUN
ejpam-4931	1013	20	and	and	CCONJ
ejpam-4931	1013	21	stability	stability	NOUN
ejpam-4931	1013	22	of	of	ADP
ejpam-4931	1013	23	weak	weak	ADJ
ejpam-4931	1013	24	solutions	solution	NOUN
ejpam-4931	1013	25	.	.	PUNCT
ejpam-4931	1014	1	nonlinearity	nonlinearity	NOUN
ejpam-4931	1014	2	,	,	PUNCT
ejpam-4931	1014	3	24(1):79–96	24(1):79–96	NUM
ejpam-4931	1014	4	,	,	PUNCT
ejpam-4931	1014	5	2011	2011	NUM
ejpam-4931	1014	6	.	.	PUNCT
ejpam-4931	1015	1	[	[	X
ejpam-4931	1015	2	4	4	NUM
ejpam-4931	1015	3	]	]	PUNCT
ejpam-4931	1015	4	eduard	eduard	PROPN
ejpam-4931	1015	5	feireisl	feireisl	PROPN
ejpam-4931	1015	6	.	.	PUNCT
ejpam-4931	1016	1	dynamics	dynamic	NOUN
ejpam-4931	1016	2	of	of	ADP
ejpam-4931	1016	3	viscous	viscous	ADJ
ejpam-4931	1016	4	compressible	compressible	ADJ
ejpam-4931	1016	5	fluids	fluid	NOUN
ejpam-4931	1016	6	.	.	PUNCT
ejpam-4931	1016	7	,	,	PUNCT
ejpam-4931	1016	8	volume	volume	NOUN
ejpam-4931	1016	9	26	26	NUM
ejpam-4931	1016	10	of	of	ADP
ejpam-4931	1016	11	oxf	oxf	PROPN
ejpam-4931	1016	12	.	.	PUNCT
ejpam-4931	1017	1	lect	lect	PROPN
ejpam-4931	1017	2	.	.	PUNCT
ejpam-4931	1018	1	ser	ser	PROPN
ejpam-4931	1018	2	.	.	PROPN
ejpam-4931	1018	3	math	math	PROPN
ejpam-4931	1018	4	.	.	PUNCT
ejpam-4931	1019	1	appl	appl	PROPN
ejpam-4931	1019	2	.	.	PUNCT
ejpam-4931	1020	1	oxford	oxford	PROPN
ejpam-4931	1020	2	:	:	PUNCT
ejpam-4931	1020	3	oxford	oxford	PROPN
ejpam-4931	1020	4	university	university	PROPN
ejpam-4931	1020	5	press	press	NOUN
ejpam-4931	1020	6	,	,	PUNCT
ejpam-4931	1020	7	2004	2004	NUM
ejpam-4931	1020	8	.	.	PUNCT
ejpam-4931	1021	1	[	[	X
ejpam-4931	1021	2	5	5	NUM
ejpam-4931	1021	3	]	]	PUNCT
ejpam-4931	1021	4	eduard	eduard	PROPN
ejpam-4931	1021	5	feireisl	feireisl	PROPN
ejpam-4931	1021	6	,	,	PUNCT
ejpam-4931	1021	7	antońın	antońın	X
ejpam-4931	1021	8	novotný	novotný	NOUN
ejpam-4931	1021	9	,	,	PUNCT
ejpam-4931	1021	10	and	and	CCONJ
ejpam-4931	1021	11	hana	hana	PROPN
ejpam-4931	1021	12	petzeltová.	petzeltová.	PROPN
ejpam-4931	1021	13	on	on	ADP
ejpam-4931	1021	14	the	the	DET
ejpam-4931	1021	15	existence	existence	NOUN
ejpam-4931	1021	16	of	of	ADP
ejpam-4931	1021	17	globally	globally	ADV
ejpam-4931	1021	18	defined	define	VERB
ejpam-4931	1021	19	weak	weak	ADJ
ejpam-4931	1021	20	solutions	solution	NOUN
ejpam-4931	1021	21	to	to	ADP
ejpam-4931	1021	22	the	the	DET
ejpam-4931	1021	23	navier	navier	NOUN
ejpam-4931	1021	24	-	-	PUNCT
ejpam-4931	1021	25	stokes	stokes	PROPN
ejpam-4931	1021	26	equations	equation	NOUN
ejpam-4931	1021	27	.	.	PUNCT
ejpam-4931	1022	1	j.	j.	PROPN
ejpam-4931	1022	2	math	math	PROPN
ejpam-4931	1022	3	.	.	PUNCT
ejpam-4931	1023	1	fluid	fluid	ADJ
ejpam-4931	1023	2	mech	mech	NOUN
ejpam-4931	1023	3	.	.	PUNCT
ejpam-4931	1023	4	,	,	PUNCT
ejpam-4931	1023	5	3(4):358–392	3(4):358–392	NUM
ejpam-4931	1023	6	,	,	PUNCT
ejpam-4931	1023	7	2001	2001	NUM
ejpam-4931	1023	8	.	.	PUNCT
ejpam-4931	1024	1	[	[	X
ejpam-4931	1024	2	6	6	NUM
ejpam-4931	1024	3	]	]	X
ejpam-4931	1024	4	hongjun	hongjun	NOUN
ejpam-4931	1024	5	gao	gao	PROPN
ejpam-4931	1024	6	,	,	PUNCT
ejpam-4931	1024	7	šárka	šárka	NOUN
ejpam-4931	1024	8	nečasová	nečasová	NUM
ejpam-4931	1024	9	,	,	PUNCT
ejpam-4931	1024	10	and	and	CCONJ
ejpam-4931	1024	11	tong	tong	PROPN
ejpam-4931	1024	12	tang	tang	PROPN
ejpam-4931	1024	13	.	.	PUNCT
ejpam-4931	1025	1	on	on	ADP
ejpam-4931	1025	2	the	the	DET
ejpam-4931	1025	3	hydrostatic	hydrostatic	ADJ
ejpam-4931	1025	4	approximation	approximation	NOUN
ejpam-4931	1025	5	of	of	ADP
ejpam-4931	1025	6	compressible	compressible	ADJ
ejpam-4931	1025	7	anisotropic	anisotropic	NOUN
ejpam-4931	1025	8	navier	navier	NOUN
ejpam-4931	1025	9	-	-	PUNCT
ejpam-4931	1025	10	stokes	stoke	NOUN
ejpam-4931	1025	11	equations	equation	NOUN
ejpam-4931	1025	12	.	.	PUNCT
ejpam-4931	1026	1	c.	c.	PROPN
ejpam-4931	1026	2	r.	r.	PROPN
ejpam-4931	1026	3	,	,	PUNCT
ejpam-4931	1026	4	math	math	NOUN
ejpam-4931	1026	5	.	.	PROPN
ejpam-4931	1026	6	,	,	PUNCT
ejpam-4931	1026	7	acad	acad	PROPN
ejpam-4931	1026	8	.	.	PUNCT
ejpam-4931	1027	1	sci	sci	PROPN
ejpam-4931	1027	2	.	.	PROPN
ejpam-4931	1027	3	paris	paris	PROPN
ejpam-4931	1027	4	,	,	PUNCT
ejpam-4931	1027	5	359(6):639–644	359(6):639–644	NUM
ejpam-4931	1027	6	,	,	PUNCT
ejpam-4931	1027	7	2021	2021	NUM
ejpam-4931	1027	8	.	.	PUNCT
ejpam-4931	1028	1	[	[	X
ejpam-4931	1028	2	7	7	X
ejpam-4931	1028	3	]	]	X
ejpam-4931	1028	4	m.	m.	NOUN
ejpam-4931	1028	5	gisclon	gisclon	NOUN
ejpam-4931	1028	6	and	and	CCONJ
ejpam-4931	1028	7	i.	i.	PROPN
ejpam-4931	1028	8	lacroix	lacroix	PROPN
ejpam-4931	1028	9	-	-	PUNCT
ejpam-4931	1028	10	violet	violet	NOUN
ejpam-4931	1028	11	.	.	PUNCT
ejpam-4931	1029	1	about	about	ADP
ejpam-4931	1029	2	the	the	DET
ejpam-4931	1029	3	barotropic	barotropic	ADJ
ejpam-4931	1029	4	compressible	compressible	ADJ
ejpam-4931	1029	5	quantum	quantum	ADJ
ejpam-4931	1029	6	navierstokes	navierstoke	NOUN
ejpam-4931	1029	7	equations	equation	NOUN
ejpam-4931	1029	8	.	.	PUNCT
ejpam-4931	1030	1	nonlinear	nonlinear	ADJ
ejpam-4931	1030	2	anal	anal	PROPN
ejpam-4931	1030	3	.	.	PUNCT
ejpam-4931	1030	4	,	,	PUNCT
ejpam-4931	1030	5	theory	theory	NOUN
ejpam-4931	1030	6	methods	method	NOUN
ejpam-4931	1030	7	appl	appl	PROPN
ejpam-4931	1030	8	.	.	PROPN
ejpam-4931	1030	9	,	,	PUNCT
ejpam-4931	1030	10	ser	ser	PROPN
ejpam-4931	1030	11	.	.	PUNCT
ejpam-4931	1031	1	a	a	DET
ejpam-4931	1031	2	,	,	PUNCT
ejpam-4931	1031	3	theory	theory	NOUN
ejpam-4931	1031	4	methods	method	NOUN
ejpam-4931	1031	5	,	,	PUNCT
ejpam-4931	1031	6	128:106–121	128:106–121	NUM
ejpam-4931	1031	7	,	,	PUNCT
ejpam-4931	1031	8	2015	2015	NUM
ejpam-4931	1031	9	.	.	PUNCT
ejpam-4931	1032	1	[	[	X
ejpam-4931	1032	2	8	8	NUM
ejpam-4931	1032	3	]	]	X
ejpam-4931	1032	4	quansen	quansen	PROPN
ejpam-4931	1032	5	jiu	jiu	PROPN
ejpam-4931	1032	6	,	,	PUNCT
ejpam-4931	1032	7	mingjie	mingjie	PROPN
ejpam-4931	1032	8	li	li	PROPN
ejpam-4931	1032	9	,	,	PUNCT
ejpam-4931	1032	10	and	and	CCONJ
ejpam-4931	1032	11	fengchao	fengchao	PROPN
ejpam-4931	1032	12	wang	wang	PROPN
ejpam-4931	1032	13	.	.	PUNCT
ejpam-4931	1033	1	uniqueness	uniqueness	NOUN
ejpam-4931	1033	2	of	of	ADP
ejpam-4931	1033	3	the	the	DET
ejpam-4931	1033	4	global	global	ADJ
ejpam-4931	1033	5	weak	weak	ADJ
ejpam-4931	1033	6	solutions	solution	NOUN
ejpam-4931	1033	7	to	to	ADP
ejpam-4931	1033	8	2d	2d	NUM
ejpam-4931	1033	9	compressible	compressible	ADJ
ejpam-4931	1033	10	primitive	primitive	ADJ
ejpam-4931	1033	11	equations	equation	NOUN
ejpam-4931	1033	12	.	.	PUNCT
ejpam-4931	1034	1	j.	j.	PROPN
ejpam-4931	1034	2	math	math	PROPN
ejpam-4931	1034	3	.	.	PUNCT
ejpam-4931	1035	1	anal	anal	PROPN
ejpam-4931	1035	2	.	.	PUNCT
ejpam-4931	1036	1	appl	appl	PROPN
ejpam-4931	1036	2	.	.	PROPN
ejpam-4931	1036	3	,	,	PUNCT
ejpam-4931	1036	4	461(2):1653–1671	461(2):1653–1671	NOUN
ejpam-4931	1036	5	,	,	PUNCT
ejpam-4931	1036	6	2018	2018	NUM
ejpam-4931	1036	7	.	.	PUNCT
ejpam-4931	1037	1	[	[	X
ejpam-4931	1037	2	9	9	NUM
ejpam-4931	1037	3	]	]	PUNCT
ejpam-4931	1037	4	ansgar	ansgar	PROPN
ejpam-4931	1037	5	jüngel	jüngel	PROPN
ejpam-4931	1037	6	.	.	PUNCT
ejpam-4931	1038	1	global	global	ADJ
ejpam-4931	1038	2	weak	weak	ADJ
ejpam-4931	1038	3	solutions	solution	NOUN
ejpam-4931	1038	4	to	to	PART
ejpam-4931	1038	5	compressible	compressible	ADJ
ejpam-4931	1038	6	navier	navier	NOUN
ejpam-4931	1038	7	-	-	PUNCT
ejpam-4931	1038	8	stokes	stoke	NOUN
ejpam-4931	1038	9	equations	equation	NOUN
ejpam-4931	1038	10	for	for	ADP
ejpam-4931	1038	11	quantum	quantum	NOUN
ejpam-4931	1038	12	fluids	fluid	NOUN
ejpam-4931	1038	13	.	.	PUNCT
ejpam-4931	1039	1	siam	siam	PROPN
ejpam-4931	1039	2	j.	j.	PROPN
ejpam-4931	1039	3	math	math	PROPN
ejpam-4931	1039	4	.	.	PUNCT
ejpam-4931	1040	1	anal	anal	PROPN
ejpam-4931	1040	2	.	.	PUNCT
ejpam-4931	1040	3	,	,	PUNCT
ejpam-4931	1040	4	42(3):1025–1045	42(3):1025–1045	NUM
ejpam-4931	1040	5	,	,	PUNCT
ejpam-4931	1040	6	2010	2010	NUM
ejpam-4931	1040	7	.	.	PUNCT
ejpam-4931	1041	1	references	reference	NOUN
ejpam-4931	1041	2	2285	2285	NUM
ejpam-4931	1042	1	[	[	X
ejpam-4931	1042	2	10	10	NUM
ejpam-4931	1042	3	]	]	PUNCT
ejpam-4931	1042	4	jinkai	jinkai	PROPN
ejpam-4931	1042	5	li	li	PROPN
ejpam-4931	1042	6	and	and	CCONJ
ejpam-4931	1042	7	edriss	edriss	PROPN
ejpam-4931	1042	8	s.	s.	PROPN
ejpam-4931	1042	9	titi	titi	PROPN
ejpam-4931	1042	10	.	.	PUNCT
ejpam-4931	1043	1	the	the	DET
ejpam-4931	1043	2	primitive	primitive	ADJ
ejpam-4931	1043	3	equations	equation	NOUN
ejpam-4931	1043	4	as	as	ADP
ejpam-4931	1043	5	the	the	DET
ejpam-4931	1043	6	small	small	ADJ
ejpam-4931	1043	7	aspect	aspect	NOUN
ejpam-4931	1043	8	ratio	ratio	NOUN
ejpam-4931	1043	9	limit	limit	NOUN
ejpam-4931	1043	10	of	of	ADP
ejpam-4931	1043	11	the	the	DET
ejpam-4931	1043	12	navier	navier	NOUN
ejpam-4931	1043	13	-	-	PUNCT
ejpam-4931	1043	14	stokes	stoke	NOUN
ejpam-4931	1043	15	equations	equation	NOUN
ejpam-4931	1043	16	:	:	PUNCT
ejpam-4931	1043	17	rigorous	rigorous	ADJ
ejpam-4931	1043	18	justification	justification	NOUN
ejpam-4931	1043	19	of	of	ADP
ejpam-4931	1043	20	the	the	DET
ejpam-4931	1043	21	hydrostatic	hydrostatic	ADJ
ejpam-4931	1043	22	approximation	approximation	NOUN
ejpam-4931	1043	23	.	.	PUNCT
ejpam-4931	1044	1	j.	j.	PROPN
ejpam-4931	1044	2	math	math	PROPN
ejpam-4931	1044	3	.	.	PUNCT
ejpam-4931	1045	1	pures	pure	NOUN
ejpam-4931	1045	2	appl	appl	PROPN
ejpam-4931	1045	3	.	.	PUNCT
ejpam-4931	1046	1	(	(	PUNCT
ejpam-4931	1046	2	9	9	NUM
ejpam-4931	1046	3	)	)	PUNCT
ejpam-4931	1046	4	,	,	PUNCT
ejpam-4931	1046	5	124:30–58	124:30–58	NUM
ejpam-4931	1046	6	,	,	PUNCT
ejpam-4931	1046	7	2019	2019	NUM
ejpam-4931	1046	8	.	.	PUNCT
ejpam-4931	1047	1	[	[	X
ejpam-4931	1047	2	11	11	NUM
ejpam-4931	1047	3	]	]	PUNCT
ejpam-4931	1047	4	xin	xin	PROPN
ejpam-4931	1047	5	liu	liu	PROPN
ejpam-4931	1047	6	and	and	CCONJ
ejpam-4931	1047	7	edriss	edriss	VERB
ejpam-4931	1047	8	s.	s.	PROPN
ejpam-4931	1047	9	titi	titi	PROPN
ejpam-4931	1047	10	.	.	PROPN
ejpam-4931	1047	11	global	global	ADJ
ejpam-4931	1047	12	existence	existence	NOUN
ejpam-4931	1047	13	of	of	ADP
ejpam-4931	1047	14	weak	weak	ADJ
ejpam-4931	1047	15	solutions	solution	NOUN
ejpam-4931	1047	16	to	to	ADP
ejpam-4931	1047	17	the	the	DET
ejpam-4931	1047	18	compressible	compressible	ADJ
ejpam-4931	1047	19	primitive	primitive	ADJ
ejpam-4931	1047	20	equations	equation	NOUN
ejpam-4931	1047	21	of	of	ADP
ejpam-4931	1047	22	atmospheric	atmospheric	ADJ
ejpam-4931	1047	23	dynamics	dynamic	NOUN
ejpam-4931	1047	24	with	with	ADP
ejpam-4931	1047	25	degenerate	degenerate	ADJ
ejpam-4931	1047	26	viscosities	viscosity	NOUN
ejpam-4931	1047	27	.	.	PUNCT
ejpam-4931	1048	1	siam	siam	PROPN
ejpam-4931	1048	2	j.	j.	PROPN
ejpam-4931	1048	3	math	math	PROPN
ejpam-4931	1048	4	.	.	PUNCT
ejpam-4931	1049	1	anal	anal	PROPN
ejpam-4931	1049	2	.	.	PROPN
ejpam-4931	1049	3	,	,	PUNCT
ejpam-4931	1049	4	51(3):1913–1964	51(3):1913–1964	NUM
ejpam-4931	1049	5	,	,	PUNCT
ejpam-4931	1049	6	2019	2019	NUM
ejpam-4931	1049	7	.	.	PUNCT
ejpam-4931	1050	1	[	[	X
ejpam-4931	1050	2	12	12	NUM
ejpam-4931	1050	3	]	]	X
ejpam-4931	1050	4	alessandra	alessandra	PROPN
ejpam-4931	1050	5	lunardi	lunardi	PROPN
ejpam-4931	1050	6	.	.	PUNCT
ejpam-4931	1051	1	analytic	analytic	ADJ
ejpam-4931	1051	2	semigroups	semigroup	NOUN
ejpam-4931	1051	3	and	and	CCONJ
ejpam-4931	1051	4	optimal	optimal	ADJ
ejpam-4931	1051	5	regularity	regularity	NOUN
ejpam-4931	1051	6	in	in	ADP
ejpam-4931	1051	7	parabolic	parabolic	ADJ
ejpam-4931	1051	8	problems	problem	NOUN
ejpam-4931	1051	9	,	,	PUNCT
ejpam-4931	1051	10	volume	volume	NOUN
ejpam-4931	1051	11	16	16	NUM
ejpam-4931	1051	12	of	of	ADP
ejpam-4931	1051	13	prog	prog	PROPN
ejpam-4931	1051	14	.	.	PUNCT
ejpam-4931	1052	1	nonlinear	nonlinear	NOUN
ejpam-4931	1052	2	differ	differ	VERB
ejpam-4931	1052	3	.	.	PUNCT
ejpam-4931	1053	1	equ	equ	PROPN
ejpam-4931	1053	2	.	.	PUNCT
ejpam-4931	1053	3	appl	appl	PROPN
ejpam-4931	1053	4	.	.	PUNCT
ejpam-4931	1054	1	basel	basel	PROPN
ejpam-4931	1054	2	:	:	PUNCT
ejpam-4931	1054	3	birkhäuser	birkhäuser	NOUN
ejpam-4931	1054	4	,	,	PUNCT
ejpam-4931	1054	5	1995	1995	NUM
ejpam-4931	1054	6	.	.	PUNCT
ejpam-4931	1055	1	[	[	X
ejpam-4931	1055	2	13	13	NUM
ejpam-4931	1055	3	]	]	PUNCT
ejpam-4931	1055	4	a.	a.	NOUN
ejpam-4931	1055	5	mellet	mellet	NOUN
ejpam-4931	1055	6	and	and	CCONJ
ejpam-4931	1055	7	a.	a.	NOUN
ejpam-4931	1055	8	vasseur	vasseur	PROPN
ejpam-4931	1055	9	.	.	PUNCT
ejpam-4931	1056	1	on	on	ADP
ejpam-4931	1056	2	the	the	DET
ejpam-4931	1056	3	barotropic	barotropic	PROPN
ejpam-4931	1056	4	compressible	compressible	ADJ
ejpam-4931	1056	5	navier	navier	NOUN
ejpam-4931	1056	6	-	-	PUNCT
ejpam-4931	1056	7	stokes	stoke	NOUN
ejpam-4931	1056	8	equations	equation	NOUN
ejpam-4931	1056	9	.	.	PUNCT
ejpam-4931	1057	1	commun	commun	PROPN
ejpam-4931	1057	2	.	.	PUNCT
ejpam-4931	1058	1	partial	partial	ADJ
ejpam-4931	1058	2	differ	differ	VERB
ejpam-4931	1058	3	.	.	PUNCT
ejpam-4931	1059	1	equations	equation	NOUN
ejpam-4931	1059	2	,	,	PUNCT
ejpam-4931	1059	3	32(3):431–452	32(3):431–452	PROPN
ejpam-4931	1059	4	,	,	PUNCT
ejpam-4931	1059	5	2007	2007	NUM
ejpam-4931	1059	6	.	.	PUNCT
ejpam-4931	1060	1	[	[	X
ejpam-4931	1060	2	14	14	NUM
ejpam-4931	1060	3	]	]	SYM
ejpam-4931	1060	4	louis	louis	PROPN
ejpam-4931	1060	5	nirenberg	nirenberg	PROPN
ejpam-4931	1060	6	.	.	PUNCT
ejpam-4931	1061	1	on	on	ADP
ejpam-4931	1061	2	elliptic	elliptic	ADJ
ejpam-4931	1061	3	partial	partial	ADJ
ejpam-4931	1061	4	differential	differential	NOUN
ejpam-4931	1061	5	equations	equation	NOUN
ejpam-4931	1061	6	.	.	PUNCT
ejpam-4931	1062	1	c.i.m.e	c.i.m.e	PROPN
ejpam-4931	1062	2	.	.	PROPN
ejpam-4931	1062	3	,	,	PUNCT
ejpam-4931	1062	4	principio	principio	PROPN
ejpam-4931	1062	5	di	di	X
ejpam-4931	1062	6	minimo	minimo	PROPN
ejpam-4931	1062	7	e	e	PROPN
ejpam-4931	1062	8	sue	sue	PROPN
ejpam-4931	1062	9	applicazioni	applicazioni	PROPN
ejpam-4931	1062	10	alle	alle	PROPN
ejpam-4931	1062	11	equazioni	equazioni	PROPN
ejpam-4931	1062	12	funzionali	funzionali	VERB
ejpam-4931	1062	13	1	1	NUM
ejpam-4931	1062	14	-	-	SYM
ejpam-4931	1062	15	48	48	NUM
ejpam-4931	1062	16	(	(	PUNCT
ejpam-4931	1062	17	1960	1960	NUM
ejpam-4931	1062	18	)	)	PUNCT
ejpam-4931	1062	19	.	.	PUNCT
ejpam-4931	1062	20	,	,	PUNCT
ejpam-4931	1062	21	1960	1960	NUM
ejpam-4931	1062	22	.	.	PUNCT
ejpam-4931	1063	1	[	[	X
ejpam-4931	1063	2	15	15	NUM
ejpam-4931	1063	3	]	]	X
ejpam-4931	1063	4	frédéric	frédéric	ADJ
ejpam-4931	1063	5	rousset	rousset	NOUN
ejpam-4931	1063	6	.	.	PUNCT
ejpam-4931	1064	1	weak	weak	ADJ
ejpam-4931	1064	2	solutions	solution	NOUN
ejpam-4931	1064	3	to	to	ADP
ejpam-4931	1064	4	the	the	DET
ejpam-4931	1064	5	navier	navier	NOUN
ejpam-4931	1064	6	-	-	PUNCT
ejpam-4931	1064	7	stokes	stoke	NOUN
ejpam-4931	1064	8	equation	equation	NOUN
ejpam-4931	1064	9	for	for	ADP
ejpam-4931	1064	10	compressible	compressible	ADJ
ejpam-4931	1064	11	fluids	fluid	NOUN
ejpam-4931	1064	12	[	[	X
ejpam-4931	1064	13	after	after	ADP
ejpam-4931	1064	14	a.	a.	NOUN
ejpam-4931	1064	15	vasseur	vasseur	PROPN
ejpam-4931	1064	16	and	and	CCONJ
ejpam-4931	1064	17	c.	c.	PROPN
ejpam-4931	1064	18	yu	yu	PROPN
ejpam-4931	1064	19	]	]	PROPN
ejpam-4931	1064	20	.	.	PUNCT
ejpam-4931	1065	1	in	in	ADP
ejpam-4931	1065	2	séminaire	séminaire	PROPN
ejpam-4931	1065	3	bourbaki	bourbaki	NOUN
ejpam-4931	1065	4	.	.	PUNCT
ejpam-4931	1066	1	volume	volume	NOUN
ejpam-4931	1066	2	2016/2017	2016/2017	NUM
ejpam-4931	1066	3	.	.	PUNCT
ejpam-4931	1067	1	exposés	exposé	NOUN
ejpam-4931	1067	2	1120–1135	1120–1135	NOUN
ejpam-4931	1067	3	,	,	PUNCT
ejpam-4931	1067	4	page	page	NOUN
ejpam-4931	1067	5	ex	ex	NOUN
ejpam-4931	1067	6	.	.	PUNCT
ejpam-4931	1068	1	société	société	PROPN
ejpam-4931	1068	2	mathématique	mathématique	PROPN
ejpam-4931	1068	3	de	de	X
ejpam-4931	1068	4	france	france	PROPN
ejpam-4931	1068	5	(	(	PUNCT
ejpam-4931	1068	6	smf	smf	PROPN
ejpam-4931	1068	7	)	)	PUNCT
ejpam-4931	1068	8	,	,	PUNCT
ejpam-4931	1068	9	2019	2019	NUM
ejpam-4931	1068	10	.	.	PUNCT
ejpam-4931	1069	1	[	[	X
ejpam-4931	1069	2	16	16	NUM
ejpam-4931	1069	3	]	]	X
ejpam-4931	1069	4	jacques	jacques	PROPN
ejpam-4931	1069	5	simon	simon	PROPN
ejpam-4931	1069	6	.	.	PUNCT
ejpam-4931	1070	1	compact	compact	ADJ
ejpam-4931	1070	2	sets	set	NOUN
ejpam-4931	1070	3	in	in	ADP
ejpam-4931	1070	4	the	the	DET
ejpam-4931	1070	5	space	space	NOUN
ejpam-4931	1070	6	lp(0	lp(0	NOUN
ejpam-4931	1070	7	,	,	PUNCT
ejpam-4931	1070	8	t	t	NOUN
ejpam-4931	1070	9	;	;	PUNCT
ejpam-4931	1070	10	b	b	X
ejpam-4931	1070	11	)	)	PUNCT
ejpam-4931	1070	12	.	.	PUNCT
ejpam-4931	1071	1	ann	ann	PROPN
ejpam-4931	1071	2	.	.	PUNCT
ejpam-4931	1071	3	mat	mat	PROPN
ejpam-4931	1071	4	.	.	PUNCT
ejpam-4931	1071	5	pura	pura	NOUN
ejpam-4931	1071	6	appl	appl	NOUN
ejpam-4931	1071	7	.	.	PUNCT
ejpam-4931	1072	1	(	(	PUNCT
ejpam-4931	1072	2	4	4	NUM
ejpam-4931	1072	3	)	)	PUNCT
ejpam-4931	1072	4	,	,	PUNCT
ejpam-4931	1072	5	146:65–96	146:65–96	NUM
ejpam-4931	1072	6	,	,	PUNCT
ejpam-4931	1072	7	1987	1987	NUM
ejpam-4931	1072	8	.	.	PUNCT
ejpam-4931	1073	1	[	[	X
ejpam-4931	1073	2	17	17	NUM
ejpam-4931	1073	3	]	]	PUNCT
ejpam-4931	1073	4	alexis	alexis	PROPN
ejpam-4931	1073	5	f.	f.	PROPN
ejpam-4931	1073	6	vasseur	vasseur	PROPN
ejpam-4931	1073	7	and	and	CCONJ
ejpam-4931	1073	8	cheng	cheng	PROPN
ejpam-4931	1073	9	yu	yu	PROPN
ejpam-4931	1073	10	.	.	PROPN
ejpam-4931	1073	11	existence	existence	NOUN
ejpam-4931	1073	12	of	of	ADP
ejpam-4931	1073	13	global	global	ADJ
ejpam-4931	1073	14	weak	weak	ADJ
ejpam-4931	1073	15	solutions	solution	NOUN
ejpam-4931	1073	16	for	for	ADP
ejpam-4931	1073	17	3d	3d	NUM
ejpam-4931	1073	18	degenerate	degenerate	ADJ
ejpam-4931	1073	19	compressible	compressible	ADJ
ejpam-4931	1073	20	navier	navier	NOUN
ejpam-4931	1073	21	-	-	PUNCT
ejpam-4931	1073	22	stokes	stoke	NOUN
ejpam-4931	1073	23	equations	equation	NOUN
ejpam-4931	1073	24	.	.	PUNCT
ejpam-4931	1074	1	invent	invent	NOUN
ejpam-4931	1074	2	.	.	PUNCT
ejpam-4931	1075	1	math	math	NOUN
ejpam-4931	1075	2	.	.	PUNCT
ejpam-4931	1075	3	,	,	PUNCT
ejpam-4931	1075	4	206(3):935–974	206(3):935–974	NUM
ejpam-4931	1075	5	,	,	PUNCT
ejpam-4931	1075	6	2016	2016	NUM
ejpam-4931	1075	7	.	.	PUNCT
ejpam-4931	1076	1	[	[	X
ejpam-4931	1076	2	18	18	NUM
ejpam-4931	1076	3	]	]	PUNCT
ejpam-4931	1076	4	alexis	alexis	PROPN
ejpam-4931	1076	5	f.	f.	PROPN
ejpam-4931	1076	6	vasseur	vasseur	PROPN
ejpam-4931	1076	7	and	and	CCONJ
ejpam-4931	1076	8	cheng	cheng	PROPN
ejpam-4931	1076	9	yu	yu	PROPN
ejpam-4931	1076	10	.	.	PUNCT
ejpam-4931	1076	11	global	global	ADJ
ejpam-4931	1076	12	weak	weak	ADJ
ejpam-4931	1076	13	solutions	solution	NOUN
ejpam-4931	1076	14	to	to	ADP
ejpam-4931	1076	15	the	the	DET
ejpam-4931	1076	16	compressible	compressible	ADJ
ejpam-4931	1076	17	quantum	quantum	NOUN
ejpam-4931	1076	18	navier	navier	NOUN
ejpam-4931	1076	19	-	-	PUNCT
ejpam-4931	1076	20	stokes	stoke	NOUN
ejpam-4931	1076	21	equations	equation	NOUN
ejpam-4931	1076	22	with	with	ADP
ejpam-4931	1076	23	damping	damp	VERB
ejpam-4931	1076	24	.	.	PUNCT
ejpam-4931	1077	1	siam	siam	PROPN
ejpam-4931	1077	2	j.	j.	PROPN
ejpam-4931	1077	3	math	math	PROPN
ejpam-4931	1077	4	.	.	PUNCT
ejpam-4931	1078	1	anal	anal	PROPN
ejpam-4931	1078	2	.	.	PROPN
ejpam-4931	1078	3	,	,	PUNCT
ejpam-4931	1078	4	48(2):1489–1511	48(2):1489–1511	PROPN
ejpam-4931	1078	5	,	,	PUNCT
ejpam-4931	1078	6	2016	2016	NUM
ejpam-4931	1078	7	.	.	PUNCT
ejpam-4931	1079	1	[	[	X
ejpam-4931	1079	2	19	19	NUM
ejpam-4931	1079	3	]	]	X
ejpam-4931	1079	4	fengchao	fengchao	PROPN
ejpam-4931	1079	5	wang	wang	PROPN
ejpam-4931	1079	6	,	,	PUNCT
ejpam-4931	1079	7	changsheng	changsheng	PROPN
ejpam-4931	1079	8	dou	dou	PROPN
ejpam-4931	1079	9	,	,	PUNCT
ejpam-4931	1079	10	and	and	CCONJ
ejpam-4931	1079	11	quansen	quansen	PROPN
ejpam-4931	1079	12	jiu	jiu	PROPN
ejpam-4931	1079	13	.	.	PUNCT
ejpam-4931	1080	1	global	global	ADJ
ejpam-4931	1080	2	existence	existence	NOUN
ejpam-4931	1080	3	of	of	ADP
ejpam-4931	1080	4	weak	weak	ADJ
ejpam-4931	1080	5	solutions	solution	NOUN
ejpam-4931	1080	6	to	to	ADP
ejpam-4931	1080	7	3d	3d	PROPN
ejpam-4931	1080	8	compressible	compressible	ADJ
ejpam-4931	1080	9	primitive	primitive	ADJ
ejpam-4931	1080	10	equations	equation	NOUN
ejpam-4931	1080	11	with	with	ADP
ejpam-4931	1080	12	degenerate	degenerate	ADJ
ejpam-4931	1080	13	viscosity	viscosity	NOUN
ejpam-4931	1080	14	.	.	PUNCT
ejpam-4931	1081	1	j.	j.	PROPN
ejpam-4931	1081	2	math	math	PROPN
ejpam-4931	1081	3	.	.	PUNCT
ejpam-4931	1082	1	phys	phy	NOUN
ejpam-4931	1082	2	.	.	PUNCT
ejpam-4931	1082	3	,	,	PUNCT
ejpam-4931	1082	4	61(2):021507	61(2):021507	NUM
ejpam-4931	1082	5	,	,	PUNCT
ejpam-4931	1082	6	33	33	NUM
ejpam-4931	1082	7	,	,	PUNCT
ejpam-4931	1082	8	2020	2020	NUM
ejpam-4931	1082	9	.	.	PUNCT