id	sid	tid	token	lemma	pos
ap-6142	1	1	acta	acta	PROPN
ap-6142	1	2	polytechnica	polytechnica	PROPN
ap-6142	1	3	https://doi.org/10.14311/ap.2021.61.0089	https://doi.org/10.14311/ap.2021.61.0089	PROPN
ap-6142	1	4	acta	acta	PROPN
ap-6142	1	5	polytechnica	polytechnica	PROPN
ap-6142	1	6	61(si):89–98	61(si):89–98	NUM
ap-6142	1	7	,	,	PUNCT
ap-6142	1	8	2021	2021	NUM
ap-6142	1	9	©	©	ADP
ap-6142	1	10	2021	2021	NUM
ap-6142	1	11	the	the	DET
ap-6142	1	12	author(s	author(s	NOUN
ap-6142	1	13	)	)	PUNCT
ap-6142	1	14	.	.	PUNCT
ap-6142	2	1	licensed	license	VERB
ap-6142	2	2	under	under	ADP
ap-6142	2	3	a	a	DET
ap-6142	2	4	cc	cc	NOUN
ap-6142	2	5	-	-	PUNCT
ap-6142	2	6	by	by	ADP
ap-6142	2	7	4.0	4.0	NUM
ap-6142	2	8	licence	licence	NOUN
ap-6142	2	9	published	publish	VERB
ap-6142	2	10	by	by	ADP
ap-6142	2	11	the	the	DET
ap-6142	2	12	czech	czech	PROPN
ap-6142	2	13	technical	technical	PROPN
ap-6142	2	14	university	university	PROPN
ap-6142	2	15	in	in	ADP
ap-6142	2	16	prague	prague	PROPN
ap-6142	2	17	modeling	modeling	NOUN
ap-6142	2	18	of	of	ADP
ap-6142	2	19	flows	flow	NOUN
ap-6142	2	20	through	through	ADP
ap-6142	2	21	a	a	DET
ap-6142	2	22	channel	channel	NOUN
ap-6142	2	23	by	by	ADP
ap-6142	2	24	the	the	DET
ap-6142	2	25	navier	navier	NOUN
ap-6142	2	26	–	–	PUNCT
ap-6142	2	27	stokes	stokes	PROPN
ap-6142	2	28	variational	variational	ADJ
ap-6142	2	29	inequalities	inequalities	PROPN
ap-6142	2	30	stanislav	stanislav	PROPN
ap-6142	2	31	kračmara	kračmara	PROPN
ap-6142	2	32	,	,	PUNCT
ap-6142	2	33	jiří	jiří	NOUN
ap-6142	2	34	neustupab	neustupab	NOUN
ap-6142	2	35	,	,	PUNCT
ap-6142	2	36	a,∗	a,∗	VERB
ap-6142	2	37	a	a	DET
ap-6142	2	38	czech	czech	PROPN
ap-6142	2	39	technical	technical	PROPN
ap-6142	2	40	university	university	NOUN
ap-6142	2	41	,	,	PUNCT
ap-6142	2	42	faculty	faculty	NOUN
ap-6142	2	43	of	of	ADP
ap-6142	2	44	mechanical	mechanical	ADJ
ap-6142	2	45	engineering	engineering	NOUN
ap-6142	2	46	,	,	PUNCT
ap-6142	2	47	department	department	NOUN
ap-6142	2	48	of	of	ADP
ap-6142	2	49	technical	technical	ADJ
ap-6142	2	50	mathematics	mathematic	NOUN
ap-6142	2	51	,	,	PUNCT
ap-6142	2	52	karlovo	karlovo	PROPN
ap-6142	2	53	nám	nám	PROPN
ap-6142	2	54	.	.	PROPN
ap-6142	3	1	13	13	NUM
ap-6142	3	2	,	,	PUNCT
ap-6142	3	3	121	121	NUM
ap-6142	3	4	35	35	NUM
ap-6142	3	5	praha	praha	NOUN
ap-6142	3	6	,	,	PUNCT
ap-6142	3	7	czech	czech	PROPN
ap-6142	3	8	republic	republic	PROPN
ap-6142	3	9	b	b	PROPN
ap-6142	3	10	czech	czech	PROPN
ap-6142	3	11	academy	academy	PROPN
ap-6142	3	12	of	of	ADP
ap-6142	3	13	sciences	sciences	PROPN
ap-6142	3	14	,	,	PUNCT
ap-6142	3	15	institute	institute	NOUN
ap-6142	3	16	of	of	ADP
ap-6142	3	17	mathematics	mathematics	PROPN
ap-6142	3	18	,	,	PUNCT
ap-6142	3	19	žitná	žitná	NOUN
ap-6142	3	20	25	25	NUM
ap-6142	3	21	,	,	PUNCT
ap-6142	3	22	115	115	NUM
ap-6142	3	23	67	67	NUM
ap-6142	3	24	praha	praha	NOUN
ap-6142	3	25	,	,	PUNCT
ap-6142	3	26	czech	czech	PROPN
ap-6142	3	27	republic	republic	NOUN
ap-6142	3	28	∗	∗	NOUN
ap-6142	3	29	corresponding	correspond	VERB
ap-6142	3	30	author	author	NOUN
ap-6142	3	31	:	:	PUNCT
ap-6142	3	32	neustupa@math.cas.cz	neustupa@math.cas.cz	NOUN
ap-6142	3	33	abstract	abstract	NOUN
ap-6142	3	34	.	.	PUNCT
ap-6142	4	1	we	we	PRON
ap-6142	4	2	deal	deal	VERB
ap-6142	4	3	with	with	ADP
ap-6142	4	4	a	a	DET
ap-6142	4	5	mathematical	mathematical	ADJ
ap-6142	4	6	model	model	NOUN
ap-6142	4	7	of	of	ADP
ap-6142	4	8	a	a	DET
ap-6142	4	9	flow	flow	NOUN
ap-6142	4	10	of	of	ADP
ap-6142	4	11	an	an	DET
ap-6142	4	12	incompressible	incompressible	ADJ
ap-6142	4	13	newtonian	newtonian	ADJ
ap-6142	4	14	fluid	fluid	NOUN
ap-6142	4	15	through	through	ADP
ap-6142	4	16	a	a	DET
ap-6142	4	17	channel	channel	NOUN
ap-6142	4	18	with	with	ADP
ap-6142	4	19	an	an	DET
ap-6142	4	20	artificial	artificial	ADJ
ap-6142	4	21	boundary	boundary	ADJ
ap-6142	4	22	condition	condition	NOUN
ap-6142	4	23	on	on	ADP
ap-6142	4	24	the	the	DET
ap-6142	4	25	outflow	outflow	NOUN
ap-6142	4	26	.	.	PUNCT
ap-6142	5	1	we	we	PRON
ap-6142	5	2	explain	explain	VERB
ap-6142	5	3	how	how	SCONJ
ap-6142	5	4	several	several	ADJ
ap-6142	5	5	artificial	artificial	ADJ
ap-6142	5	6	boundary	boundary	ADJ
ap-6142	5	7	conditions	condition	NOUN
ap-6142	5	8	formally	formally	ADV
ap-6142	5	9	follow	follow	VERB
ap-6142	5	10	from	from	ADP
ap-6142	5	11	appropriate	appropriate	ADJ
ap-6142	5	12	variational	variational	ADJ
ap-6142	5	13	formulations	formulation	NOUN
ap-6142	5	14	and	and	CCONJ
ap-6142	5	15	the	the	DET
ap-6142	5	16	way	way	NOUN
ap-6142	5	17	one	one	PRON
ap-6142	5	18	expresses	express	VERB
ap-6142	5	19	the	the	DET
ap-6142	5	20	dynamic	dynamic	ADJ
ap-6142	5	21	stress	stress	NOUN
ap-6142	5	22	tensor	tensor	NOUN
ap-6142	5	23	.	.	PUNCT
ap-6142	6	1	as	as	ADP
ap-6142	6	2	the	the	DET
ap-6142	6	3	boundary	boundary	ADJ
ap-6142	6	4	condition	condition	NOUN
ap-6142	6	5	of	of	ADP
ap-6142	6	6	the	the	DET
ap-6142	6	7	“	"	PUNCT
ap-6142	6	8	do	do	AUX
ap-6142	6	9	nothing”-type	nothing”-type	NOUN
ap-6142	6	10	,	,	PUNCT
ap-6142	6	11	that	that	PRON
ap-6142	6	12	is	be	AUX
ap-6142	6	13	predominantly	predominantly	ADV
ap-6142	6	14	considered	consider	VERB
ap-6142	6	15	to	to	PART
ap-6142	6	16	be	be	AUX
ap-6142	6	17	the	the	DET
ap-6142	6	18	most	most	ADV
ap-6142	6	19	appropriate	appropriate	ADJ
ap-6142	6	20	from	from	ADP
ap-6142	6	21	the	the	DET
ap-6142	6	22	physical	physical	ADJ
ap-6142	6	23	point	point	NOUN
ap-6142	6	24	of	of	ADP
ap-6142	6	25	view	view	NOUN
ap-6142	6	26	,	,	PUNCT
ap-6142	6	27	does	do	AUX
ap-6142	6	28	not	not	PART
ap-6142	6	29	enable	enable	VERB
ap-6142	6	30	one	one	NUM
ap-6142	6	31	to	to	PART
ap-6142	6	32	derive	derive	VERB
ap-6142	6	33	an	an	DET
ap-6142	6	34	energy	energy	NOUN
ap-6142	6	35	inequality	inequality	NOUN
ap-6142	6	36	,	,	PUNCT
ap-6142	6	37	we	we	PRON
ap-6142	6	38	explain	explain	VERB
ap-6142	6	39	how	how	SCONJ
ap-6142	6	40	this	this	DET
ap-6142	6	41	problem	problem	NOUN
ap-6142	6	42	can	can	AUX
ap-6142	6	43	be	be	AUX
ap-6142	6	44	overcome	overcome	VERB
ap-6142	6	45	by	by	ADP
ap-6142	6	46	using	use	VERB
ap-6142	6	47	variational	variational	ADJ
ap-6142	6	48	inequalities	inequality	NOUN
ap-6142	6	49	.	.	PUNCT
ap-6142	7	1	we	we	PRON
ap-6142	7	2	derive	derive	VERB
ap-6142	7	3	a	a	DET
ap-6142	7	4	priori	priori	ADJ
ap-6142	7	5	estimates	estimate	NOUN
ap-6142	7	6	,	,	PUNCT
ap-6142	7	7	which	which	PRON
ap-6142	7	8	are	be	AUX
ap-6142	7	9	the	the	DET
ap-6142	7	10	core	core	NOUN
ap-6142	7	11	of	of	ADP
ap-6142	7	12	the	the	DET
ap-6142	7	13	proofs	proof	NOUN
ap-6142	7	14	,	,	PUNCT
ap-6142	7	15	and	and	CCONJ
ap-6142	7	16	present	present	ADJ
ap-6142	7	17	theorems	theorem	NOUN
ap-6142	7	18	on	on	ADP
ap-6142	7	19	the	the	DET
ap-6142	7	20	existence	existence	NOUN
ap-6142	7	21	of	of	ADP
ap-6142	7	22	solutions	solution	NOUN
ap-6142	7	23	in	in	ADP
ap-6142	7	24	the	the	DET
ap-6142	7	25	unsteady	unsteady	ADJ
ap-6142	7	26	and	and	CCONJ
ap-6142	7	27	steady	steady	ADJ
ap-6142	7	28	cases	case	NOUN
ap-6142	7	29	.	.	PUNCT
ap-6142	8	1	keywords	keyword	NOUN
ap-6142	8	2	:	:	PUNCT
ap-6142	8	3	variational	variational	ADJ
ap-6142	8	4	inequality	inequality	NOUN
ap-6142	8	5	,	,	PUNCT
ap-6142	8	6	navier	navier	NOUN
ap-6142	8	7	-	-	PUNCT
ap-6142	8	8	stokes	stoke	NOUN
ap-6142	8	9	equation	equation	NOUN
ap-6142	8	10	,	,	PUNCT
ap-6142	8	11	“	"	PUNCT
ap-6142	8	12	do	do	VERB
ap-6142	8	13	nothing	nothing	PRON
ap-6142	8	14	”	"	PUNCT
ap-6142	8	15	outflow	outflow	ADJ
ap-6142	8	16	boundary	boundary	ADJ
ap-6142	8	17	condition	condition	NOUN
ap-6142	8	18	.	.	PUNCT
ap-6142	9	1	1	1	X
ap-6142	9	2	.	.	X
ap-6142	9	3	introduction	introduction	NOUN
ap-6142	9	4	1.1	1.1	NUM
ap-6142	9	5	.	.	PUNCT
ap-6142	10	1	the	the	DET
ap-6142	10	2	considered	consider	VERB
ap-6142	10	3	initial	initial	ADJ
ap-6142	10	4	–	–	PUNCT
ap-6142	10	5	boundary	boundary	ADJ
ap-6142	10	6	value	value	NOUN
ap-6142	10	7	problem	problem	NOUN
ap-6142	10	8	we	we	PRON
ap-6142	10	9	denote	denote	VERB
ap-6142	10	10	by	by	ADP
ap-6142	10	11	ω	ω	PROPN
ap-6142	10	12	a	a	DET
ap-6142	10	13	lipschitzian	lipschitzian	ADJ
ap-6142	10	14	domain	domain	NOUN
ap-6142	10	15	in	in	ADP
ap-6142	10	16	r3	r3	PROPN
ap-6142	10	17	,	,	PUNCT
ap-6142	10	18	which	which	PRON
ap-6142	10	19	represents	represent	VERB
ap-6142	10	20	a	a	DET
ap-6142	10	21	channel	channel	NOUN
ap-6142	10	22	.	.	PUNCT
ap-6142	11	1	an	an	DET
ap-6142	11	2	incompressible	incompressible	ADJ
ap-6142	11	3	newtonian	newtonian	ADJ
ap-6142	11	4	fluid	fluid	NOUN
ap-6142	11	5	is	be	AUX
ap-6142	11	6	supposed	suppose	VERB
ap-6142	11	7	to	to	PART
ap-6142	11	8	flow	flow	VERB
ap-6142	11	9	into	into	ADP
ap-6142	11	10	the	the	DET
ap-6142	11	11	channel	channel	NOUN
ap-6142	11	12	through	through	ADP
ap-6142	11	13	the	the	DET
ap-6142	11	14	part	part	NOUN
ap-6142	11	15	γ1	γ1	NOUN
ap-6142	11	16	of	of	ADP
ap-6142	11	17	the	the	DET
ap-6142	11	18	boundary	boundary	ADJ
ap-6142	11	19	∂ω	∂ω	PROPN
ap-6142	11	20	and	and	CCONJ
ap-6142	11	21	to	to	PART
ap-6142	11	22	flow	flow	VERB
ap-6142	11	23	essentially	essentially	ADV
ap-6142	11	24	out	out	ADP
ap-6142	11	25	of	of	ADP
ap-6142	11	26	the	the	DET
ap-6142	11	27	channel	channel	NOUN
ap-6142	11	28	through	through	ADP
ap-6142	11	29	the	the	DET
ap-6142	11	30	part	part	NOUN
ap-6142	11	31	γ2	γ2	NOUN
ap-6142	11	32	of	of	ADP
ap-6142	11	33	∂ω	∂ω	PROPN
ap-6142	11	34	.	.	PUNCT
ap-6142	12	1	(	(	PUNCT
ap-6142	12	2	see	see	VERB
ap-6142	12	3	fig	fig	NOUN
ap-6142	12	4	.	.	PUNCT
ap-6142	13	1	1	1	NUM
ap-6142	13	2	.	.	NUM
ap-6142	13	3	)	)	PUNCT
ap-6142	13	4	by	by	ADP
ap-6142	13	5	“	"	PUNCT
ap-6142	13	6	essentially	essentially	ADV
ap-6142	13	7	”	"	PUNCT
ap-6142	13	8	we	we	PRON
ap-6142	13	9	mean	mean	VERB
ap-6142	13	10	that	that	SCONJ
ap-6142	13	11	we	we	PRON
ap-6142	13	12	do	do	AUX
ap-6142	13	13	not	not	PART
ap-6142	13	14	exclude	exclude	VERB
ap-6142	13	15	possible	possible	ADJ
ap-6142	13	16	backward	backward	ADJ
ap-6142	13	17	flows	flow	NOUN
ap-6142	13	18	on	on	ADP
ap-6142	13	19	γ2	γ2	PROPN
ap-6142	13	20	.	.	PUNCT
ap-6142	14	1	a	a	DET
ap-6142	14	2	fixed	fix	VERB
ap-6142	14	3	wall	wall	NOUN
ap-6142	14	4	of	of	ADP
ap-6142	14	5	the	the	DET
ap-6142	14	6	channel	channel	NOUN
ap-6142	14	7	is	be	AUX
ap-6142	14	8	denoted	denote	VERB
ap-6142	14	9	by	by	ADP
ap-6142	14	10	γ0	γ0	NOUN
ap-6142	14	11	.	.	PUNCT
ap-6142	15	1	the	the	DET
ap-6142	15	2	flow	flow	NOUN
ap-6142	15	3	is	be	AUX
ap-6142	15	4	described	describe	VERB
ap-6142	15	5	by	by	ADP
ap-6142	15	6	the	the	DET
ap-6142	15	7	equations	equation	NOUN
ap-6142	15	8	of	of	ADP
ap-6142	15	9	motion	motion	NOUN
ap-6142	15	10	∂tv	∂tv	PROPN
ap-6142	15	11	+	+	CCONJ
ap-6142	15	12	v	v	X
ap-6142	15	13	·	·	PUNCT
ap-6142	15	14	∇v	∇v	ADJ
ap-6142	15	15	−	−	NOUN
ap-6142	15	16	div	div	X
ap-6142	15	17	sd	sd	ADP
ap-6142	15	18	+	+	PROPN
ap-6142	15	19	∇p	∇p	PROPN
ap-6142	15	20	=	=	SYM
ap-6142	15	21	f	f	PROPN
ap-6142	15	22	,	,	PUNCT
ap-6142	15	23	(	(	PUNCT
ap-6142	15	24	1	1	X
ap-6142	15	25	)	)	PUNCT
ap-6142	15	26	div	div	X
ap-6142	15	27	v	v	NOUN
ap-6142	15	28	=	=	SYM
ap-6142	15	29	0	0	PROPN
ap-6142	15	30	,	,	PUNCT
ap-6142	15	31	(	(	PUNCT
ap-6142	15	32	2	2	X
ap-6142	15	33	)	)	PUNCT
ap-6142	15	34	6	6	NUM
ap-6142	15	35	�	�	PROPN
ap-6142	15	36	�	�	PROPN
ap-6142	15	37	�	�	PROPN
ap-6142	15	38	�	�	PROPN
ap-6142	15	39	�	�	PROPN
ap-6142	15	40	�	�	PROPN
ap-6142	15	41	�	�	PROPN
ap-6142	15	42	3	3	NUM
ap-6142	15	43	�	�	PROPN
ap-6142	15	44	�	�	PROPN
ap-6142	15	45	�	�	PROPN
ap-6142	15	46	�	�	PROPN
ap-6142	15	47	�	�	PROPN
ap-6142	15	48	�	�	PROPN
ap-6142	15	49	q	q	PROPN
ap-6142	15	50	q	q	X
ap-6142	15	51	q	q	X
ap-6142	15	52	q	q	X
ap-6142	16	1	qqs	qqs	ADJ
ap-6142	16	2	q	q	X
ap-6142	16	3	q	q	X
ap-6142	16	4	q	q	X
ap-6142	16	5	q	q	X
ap-6142	16	6	q	q	X
ap-6142	16	7	qq	qq	PROPN
ap-6142	16	8	�	�	PROPN
ap-6142	16	9	�	�	PROPN
ap-6142	16	10	�	�	PROPN
ap-6142	16	11	:	:	PUNCT
ap-6142	16	12	�	�	PROPN
ap-6142	16	13	�	�	PROPN
ap-6142	16	14	�	�	PROPN
ap-6142	16	15	:	:	PUNCT
ap-6142	16	16	�	�	PROPN
ap-6142	16	17	�	�	PROPN
ap-6142	16	18	�	�	PROPN
ap-6142	16	19	:	:	PUNCT
ap-6142	16	20	ω	ω	PROPN
ap-6142	16	21	γ0	γ0	PROPN
ap-6142	16	22	γ1	γ1	PROPN
ap-6142	16	23	γ2	γ2	PROPN
ap-6142	17	1	x1	x1	PROPN
ap-6142	17	2	x2	x2	PROPN
ap-6142	17	3	x3	x3	ADJ
ap-6142	17	4	fig	fig	NOUN
ap-6142	17	5	.	.	PUNCT
ap-6142	18	1	1	1	NUM
ap-6142	18	2	the	the	DET
ap-6142	18	3	channel	channel	NOUN
ap-6142	18	4	.	.	PUNCT
ap-6142	19	1	where	where	SCONJ
ap-6142	19	2	v	v	NOUN
ap-6142	19	3	denotes	denote	VERB
ap-6142	19	4	the	the	DET
ap-6142	19	5	velocity	velocity	NOUN
ap-6142	19	6	,	,	PUNCT
ap-6142	19	7	p	p	NOUN
ap-6142	19	8	is	be	AUX
ap-6142	19	9	the	the	DET
ap-6142	19	10	pressure	pressure	NOUN
ap-6142	19	11	,	,	PUNCT
ap-6142	19	12	sd	sd	NOUN
ap-6142	19	13	is	be	AUX
ap-6142	19	14	the	the	DET
ap-6142	19	15	dynamic	dynamic	ADJ
ap-6142	19	16	stress	stress	NOUN
ap-6142	19	17	tensor	tensor	NOUN
ap-6142	19	18	and	and	CCONJ
ap-6142	19	19	f	f	PROPN
ap-6142	19	20	represents	represent	VERB
ap-6142	19	21	an	an	DET
ap-6142	19	22	external	external	ADJ
ap-6142	19	23	body	body	NOUN
ap-6142	19	24	force	force	NOUN
ap-6142	19	25	.	.	PUNCT
ap-6142	20	1	for	for	ADP
ap-6142	20	2	simplicity	simplicity	NOUN
ap-6142	20	3	,	,	PUNCT
ap-6142	20	4	we	we	PRON
ap-6142	20	5	assume	assume	VERB
ap-6142	20	6	that	that	SCONJ
ap-6142	20	7	the	the	DET
ap-6142	20	8	density	density	NOUN
ap-6142	20	9	of	of	ADP
ap-6142	20	10	the	the	DET
ap-6142	20	11	fluid	fluid	NOUN
ap-6142	20	12	is	be	AUX
ap-6142	20	13	equal	equal	ADJ
ap-6142	20	14	to	to	ADP
ap-6142	20	15	one	one	NUM
ap-6142	20	16	.	.	PUNCT
ap-6142	21	1	we	we	PRON
ap-6142	21	2	use	use	VERB
ap-6142	21	3	the	the	DET
ap-6142	21	4	homogeneous	homogeneous	ADJ
ap-6142	21	5	dirichlet	dirichlet	PROPN
ap-6142	21	6	boundary	boundary	PROPN
ap-6142	21	7	condition	condition	NOUN
ap-6142	21	8	v	v	ADP
ap-6142	21	9	=	=	SYM
ap-6142	21	10	0	0	NUM
ap-6142	22	1	on	on	ADP
ap-6142	22	2	γ0	γ0	PROPN
ap-6142	22	3	×	×	PROPN
ap-6142	22	4	(	(	PUNCT
ap-6142	22	5	0	0	NUM
ap-6142	22	6	,	,	PUNCT
ap-6142	22	7	t	t	NOUN
ap-6142	22	8	)	)	PUNCT
ap-6142	22	9	,	,	PUNCT
ap-6142	22	10	(	(	PUNCT
ap-6142	22	11	3	3	X
ap-6142	22	12	)	)	PUNCT
ap-6142	22	13	where	where	SCONJ
ap-6142	22	14	(	(	PUNCT
ap-6142	22	15	0	0	NUM
ap-6142	22	16	,	,	PUNCT
ap-6142	22	17	t	t	PROPN
ap-6142	22	18	)	)	PUNCT
ap-6142	22	19	is	be	AUX
ap-6142	22	20	a	a	DET
ap-6142	22	21	time	time	NOUN
ap-6142	22	22	interval	interval	NOUN
ap-6142	22	23	.	.	PUNCT
ap-6142	23	1	the	the	DET
ap-6142	23	2	velocity	velocity	NOUN
ap-6142	23	3	on	on	ADP
ap-6142	23	4	γ1	γ1	PROPN
ap-6142	23	5	can	can	AUX
ap-6142	23	6	be	be	AUX
ap-6142	23	7	naturally	naturally	ADV
ap-6142	23	8	assumed	assume	VERB
ap-6142	23	9	to	to	PART
ap-6142	23	10	be	be	AUX
ap-6142	23	11	known	know	VERB
ap-6142	23	12	,	,	PUNCT
ap-6142	23	13	which	which	PRON
ap-6142	23	14	yields	yield	VERB
ap-6142	23	15	the	the	DET
ap-6142	23	16	inhomogeneous	inhomogeneous	ADJ
ap-6142	23	17	dirichlet	dirichlet	PROPN
ap-6142	23	18	boundary	boundary	ADJ
ap-6142	23	19	condition	condition	NOUN
ap-6142	23	20	v	v	ADP
ap-6142	23	21	=	=	SYM
ap-6142	23	22	v∗	v∗	PROPN
ap-6142	23	23	on	on	ADP
ap-6142	23	24	γ1	γ1	PROPN
ap-6142	23	25	×	×	PROPN
ap-6142	23	26	(	(	PUNCT
ap-6142	23	27	0	0	NUM
ap-6142	23	28	,	,	PUNCT
ap-6142	23	29	t	t	NOUN
ap-6142	23	30	)	)	PUNCT
ap-6142	23	31	.	.	PUNCT
ap-6142	24	1	(	(	PUNCT
ap-6142	24	2	4	4	X
ap-6142	24	3	)	)	PUNCT
ap-6142	24	4	on	on	ADP
ap-6142	24	5	the	the	DET
ap-6142	24	6	other	other	ADJ
ap-6142	24	7	hand	hand	NOUN
ap-6142	24	8	,	,	PUNCT
ap-6142	24	9	since	since	SCONJ
ap-6142	24	10	the	the	DET
ap-6142	24	11	velocity	velocity	NOUN
ap-6142	24	12	profile	profile	NOUN
ap-6142	24	13	on	on	ADP
ap-6142	24	14	γ2	γ2	NOUN
ap-6142	24	15	can	can	AUX
ap-6142	24	16	not	not	PART
ap-6142	24	17	be	be	AUX
ap-6142	24	18	predicted	predict	VERB
ap-6142	24	19	in	in	ADP
ap-6142	24	20	advance	advance	NOUN
ap-6142	24	21	,	,	PUNCT
ap-6142	24	22	it	it	PRON
ap-6142	24	23	is	be	AUX
ap-6142	24	24	logical	logical	ADJ
ap-6142	24	25	to	to	PART
ap-6142	24	26	apply	apply	VERB
ap-6142	24	27	some	some	DET
ap-6142	24	28	“	"	PUNCT
ap-6142	24	29	artificial	artificial	ADJ
ap-6142	24	30	”	"	PUNCT
ap-6142	24	31	boundary	boundary	ADJ
ap-6142	24	32	condition	condition	NOUN
ap-6142	24	33	.	.	PUNCT
ap-6142	25	1	there	there	PRON
ap-6142	25	2	appear	appear	VERB
ap-6142	25	3	various	various	ADJ
ap-6142	25	4	artificial	artificial	ADJ
ap-6142	25	5	boundary	boundary	ADJ
ap-6142	25	6	conditions	condition	NOUN
ap-6142	25	7	in	in	ADP
ap-6142	25	8	the	the	DET
ap-6142	25	9	literature	literature	NOUN
ap-6142	25	10	,	,	PUNCT
ap-6142	25	11	see	see	VERB
ap-6142	25	12	e.g.	e.g.	ADV
ap-6142	25	13	[	[	X
ap-6142	25	14	1–8	1–8	X
ap-6142	25	15	]	]	PUNCT
ap-6142	25	16	.	.	PUNCT
ap-6142	26	1	boundary	boundary	ADJ
ap-6142	26	2	conditions	condition	NOUN
ap-6142	26	3	,	,	PUNCT
ap-6142	26	4	that	that	PRON
ap-6142	26	5	follow	follow	VERB
ap-6142	26	6	automatically	automatically	ADV
ap-6142	26	7	from	from	ADP
ap-6142	26	8	an	an	DET
ap-6142	26	9	appropriate	appropriate	ADJ
ap-6142	26	10	weak	weak	ADJ
ap-6142	26	11	formulation	formulation	NOUN
ap-6142	26	12	of	of	ADP
ap-6142	26	13	the	the	DET
ap-6142	26	14	considered	consider	VERB
ap-6142	26	15	problem	problem	NOUN
ap-6142	26	16	if	if	SCONJ
ap-6142	26	17	one	one	NUM
ap-6142	26	18	a	a	PRON
ap-6142	26	19	priori	priori	ADV
ap-6142	26	20	assumes	assume	VERB
ap-6142	26	21	a	a	DET
ap-6142	26	22	sufficient	sufficient	ADJ
ap-6142	26	23	regularity	regularity	NOUN
ap-6142	26	24	of	of	ADP
ap-6142	26	25	asolution	asolution	NOUN
ap-6142	26	26	,	,	PUNCT
ap-6142	26	27	are	be	AUX
ap-6142	26	28	usually	usually	ADV
ap-6142	26	29	called	call	VERB
ap-6142	26	30	the	the	DET
ap-6142	26	31	“	"	PUNCT
ap-6142	26	32	do	do	AUX
ap-6142	26	33	nothing	nothing	PRON
ap-6142	26	34	”	"	PUNCT
ap-6142	26	35	conditions	condition	NOUN
ap-6142	26	36	.	.	PUNCT
ap-6142	27	1	(	(	PUNCT
ap-6142	27	2	see	see	VERB
ap-6142	27	3	e.g.	e.g.	ADV
ap-6142	27	4	[	[	X
ap-6142	27	5	1	1	NUM
ap-6142	27	6	,	,	PUNCT
ap-6142	27	7	6	6	NUM
ap-6142	27	8	,	,	PUNCT
ap-6142	27	9	9	9	NUM
ap-6142	27	10	]	]	PUNCT
ap-6142	27	11	for	for	ADP
ap-6142	27	12	more	more	ADJ
ap-6142	27	13	details	detail	NOUN
ap-6142	27	14	.	.	PUNCT
ap-6142	27	15	)	)	PUNCT
ap-6142	28	1	an	an	DET
ap-6142	28	2	example	example	NOUN
ap-6142	28	3	,	,	PUNCT
ap-6142	28	4	and	and	CCONJ
ap-6142	28	5	probably	probably	ADV
ap-6142	28	6	the	the	DET
ap-6142	28	7	most	most	ADV
ap-6142	28	8	often	often	ADV
ap-6142	28	9	used	use	VERB
ap-6142	28	10	artificial	artificial	ADJ
ap-6142	28	11	boundary	boundary	ADJ
ap-6142	28	12	condition	condition	NOUN
ap-6142	28	13	is	be	AUX
ap-6142	28	14	−	−	PROPN
ap-6142	28	15	pn+	pn+	NOUN
ap-6142	28	16	ν	ν	X
ap-6142	28	17	∂v	∂v	PROPN
ap-6142	28	18	∂n	∂n	PROPN
ap-6142	28	19	=	=	PUNCT
ap-6142	28	20	g	g	PROPN
ap-6142	28	21	on	on	ADP
ap-6142	28	22	γ2	γ2	PROPN
ap-6142	28	23	×	×	NOUN
ap-6142	28	24	(	(	PUNCT
ap-6142	28	25	0	0	NUM
ap-6142	28	26	,	,	PUNCT
ap-6142	28	27	t	t	NOUN
ap-6142	28	28	)	)	PUNCT
ap-6142	28	29	,	,	PUNCT
ap-6142	28	30	(	(	PUNCT
ap-6142	28	31	5	5	X
ap-6142	28	32	)	)	PUNCT
ap-6142	28	33	where	where	SCONJ
ap-6142	28	34	n	n	PRON
ap-6142	28	35	denotes	denote	VERB
ap-6142	28	36	the	the	DET
ap-6142	28	37	outer	outer	ADJ
ap-6142	28	38	normal	normal	ADJ
ap-6142	28	39	vector	vector	NOUN
ap-6142	28	40	field	field	NOUN
ap-6142	28	41	on	on	ADP
ap-6142	28	42	∂ω	∂ω	PROPN
ap-6142	28	43	,	,	PUNCT
ap-6142	28	44	ν	ν	PROPN
ap-6142	28	45	is	be	AUX
ap-6142	28	46	the	the	DET
ap-6142	28	47	coefficient	coefficient	NOUN
ap-6142	28	48	of	of	ADP
ap-6142	28	49	viscosity	viscosity	NOUN
ap-6142	28	50	and	and	CCONJ
ap-6142	28	51	g	g	NOUN
ap-6142	28	52	is	be	AUX
ap-6142	28	53	a	a	DET
ap-6142	28	54	given	give	VERB
ap-6142	28	55	function	function	NOUN
ap-6142	28	56	.	.	PUNCT
ap-6142	29	1	the	the	DET
ap-6142	29	2	non	non	ADJ
ap-6142	29	3	–	–	PUNCT
ap-6142	29	4	steady	steady	ADJ
ap-6142	29	5	problem	problem	NOUN
ap-6142	29	6	also	also	ADV
ap-6142	29	7	contains	contain	VERB
ap-6142	29	8	the	the	DET
ap-6142	29	9	initial	initial	ADJ
ap-6142	29	10	condition	condition	NOUN
ap-6142	29	11	v	v	ADP
ap-6142	29	12	=	=	SYM
ap-6142	29	13	v0	v0	NOUN
ap-6142	29	14	in	in	ADP
ap-6142	29	15	ω×	ω×	PROPN
ap-6142	29	16	{	{	PUNCT
ap-6142	29	17	0	0	NUM
ap-6142	29	18	}	}	PUNCT
ap-6142	29	19	.	.	PUNCT
ap-6142	30	1	(	(	PUNCT
ap-6142	30	2	6	6	NUM
ap-6142	30	3	)	)	PUNCT
ap-6142	30	4	1.2	1.2	NUM
ap-6142	30	5	.	.	PUNCT
ap-6142	31	1	on	on	ADP
ap-6142	31	2	some	some	DET
ap-6142	31	3	previous	previous	ADJ
ap-6142	31	4	related	related	ADJ
ap-6142	31	5	existential	existential	ADJ
ap-6142	31	6	results	result	NOUN
ap-6142	31	7	the	the	DET
ap-6142	31	8	existential	existential	ADJ
ap-6142	31	9	theory	theory	NOUN
ap-6142	31	10	for	for	ADP
ap-6142	31	11	the	the	DET
ap-6142	31	12	system	system	NOUN
ap-6142	31	13	(	(	PUNCT
ap-6142	31	14	1)–(6	1)–(6	X
ap-6142	31	15	)	)	PUNCT
ap-6142	31	16	is	be	AUX
ap-6142	31	17	based	base	VERB
ap-6142	31	18	on	on	ADP
ap-6142	31	19	appropriate	appropriate	ADJ
ap-6142	31	20	a	a	DET
ap-6142	31	21	priori	priori	ADJ
ap-6142	31	22	estimates	estimate	NOUN
ap-6142	31	23	.	.	PUNCT
ap-6142	32	1	as	as	SCONJ
ap-6142	32	2	the	the	DET
ap-6142	32	3	boundary	boundary	ADJ
ap-6142	32	4	condition	condition	NOUN
ap-6142	32	5	(	(	PUNCT
ap-6142	32	6	5	5	X
ap-6142	32	7	)	)	PUNCT
ap-6142	32	8	admits	admit	VERB
ap-6142	32	9	a	a	DET
ap-6142	32	10	possible	possible	ADJ
ap-6142	32	11	reverse	reverse	ADJ
ap-6142	32	12	flow	flow	NOUN
ap-6142	32	13	on	on	ADP
ap-6142	32	14	γ2	γ2	PROPN
ap-6142	32	15	,	,	PUNCT
ap-6142	32	16	which	which	PRON
ap-6142	32	17	may	may	AUX
ap-6142	32	18	bring	bring	VERB
ap-6142	32	19	to	to	ADP
ap-6142	32	20	ω	ω	NUM
ap-6142	32	21	an	an	DET
ap-6142	32	22	arbitrarily	arbitrarily	ADV
ap-6142	32	23	large	large	ADJ
ap-6142	32	24	amount	amount	NOUN
ap-6142	32	25	of	of	ADP
ap-6142	32	26	kinetic	kinetic	ADJ
ap-6142	32	27	energy	energy	NOUN
ap-6142	32	28	from	from	ADP
ap-6142	32	29	the	the	DET
ap-6142	32	30	outside	outside	NOUN
ap-6142	32	31	,	,	PUNCT
ap-6142	32	32	the	the	DET
ap-6142	32	33	usual	usual	ADJ
ap-6142	32	34	energy	energy	NOUN
ap-6142	32	35	inequality	inequality	NOUN
ap-6142	32	36	does	do	AUX
ap-6142	32	37	not	not	PART
ap-6142	32	38	hold	hold	VERB
ap-6142	32	39	.	.	PUNCT
ap-6142	33	1	this	this	PRON
ap-6142	33	2	does	do	AUX
ap-6142	33	3	not	not	PART
ap-6142	33	4	matter	matter	VERB
ap-6142	33	5	if	if	SCONJ
ap-6142	33	6	the	the	DET
ap-6142	33	7	given	give	VERB
ap-6142	33	8	data	datum	NOUN
ap-6142	33	9	of	of	ADP
ap-6142	33	10	the	the	DET
ap-6142	33	11	problem	problem	NOUN
ap-6142	33	12	are	be	AUX
ap-6142	33	13	in	in	ADP
ap-6142	33	14	an	an	DET
ap-6142	33	15	appropriate	appropriate	ADJ
ap-6142	33	16	sense	sense	NOUN
ap-6142	33	17	89	89	NUM
ap-6142	33	18	https://doi.org/10.14311/ap.2021.61.0089	https://doi.org/10.14311/ap.2021.61.0089	NOUN
ap-6142	33	19	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-6142	33	20	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-6142	33	21	stanislav	stanislav	PROPN
ap-6142	33	22	kračmar	kračmar	PROPN
ap-6142	33	23	,	,	PUNCT
ap-6142	33	24	jiří	jiří	NOUN
ap-6142	33	25	neustupa	neustupa	PROPN
ap-6142	33	26	acta	acta	PROPN
ap-6142	33	27	polytechnica	polytechnica	PROPN
ap-6142	33	28	“	"	PUNCT
ap-6142	33	29	sufficiently	sufficiently	ADV
ap-6142	33	30	small	small	ADJ
ap-6142	33	31	”	"	PUNCT
ap-6142	33	32	or	or	CCONJ
ap-6142	33	33	if	if	SCONJ
ap-6142	33	34	the	the	DET
ap-6142	33	35	number	number	NOUN
ap-6142	33	36	t	t	NOUN
ap-6142	33	37	is	be	AUX
ap-6142	33	38	“	"	PUNCT
ap-6142	33	39	sufficiently	sufficiently	ADV
ap-6142	33	40	small	small	ADJ
ap-6142	33	41	”	"	PUNCT
ap-6142	33	42	in	in	ADP
ap-6142	33	43	the	the	DET
ap-6142	33	44	non	non	ADJ
ap-6142	33	45	–	–	ADJ
ap-6142	33	46	steady	steady	ADJ
ap-6142	33	47	case	case	NOUN
ap-6142	33	48	.	.	PUNCT
ap-6142	34	1	(	(	PUNCT
ap-6142	34	2	see	see	VERB
ap-6142	34	3	[	[	X
ap-6142	34	4	1	1	NUM
ap-6142	34	5	,	,	PUNCT
ap-6142	34	6	9	9	NUM
ap-6142	34	7	,	,	PUNCT
ap-6142	34	8	10	10	NUM
ap-6142	34	9	]	]	PUNCT
ap-6142	34	10	.	.	PUNCT
ap-6142	34	11	)	)	PUNCT
ap-6142	35	1	the	the	DET
ap-6142	35	2	existence	existence	NOUN
ap-6142	35	3	of	of	ADP
ap-6142	35	4	a	a	DET
ap-6142	35	5	weak	weak	ADJ
ap-6142	35	6	solution	solution	NOUN
ap-6142	35	7	of	of	ADP
ap-6142	35	8	the	the	DET
ap-6142	35	9	problem	problem	NOUN
ap-6142	35	10	(	(	PUNCT
ap-6142	35	11	1)–(6	1)–(6	X
ap-6142	35	12	)	)	PUNCT
ap-6142	35	13	on	on	ADP
ap-6142	35	14	an	an	DET
ap-6142	35	15	arbitrarily	arbitrarily	ADV
ap-6142	35	16	large	large	ADJ
ap-6142	35	17	time	time	NOUN
ap-6142	35	18	interval	interval	NOUN
ap-6142	35	19	for	for	ADP
ap-6142	35	20	“	"	PUNCT
ap-6142	35	21	large	large	ADJ
ap-6142	35	22	”	"	PUNCT
ap-6142	35	23	data	datum	NOUN
ap-6142	35	24	(	(	PUNCT
ap-6142	35	25	which	which	PRON
ap-6142	35	26	is	be	AUX
ap-6142	35	27	well	well	ADV
ap-6142	35	28	known	known	ADJ
ap-6142	35	29	for	for	ADP
ap-6142	35	30	the	the	DET
ap-6142	35	31	navier	navier	NOUN
ap-6142	35	32	–	–	PUNCT
ap-6142	35	33	stokes	stoke	NOUN
ap-6142	35	34	equations	equation	NOUN
ap-6142	35	35	with	with	ADP
ap-6142	35	36	the	the	DET
ap-6142	35	37	dirichlet	dirichlet	PROPN
ap-6142	35	38	or	or	CCONJ
ap-6142	35	39	navier	navier	NOUN
ap-6142	35	40	boundary	boundary	ADJ
ap-6142	35	41	conditions	condition	NOUN
ap-6142	35	42	on	on	ADP
ap-6142	35	43	∂ω	∂ω	PROPN
ap-6142	35	44	)	)	PUNCT
ap-6142	35	45	,	,	PUNCT
ap-6142	35	46	is	be	AUX
ap-6142	35	47	an	an	DET
ap-6142	35	48	open	open	ADJ
ap-6142	35	49	problem	problem	NOUN
ap-6142	35	50	.	.	PUNCT
ap-6142	36	1	a	a	DET
ap-6142	36	2	similar	similar	ADJ
ap-6142	36	3	problem	problem	NOUN
ap-6142	36	4	arises	arise	VERB
ap-6142	36	5	if	if	SCONJ
ap-6142	36	6	one	one	NUM
ap-6142	36	7	studies	study	NOUN
ap-6142	36	8	a	a	DET
ap-6142	36	9	flow	flow	NOUN
ap-6142	36	10	through	through	ADP
ap-6142	36	11	a	a	DET
ap-6142	36	12	2d	2d	NUM
ap-6142	36	13	turbine	turbine	NOUN
ap-6142	36	14	cascade	cascade	NOUN
ap-6142	36	15	,	,	PUNCT
ap-6142	36	16	see	see	VERB
ap-6142	36	17	[	[	X
ap-6142	36	18	3	3	NUM
ap-6142	36	19	,	,	PUNCT
ap-6142	36	20	4	4	NUM
ap-6142	36	21	]	]	PUNCT
ap-6142	36	22	.	.	PUNCT
ap-6142	37	1	some	some	DET
ap-6142	37	2	authors	author	NOUN
ap-6142	37	3	use	use	VERB
ap-6142	37	4	boundary	boundary	ADJ
ap-6142	37	5	conditions	condition	NOUN
ap-6142	37	6	on	on	ADP
ap-6142	37	7	γ2	γ2	ADJ
ap-6142	37	8	,	,	PUNCT
ap-6142	37	9	modified	modify	VERB
ap-6142	37	10	in	in	ADP
ap-6142	37	11	such	such	DET
ap-6142	37	12	a	a	DET
ap-6142	37	13	way	way	NOUN
ap-6142	37	14	that	that	PRON
ap-6142	37	15	it	it	PRON
ap-6142	37	16	enables	enable	VERB
ap-6142	37	17	one	one	NUM
ap-6142	37	18	to	to	PART
ap-6142	37	19	estimate	estimate	VERB
ap-6142	37	20	the	the	DET
ap-6142	37	21	kinetic	kinetic	ADJ
ap-6142	37	22	energy	energy	NOUN
ap-6142	37	23	of	of	ADP
ap-6142	37	24	the	the	DET
ap-6142	37	25	fluid	fluid	NOUN
ap-6142	37	26	flowing	flow	VERB
ap-6142	37	27	to	to	ADP
ap-6142	37	28	ω	ω	PROPN
ap-6142	37	29	through	through	ADP
ap-6142	37	30	γ2	γ2	PROPN
ap-6142	37	31	.	.	PUNCT
ap-6142	38	1	examples	example	NOUN
ap-6142	38	2	of	of	ADP
ap-6142	38	3	such	such	ADJ
ap-6142	38	4	modifications	modification	NOUN
ap-6142	38	5	can	can	AUX
ap-6142	38	6	be	be	AUX
ap-6142	38	7	found	find	VERB
ap-6142	38	8	in	in	ADP
ap-6142	38	9	[	[	X
ap-6142	38	10	2	2	NUM
ap-6142	38	11	,	,	PUNCT
ap-6142	38	12	5	5	NUM
ap-6142	38	13	,	,	PUNCT
ap-6142	38	14	7	7	NUM
ap-6142	38	15	,	,	PUNCT
ap-6142	38	16	11	11	NUM
ap-6142	38	17	,	,	PUNCT
ap-6142	38	18	12	12	NUM
ap-6142	38	19	]	]	PUNCT
ap-6142	38	20	.	.	PUNCT
ap-6142	39	1	another	another	DET
ap-6142	39	2	modification	modification	NOUN
ap-6142	39	3	,	,	PUNCT
ap-6142	39	4	used	use	VERB
ap-6142	39	5	in	in	ADP
ap-6142	39	6	connection	connection	NOUN
ap-6142	39	7	with	with	ADP
ap-6142	39	8	the	the	DET
ap-6142	39	9	heat	heat	NOUN
ap-6142	39	10	transfer	transfer	NOUN
ap-6142	39	11	,	,	PUNCT
ap-6142	39	12	can	can	AUX
ap-6142	39	13	be	be	AUX
ap-6142	39	14	found	find	VERB
ap-6142	39	15	in	in	ADP
ap-6142	39	16	[	[	X
ap-6142	39	17	8	8	NUM
ap-6142	39	18	]	]	PUNCT
ap-6142	39	19	.	.	PUNCT
ap-6142	40	1	a	a	DET
ap-6142	40	2	different	different	ADJ
ap-6142	40	3	approach	approach	NOUN
ap-6142	40	4	has	have	AUX
ap-6142	40	5	been	be	AUX
ap-6142	40	6	suggested	suggest	VERB
ap-6142	40	7	in	in	ADP
ap-6142	40	8	papers	paper	NOUN
ap-6142	40	9	[	[	X
ap-6142	40	10	13–15	13–15	NUM
ap-6142	40	11	]	]	PUNCT
ap-6142	40	12	.	.	PUNCT
ap-6142	41	1	there	there	ADV
ap-6142	41	2	the	the	DET
ap-6142	41	3	authors	author	NOUN
ap-6142	41	4	have	have	AUX
ap-6142	41	5	considered	consider	VERB
ap-6142	41	6	the	the	DET
ap-6142	41	7	stationary	stationary	ADJ
ap-6142	41	8	and	and	CCONJ
ap-6142	41	9	non	non	ADJ
ap-6142	41	10	-	-	ADJ
ap-6142	41	11	stationary	stationary	ADJ
ap-6142	41	12	problems	problem	NOUN
ap-6142	41	13	and	and	CCONJ
ap-6142	41	14	impose	impose	VERB
ap-6142	41	15	an	an	DET
ap-6142	41	16	additional	additional	ADJ
ap-6142	41	17	condition	condition	NOUN
ap-6142	41	18	on	on	ADP
ap-6142	41	19	γ2	γ2	PROPN
ap-6142	41	20	,	,	PUNCT
ap-6142	41	21	that	that	PRON
ap-6142	41	22	enables	enable	VERB
ap-6142	41	23	one	one	NUM
ap-6142	41	24	to	to	PART
ap-6142	41	25	estimate	estimate	VERB
ap-6142	41	26	the	the	DET
ap-6142	41	27	kinetic	kinetic	ADJ
ap-6142	41	28	energy	energy	NOUN
ap-6142	41	29	of	of	ADP
ap-6142	41	30	a	a	DET
ap-6142	41	31	possible	possible	ADJ
ap-6142	41	32	reverse	reverse	NOUN
ap-6142	41	33	flow	flow	NOUN
ap-6142	41	34	and	and	CCONJ
ap-6142	41	35	obtain	obtain	VERB
ap-6142	41	36	an	an	DET
ap-6142	41	37	a	a	DET
ap-6142	41	38	priori	priori	ADJ
ap-6142	41	39	estimate	estimate	NOUN
ap-6142	41	40	of	of	ADP
ap-6142	41	41	the	the	DET
ap-6142	41	42	energy	energy	NOUN
ap-6142	41	43	type	type	NOUN
ap-6142	41	44	.	.	PUNCT
ap-6142	42	1	however	however	ADV
ap-6142	42	2	,	,	PUNCT
ap-6142	42	3	the	the	DET
ap-6142	42	4	new	new	ADJ
ap-6142	42	5	additional	additional	ADJ
ap-6142	42	6	condition	condition	NOUN
ap-6142	42	7	implies	imply	VERB
ap-6142	42	8	that	that	SCONJ
ap-6142	42	9	the	the	DET
ap-6142	42	10	solution	solution	NOUN
ap-6142	42	11	can	can	AUX
ap-6142	42	12	not	not	PART
ap-6142	42	13	lie	lie	VERB
ap-6142	42	14	in	in	ADP
ap-6142	42	15	the	the	DET
ap-6142	42	16	whole	whole	ADJ
ap-6142	42	17	sobolev	sobolev	NOUN
ap-6142	42	18	space	space	PROPN
ap-6142	42	19	w	w	PROPN
ap-6142	42	20	1,2(ω	1,2(ω	NUM
ap-6142	42	21	)	)	PUNCT
ap-6142	42	22	,	,	PUNCT
ap-6142	42	23	but	but	CCONJ
ap-6142	42	24	only	only	ADV
ap-6142	42	25	in	in	ADP
ap-6142	42	26	a	a	DET
ap-6142	42	27	certain	certain	ADJ
ap-6142	42	28	closed	closed	ADJ
ap-6142	42	29	convex	convex	NOUN
ap-6142	42	30	subset	subset	NOUN
ap-6142	42	31	of	of	ADP
ap-6142	42	32	this	this	DET
ap-6142	42	33	space	space	NOUN
ap-6142	42	34	.	.	PUNCT
ap-6142	43	1	since	since	SCONJ
ap-6142	43	2	one	one	PRON
ap-6142	43	3	does	do	AUX
ap-6142	43	4	not	not	PART
ap-6142	43	5	know	know	VERB
ap-6142	43	6	in	in	ADP
ap-6142	43	7	advance	advance	NOUN
ap-6142	43	8	whether	whether	SCONJ
ap-6142	43	9	the	the	DET
ap-6142	43	10	solution	solution	NOUN
ap-6142	43	11	of	of	ADP
ap-6142	43	12	the	the	DET
ap-6142	43	13	problem	problem	NOUN
ap-6142	43	14	(	(	PUNCT
ap-6142	43	15	1)–(5	1)–(5	NUM
ap-6142	43	16	)	)	PUNCT
ap-6142	43	17	falls	fall	VERB
ap-6142	43	18	into	into	ADP
ap-6142	43	19	this	this	DET
ap-6142	43	20	convex	convex	NOUN
ap-6142	43	21	set	set	NOUN
ap-6142	43	22	,	,	PUNCT
ap-6142	43	23	one	one	PRON
ap-6142	43	24	must	must	AUX
ap-6142	43	25	consider	consider	VERB
ap-6142	43	26	a	a	DET
ap-6142	43	27	variational	variational	ADJ
ap-6142	43	28	inequality	inequality	NOUN
ap-6142	43	29	instead	instead	ADV
ap-6142	43	30	of	of	ADP
ap-6142	43	31	the	the	DET
ap-6142	43	32	momentum	momentum	NOUN
ap-6142	43	33	equation	equation	NOUN
ap-6142	43	34	.	.	PUNCT
ap-6142	44	1	note	note	VERB
ap-6142	44	2	that	that	SCONJ
ap-6142	44	3	artificial	artificial	ADJ
ap-6142	44	4	boundary	boundary	ADJ
ap-6142	44	5	conditions	condition	NOUN
ap-6142	44	6	on	on	ADP
ap-6142	44	7	a	a	DET
ap-6142	44	8	part	part	NOUN
ap-6142	44	9	of	of	ADP
ap-6142	44	10	the	the	DET
ap-6142	44	11	boundary	boundary	NOUN
ap-6142	44	12	are	be	AUX
ap-6142	44	13	also	also	ADV
ap-6142	44	14	being	be	AUX
ap-6142	44	15	used	use	VERB
ap-6142	44	16	,	,	PUNCT
ap-6142	44	17	if	if	SCONJ
ap-6142	44	18	one	one	PRON
ap-6142	44	19	approximates	approximate	VERB
ap-6142	44	20	a	a	DET
ap-6142	44	21	problem	problem	NOUN
ap-6142	44	22	in	in	ADP
ap-6142	44	23	an	an	DET
ap-6142	44	24	exterior	exterior	ADJ
ap-6142	44	25	domain	domain	NOUN
ap-6142	44	26	d	d	NOUN
ap-6142	44	27	by	by	ADP
ap-6142	44	28	a	a	DET
ap-6142	44	29	problem	problem	NOUN
ap-6142	44	30	in	in	ADP
ap-6142	44	31	a	a	DET
ap-6142	44	32	bounded	bounded	ADJ
ap-6142	44	33	domain	domain	NOUN
ap-6142	44	34	d	d	NOUN
ap-6142	44	35	∩	∩	X
ap-6142	44	36	br(0	br(0	NOUN
ap-6142	44	37	)	)	PUNCT
ap-6142	44	38	(	(	PUNCT
ap-6142	44	39	for	for	ADP
ap-6142	44	40	“	"	PUNCT
ap-6142	44	41	large	large	ADJ
ap-6142	44	42	”	"	PUNCT
ap-6142	44	43	r	r	NOUN
ap-6142	44	44	)	)	PUNCT
ap-6142	44	45	and	and	CCONJ
ap-6142	44	46	prescribes	prescribe	VERB
ap-6142	44	47	an	an	DET
ap-6142	44	48	artificial	artificial	ADJ
ap-6142	44	49	boundary	boundary	ADJ
ap-6142	44	50	condition	condition	NOUN
ap-6142	44	51	on	on	ADP
ap-6142	44	52	∂br(0	∂br(0	PROPN
ap-6142	44	53	)	)	PUNCT
ap-6142	44	54	.	.	PUNCT
ap-6142	45	1	(	(	PUNCT
ap-6142	45	2	see	see	VERB
ap-6142	45	3	e.g.	e.g.	ADV
ap-6142	45	4	[	[	X
ap-6142	45	5	16	16	NUM
ap-6142	45	6	]	]	PUNCT
ap-6142	45	7	and	and	CCONJ
ap-6142	45	8	[	[	X
ap-6142	45	9	17	17	NUM
ap-6142	45	10	]	]	PUNCT
ap-6142	45	11	.	.	PUNCT
ap-6142	45	12	)	)	PUNCT
ap-6142	46	1	2	2	X
ap-6142	46	2	.	.	X
ap-6142	46	3	several	several	ADJ
ap-6142	46	4	boundary	boundary	ADJ
ap-6142	46	5	conditions	condition	NOUN
ap-6142	46	6	of	of	ADP
ap-6142	46	7	the	the	DET
ap-6142	46	8	“	"	PUNCT
ap-6142	46	9	do	do	AUX
ap-6142	46	10	nothing	nothing	PRON
ap-6142	46	11	”	"	PUNCT
ap-6142	46	12	type	type	NOUN
ap-6142	46	13	2.1	2.1	NUM
ap-6142	46	14	.	.	PUNCT
ap-6142	47	1	three	three	NUM
ap-6142	47	2	equivalent	equivalent	ADJ
ap-6142	47	3	forms	form	NOUN
ap-6142	47	4	of	of	ADP
ap-6142	47	5	the	the	DET
ap-6142	47	6	dynamic	dynamic	ADJ
ap-6142	47	7	stress	stress	NOUN
ap-6142	47	8	tensor	tensor	NOUN
ap-6142	47	9	in	in	ADP
ap-6142	47	10	equation	equation	NOUN
ap-6142	47	11	(	(	PUNCT
ap-6142	47	12	1	1	NUM
ap-6142	47	13	)	)	PUNCT
ap-6142	47	14	since	since	SCONJ
ap-6142	47	15	the	the	DET
ap-6142	47	16	difficulties	difficulty	NOUN
ap-6142	47	17	,	,	PUNCT
ap-6142	47	18	caused	cause	VERB
ap-6142	47	19	by	by	ADP
ap-6142	47	20	the	the	DET
ap-6142	47	21	artificial	artificial	ADJ
ap-6142	47	22	boundary	boundary	ADJ
ap-6142	47	23	conditions	condition	NOUN
ap-6142	47	24	on	on	ADP
ap-6142	47	25	γ2	γ2	NOUN
ap-6142	47	26	,	,	PUNCT
ap-6142	47	27	are	be	AUX
ap-6142	47	28	of	of	ADP
ap-6142	47	29	the	the	DET
ap-6142	47	30	same	same	ADJ
ap-6142	47	31	nature	nature	NOUN
ap-6142	47	32	in	in	ADP
ap-6142	47	33	stationary	stationary	ADJ
ap-6142	47	34	and	and	CCONJ
ap-6142	47	35	non	non	ADJ
ap-6142	47	36	-	-	ADJ
ap-6142	47	37	stationary	stationary	ADJ
ap-6142	47	38	problems	problem	NOUN
ap-6142	47	39	,	,	PUNCT
ap-6142	47	40	here	here	ADV
ap-6142	47	41	we	we	PRON
ap-6142	47	42	consider	consider	VERB
ap-6142	47	43	,	,	PUNCT
ap-6142	47	44	for	for	ADP
ap-6142	47	45	simplicity	simplicity	NOUN
ap-6142	47	46	,	,	PUNCT
ap-6142	47	47	only	only	ADV
ap-6142	47	48	the	the	DET
ap-6142	47	49	stationary	stationary	ADJ
ap-6142	47	50	problem	problem	NOUN
ap-6142	47	51	.	.	PUNCT
ap-6142	48	1	the	the	DET
ap-6142	48	2	dynamic	dynamic	ADJ
ap-6142	48	3	stress	stress	NOUN
ap-6142	48	4	tensor	tensor	NOUN
ap-6142	48	5	sd	sd	NOUN
ap-6142	48	6	,	,	PUNCT
ap-6142	48	7	in	in	ADP
ap-6142	48	8	an	an	DET
ap-6142	48	9	incompressible	incompressible	ADJ
ap-6142	48	10	newtonian	newtonian	ADJ
ap-6142	48	11	fluid	fluid	NOUN
ap-6142	48	12	,	,	PUNCT
ap-6142	48	13	equals	equal	VERB
ap-6142	48	14	2νd	2νd	ADJ
ap-6142	48	15	,	,	PUNCT
ap-6142	48	16	where	where	SCONJ
ap-6142	48	17	d	d	NOUN
ap-6142	48	18	is	be	AUX
ap-6142	48	19	the	the	DET
ap-6142	48	20	rate	rate	NOUN
ap-6142	48	21	of	of	ADP
ap-6142	48	22	the	the	DET
ap-6142	48	23	deformation	deformation	NOUN
ap-6142	48	24	tensor	tensor	NOUN
ap-6142	48	25	.	.	PUNCT
ap-6142	49	1	(	(	PUNCT
ap-6142	49	2	it	it	PRON
ap-6142	49	3	coincides	coincide	VERB
ap-6142	49	4	with	with	ADP
ap-6142	49	5	the	the	DET
ap-6142	49	6	symmetrized	symmetrize	VERB
ap-6142	49	7	gradient	gradient	NOUN
ap-6142	49	8	of	of	ADP
ap-6142	49	9	velocity	velocity	NOUN
ap-6142	49	10	.	.	PUNCT
ap-6142	49	11	)	)	PUNCT
ap-6142	50	1	the	the	DET
ap-6142	50	2	term	term	NOUN
ap-6142	50	3	div	div	PROPN
ap-6142	50	4	sd	sd	NOUN
ap-6142	50	5	,	,	PUNCT
ap-6142	50	6	which	which	PRON
ap-6142	50	7	appears	appear	VERB
ap-6142	50	8	in	in	ADP
ap-6142	50	9	equation	equation	NOUN
ap-6142	50	10	(	(	PUNCT
ap-6142	50	11	1	1	NUM
ap-6142	50	12	)	)	PUNCT
ap-6142	50	13	,	,	PUNCT
ap-6142	50	14	can	can	AUX
ap-6142	50	15	be	be	AUX
ap-6142	50	16	expressed	express	VERB
ap-6142	50	17	by	by	ADP
ap-6142	50	18	any	any	PRON
ap-6142	50	19	of	of	ADP
ap-6142	50	20	these	these	DET
ap-6142	50	21	formulas	formula	NOUN
ap-6142	50	22	:	:	PUNCT
ap-6142	50	23	a	a	X
ap-6142	50	24	)	)	PUNCT
ap-6142	50	25	div	div	X
ap-6142	50	26	sd	sd	ADP
ap-6142	50	27	=	=	PUNCT
ap-6142	50	28	ν∆v	ν∆v	PROPN
ap-6142	50	29	,	,	PUNCT
ap-6142	50	30	b	b	NOUN
ap-6142	50	31	)	)	PUNCT
ap-6142	50	32	div	div	X
ap-6142	50	33	sd	sd	NOUN
ap-6142	50	34	=	=	SYM
ap-6142	50	35	ν	ν	X
ap-6142	50	36	div	div	X
ap-6142	50	37	[	[	PUNCT
ap-6142	50	38	∇v	∇v	PROPN
ap-6142	50	39	+	+	CCONJ
ap-6142	50	40	(	(	PUNCT
ap-6142	50	41	∇v)t	∇v)t	X
ap-6142	50	42	]	]	PUNCT
ap-6142	50	43	,	,	PUNCT
ap-6142	50	44	c	c	X
ap-6142	50	45	)	)	PUNCT
ap-6142	50	46	div	div	X
ap-6142	50	47	sd	sd	ADP
ap-6142	50	48	=	=	PUNCT
ap-6142	50	49	−ν	−ν	NOUN
ap-6142	50	50	curl2v	curl2v	NOUN
ap-6142	50	51	.	.	PUNCT
ap-6142	51	1			PROPN
ap-6142	51	2	(	(	PUNCT
ap-6142	51	3	7	7	NUM
ap-6142	51	4	)	)	PUNCT
ap-6142	51	5	2.2	2.2	NUM
ap-6142	51	6	.	.	PUNCT
ap-6142	52	1	variational	variational	ADJ
ap-6142	52	2	formulations	formulation	NOUN
ap-6142	52	3	of	of	ADP
ap-6142	52	4	the	the	DET
ap-6142	52	5	initial	initial	ADJ
ap-6142	52	6	–	–	PUNCT
ap-6142	52	7	boundary	boundary	ADJ
ap-6142	52	8	value	value	NOUN
ap-6142	52	9	problem	problem	NOUN
ap-6142	52	10	a	a	DET
ap-6142	52	11	variational	variational	ADJ
ap-6142	52	12	formulation	formulation	NOUN
ap-6142	52	13	of	of	ADP
ap-6142	52	14	the	the	DET
ap-6142	52	15	system	system	NOUN
ap-6142	52	16	(	(	PUNCT
ap-6142	52	17	1	1	NUM
ap-6142	52	18	)	)	PUNCT
ap-6142	52	19	,	,	PUNCT
ap-6142	52	20	(	(	PUNCT
ap-6142	52	21	2	2	X
ap-6142	52	22	)	)	PUNCT
ap-6142	52	23	with	with	ADP
ap-6142	52	24	the	the	DET
ap-6142	52	25	boundary	boundary	ADJ
ap-6142	52	26	conditions	condition	NOUN
ap-6142	52	27	(	(	PUNCT
ap-6142	52	28	3	3	NUM
ap-6142	52	29	)	)	PUNCT
ap-6142	52	30	,	,	PUNCT
ap-6142	52	31	(	(	PUNCT
ap-6142	52	32	4	4	X
ap-6142	52	33	)	)	PUNCT
ap-6142	52	34	formally	formally	ADV
ap-6142	52	35	follows	follow	VERB
ap-6142	52	36	from	from	ADP
ap-6142	52	37	the	the	DET
ap-6142	52	38	classical	classical	ADJ
ap-6142	52	39	formulation	formulation	NOUN
ap-6142	52	40	if	if	SCONJ
ap-6142	52	41	one	one	NUM
ap-6142	52	42	multiplies	multiplie	NOUN
ap-6142	52	43	equation	equation	NOUN
ap-6142	52	44	(	(	PUNCT
ap-6142	52	45	1	1	NUM
ap-6142	52	46	)	)	PUNCT
ap-6142	52	47	by	by	ADP
ap-6142	52	48	a	a	DET
ap-6142	52	49	“	"	PUNCT
ap-6142	52	50	smooth	smooth	ADJ
ap-6142	52	51	”	"	PUNCT
ap-6142	52	52	test	test	NOUN
ap-6142	52	53	function	function	NOUN
ap-6142	52	54	φ	φ	PROPN
ap-6142	52	55	,	,	PUNCT
ap-6142	52	56	such	such	ADJ
ap-6142	52	57	that	that	DET
ap-6142	52	58	divφ	divφ	NOUN
ap-6142	52	59	=	=	SYM
ap-6142	52	60	0	0	NUM
ap-6142	52	61	,	,	PUNCT
ap-6142	52	62	and	and	CCONJ
ap-6142	52	63	integrates	integrate	NOUN
ap-6142	52	64	in	in	ADP
ap-6142	52	65	ω	ω	PROPN
ap-6142	52	66	.	.	PUNCT
ap-6142	53	1	as	as	SCONJ
ap-6142	53	2	v	v	NOUN
ap-6142	53	3	should	should	AUX
ap-6142	53	4	satisfy	satisfy	VERB
ap-6142	53	5	the	the	DET
ap-6142	53	6	dirichlet	dirichlet	PROPN
ap-6142	53	7	boundary	boundary	ADJ
ap-6142	53	8	conditions	condition	NOUN
ap-6142	53	9	(	(	PUNCT
ap-6142	53	10	3	3	NUM
ap-6142	53	11	)	)	PUNCT
ap-6142	53	12	and	and	CCONJ
ap-6142	53	13	(	(	PUNCT
ap-6142	53	14	4	4	X
ap-6142	53	15	)	)	PUNCT
ap-6142	53	16	on	on	ADP
ap-6142	53	17	γ0	γ0	NOUN
ap-6142	53	18	and	and	CCONJ
ap-6142	53	19	γ1	γ1	PROPN
ap-6142	53	20	,	,	PUNCT
ap-6142	53	21	respectively	respectively	ADV
ap-6142	53	22	,	,	PUNCT
ap-6142	53	23	it	it	PRON
ap-6142	53	24	is	be	AUX
ap-6142	53	25	logical	logical	ADJ
ap-6142	53	26	to	to	PART
ap-6142	53	27	assume	assume	VERB
ap-6142	53	28	that	that	SCONJ
ap-6142	53	29	φ	φ	PROPN
ap-6142	53	30	=	=	SYM
ap-6142	53	31	0	0	NUM
ap-6142	53	32	on	on	ADP
ap-6142	53	33	γ0∪γ1	γ0∪γ1	NOUN
ap-6142	53	34	.	.	PUNCT
ap-6142	54	1	on	on	ADP
ap-6142	54	2	the	the	DET
ap-6142	54	3	other	other	ADJ
ap-6142	54	4	hand	hand	NOUN
ap-6142	54	5	,	,	PUNCT
ap-6142	54	6	one	one	PRON
ap-6142	54	7	imposes	impose	VERB
ap-6142	54	8	no	no	DET
ap-6142	54	9	boundary	boundary	ADJ
ap-6142	54	10	condition	condition	NOUN
ap-6142	54	11	on	on	ADP
ap-6142	54	12	φ	φ	PROPN
ap-6142	54	13	on	on	ADP
ap-6142	54	14	γ2	γ2	PROPN
ap-6142	54	15	.	.	PUNCT
ap-6142	55	1	applying	apply	VERB
ap-6142	55	2	the	the	DET
ap-6142	55	3	integration	integration	NOUN
ap-6142	55	4	by	by	ADP
ap-6142	55	5	parts	part	NOUN
ap-6142	55	6	,	,	PUNCT
ap-6142	55	7	using	use	VERB
ap-6142	55	8	the	the	DET
ap-6142	55	9	forms	form	NOUN
ap-6142	55	10	a	a	PRON
ap-6142	55	11	)	)	PUNCT
ap-6142	55	12	–	–	PUNCT
ap-6142	55	13	c	c	X
ap-6142	55	14	)	)	PUNCT
ap-6142	55	15	of	of	ADP
ap-6142	55	16	the	the	DET
ap-6142	55	17	dynamic	dynamic	ADJ
ap-6142	55	18	stress	stress	NOUN
ap-6142	55	19	tensor	tensor	NOUN
ap-6142	55	20	,	,	PUNCT
ap-6142	55	21	we	we	PRON
ap-6142	55	22	successively	successively	ADV
ap-6142	55	23	obtain	obtain	VERB
ap-6142	55	24	the	the	DET
ap-6142	55	25	equations	equation	NOUN
ap-6142	55	26	a	a	PRON
ap-6142	55	27	)	)	PUNCT
ap-6142	56	1	∫	∫	PROPN
ap-6142	56	2	ω	ω	PROPN
ap-6142	56	3	[	[	PUNCT
ap-6142	56	4	v	v	NOUN
ap-6142	56	5	·	·	PUNCT
ap-6142	56	6	∇v	∇v	NOUN
ap-6142	56	7	·	·	PUNCT
ap-6142	56	8	φ+	φ+	NOUN
ap-6142	56	9	ν∇v	ν∇v	NOUN
ap-6142	56	10	:	:	PUNCT
ap-6142	57	1	∇φ	∇φ	ADJ
ap-6142	57	2	]	]	PUNCT
ap-6142	57	3	dx	dx	PROPN
ap-6142	58	1	=	=	SYM
ap-6142	58	2	∫	∫	PROPN
ap-6142	58	3	γ2	γ2	PROPN
ap-6142	58	4	[	[	X
ap-6142	58	5	−pn+	−pn+	PROPN
ap-6142	58	6	ν∇v	ν∇v	X
ap-6142	58	7	·	·	PUNCT
ap-6142	58	8	n	n	CCONJ
ap-6142	58	9	]	]	PUNCT
ap-6142	58	10	·	·	PUNCT
ap-6142	58	11	φ	φ	NUM
ap-6142	58	12	ds	ds	PROPN
ap-6142	58	13	+	+	CCONJ
ap-6142	58	14	∫	∫	PROPN
ap-6142	58	15	ω	ω	PROPN
ap-6142	58	16	f	f	PROPN
ap-6142	58	17	·	·	PUNCT
ap-6142	58	18	φ	φ	PROPN
ap-6142	58	19	dx	dx	PROPN
ap-6142	58	20	,	,	PUNCT
ap-6142	58	21	b	b	PROPN
ap-6142	58	22	)	)	PUNCT
ap-6142	58	23	∫	∫	PROPN
ap-6142	59	1	ω	ω	PROPN
ap-6142	59	2	[	[	PUNCT
ap-6142	59	3	v	v	NOUN
ap-6142	59	4	·	·	PUNCT
ap-6142	59	5	∇v	∇v	NOUN
ap-6142	59	6	·	·	PUNCT
ap-6142	59	7	φ+	φ+	NOUN
ap-6142	59	8	ν(∇v	ν(∇v	NUM
ap-6142	59	9	+	+	CCONJ
ap-6142	59	10	(	(	PUNCT
ap-6142	59	11	∇v)t	∇v)t	X
ap-6142	59	12	)	)	PUNCT
ap-6142	59	13	:	:	PUNCT
ap-6142	60	1	∇φ	∇φ	ADJ
ap-6142	60	2	dx	dx	PROPN
ap-6142	60	3	=	=	SYM
ap-6142	60	4	∫	∫	PROPN
ap-6142	60	5	γ2	γ2	PROPN
ap-6142	60	6	[	[	PUNCT
ap-6142	60	7	−pn+	−pn+	NOUN
ap-6142	60	8	ν	ν	X
ap-6142	60	9	(	(	PUNCT
ap-6142	60	10	∇v	∇v	PROPN
ap-6142	60	11	+	+	CCONJ
ap-6142	60	12	(	(	PUNCT
ap-6142	60	13	∇v)t	∇v)t	X
ap-6142	60	14	)	)	PUNCT
ap-6142	60	15	·	·	PUNCT
ap-6142	61	1	n	n	CCONJ
ap-6142	61	2	]	]	PUNCT
ap-6142	61	3	·	·	PUNCT
ap-6142	61	4	φ	φ	NUM
ap-6142	61	5	ds	ds	PROPN
ap-6142	61	6	+	+	CCONJ
ap-6142	61	7	∫	∫	PROPN
ap-6142	61	8	ω	ω	PROPN
ap-6142	61	9	f	f	PROPN
ap-6142	61	10	·	·	PUNCT
ap-6142	61	11	φ	φ	PROPN
ap-6142	61	12	dx	dx	PROPN
ap-6142	61	13	,	,	PUNCT
ap-6142	61	14	c	c	NOUN
ap-6142	61	15	)	)	PUNCT
ap-6142	61	16	∫	∫	PROPN
ap-6142	62	1	ω	ω	PROPN
ap-6142	62	2	[	[	PUNCT
ap-6142	62	3	v	v	NOUN
ap-6142	62	4	·	·	PUNCT
ap-6142	62	5	∇v	∇v	NOUN
ap-6142	62	6	·	·	PUNCT
ap-6142	62	7	φ+	φ+	NOUN
ap-6142	62	8	ν	ν	X
ap-6142	62	9	curlv	curlv	X
ap-6142	62	10	·	·	PUNCT
ap-6142	62	11	curlφ	curlφ	PROPN
ap-6142	62	12	]	]	PUNCT
ap-6142	62	13	dx	dx	PROPN
ap-6142	63	1	=	=	SYM
ap-6142	63	2	∫	∫	PROPN
ap-6142	63	3	γ2	γ2	PROPN
ap-6142	63	4	[	[	X
ap-6142	63	5	−pn−	−pn−	X
ap-6142	63	6	ν	ν	X
ap-6142	63	7	curlv	curlv	X
ap-6142	63	8	×	×	PROPN
ap-6142	63	9	n	n	CCONJ
ap-6142	63	10	]	]	PUNCT
ap-6142	63	11	·	·	PUNCT
ap-6142	63	12	φ	φ	NUM
ap-6142	63	13	ds	ds	PROPN
ap-6142	64	1	+	+	CCONJ
ap-6142	64	2	∫	∫	PROPN
ap-6142	64	3	ω	ω	PROPN
ap-6142	64	4	f	f	PROPN
ap-6142	64	5	·	·	PUNCT
ap-6142	64	6	φ	φ	PROPN
ap-6142	64	7	dx	dx	PROPN
ap-6142	64	8	.	.	PUNCT
ap-6142	65	1	however	however	ADV
ap-6142	65	2	,	,	PUNCT
ap-6142	65	3	the	the	DET
ap-6142	65	4	integrals	integral	NOUN
ap-6142	65	5	on	on	ADP
ap-6142	65	6	γ2	γ2	PROPN
ap-6142	65	7	can	can	AUX
ap-6142	65	8	not	not	PART
ap-6142	65	9	be	be	AUX
ap-6142	65	10	involved	involve	VERB
ap-6142	65	11	by	by	ADP
ap-6142	65	12	the	the	DET
ap-6142	65	13	weak	weak	ADJ
ap-6142	65	14	formulation	formulation	NOUN
ap-6142	65	15	because	because	SCONJ
ap-6142	65	16	the	the	DET
ap-6142	65	17	integrands	integrand	NOUN
ap-6142	65	18	are	be	AUX
ap-6142	65	19	generally	generally	ADV
ap-6142	65	20	not	not	PART
ap-6142	65	21	integrable	integrable	ADJ
ap-6142	65	22	if	if	SCONJ
ap-6142	65	23	one	one	NUM
ap-6142	65	24	stays	stay	VERB
ap-6142	65	25	in	in	ADP
ap-6142	65	26	the	the	DET
ap-6142	65	27	usual	usual	ADJ
ap-6142	65	28	level	level	NOUN
ap-6142	65	29	of	of	ADP
ap-6142	65	30	weak	weak	ADJ
ap-6142	65	31	solutions	solution	NOUN
ap-6142	65	32	.	.	PUNCT
ap-6142	66	1	this	this	PRON
ap-6142	66	2	is	be	AUX
ap-6142	66	3	why	why	SCONJ
ap-6142	66	4	it	it	PRON
ap-6142	66	5	is	be	AUX
ap-6142	66	6	logical	logical	ADJ
ap-6142	66	7	to	to	PART
ap-6142	66	8	neglect	neglect	VERB
ap-6142	66	9	these	these	DET
ap-6142	66	10	integrals	integral	NOUN
ap-6142	66	11	or	or	CCONJ
ap-6142	66	12	to	to	PART
ap-6142	66	13	replace	replace	VERB
ap-6142	66	14	them	they	PRON
ap-6142	66	15	just	just	ADV
ap-6142	66	16	by	by	ADP
ap-6142	66	17	∫	∫	PROPN
ap-6142	66	18	γ2	γ2	PROPN
ap-6142	66	19	g	g	PROPN
ap-6142	66	20	·	·	PROPN
ap-6142	66	21	φ	φ	X
ap-6142	66	22	ds	ds	PROPN
ap-6142	66	23	,	,	PUNCT
ap-6142	66	24	where	where	SCONJ
ap-6142	66	25	g	g	PROPN
ap-6142	66	26	is	be	AUX
ap-6142	66	27	an	an	DET
ap-6142	66	28	arbitrarily	arbitrarily	ADV
ap-6142	66	29	given	give	VERB
ap-6142	66	30	function	function	NOUN
ap-6142	66	31	on	on	ADP
ap-6142	66	32	γ2	γ2	PROPN
ap-6142	66	33	.	.	PUNCT
ap-6142	67	1	then	then	ADV
ap-6142	67	2	the	the	DET
ap-6142	67	3	variational	variational	ADJ
ap-6142	67	4	forms	form	NOUN
ap-6142	67	5	of	of	ADP
ap-6142	67	6	the	the	DET
ap-6142	67	7	system	system	NOUN
ap-6142	67	8	(	(	PUNCT
ap-6142	67	9	1	1	NUM
ap-6142	67	10	)	)	PUNCT
ap-6142	67	11	,	,	PUNCT
ap-6142	67	12	(	(	PUNCT
ap-6142	67	13	2	2	X
ap-6142	67	14	)	)	PUNCT
ap-6142	67	15	are	be	AUX
ap-6142	67	16	a	a	PRON
ap-6142	67	17	)	)	PUNCT
ap-6142	68	1	∫	∫	PROPN
ap-6142	68	2	ω	ω	PROPN
ap-6142	68	3	[	[	PUNCT
ap-6142	68	4	v	v	NOUN
ap-6142	68	5	·	·	PUNCT
ap-6142	68	6	∇v	∇v	NOUN
ap-6142	68	7	·	·	PUNCT
ap-6142	68	8	φ+	φ+	NOUN
ap-6142	68	9	ν∇v	ν∇v	NOUN
ap-6142	68	10	:	:	PUNCT
ap-6142	69	1	∇φ	∇φ	ADJ
ap-6142	69	2	]	]	PUNCT
ap-6142	69	3	dx	dx	PROPN
ap-6142	70	1	=	=	SYM
ap-6142	70	2	∫	∫	PROPN
ap-6142	70	3	γ2	γ2	PROPN
ap-6142	70	4	g	g	PROPN
ap-6142	70	5	·	·	PUNCT
ap-6142	70	6	φ	φ	PROPN
ap-6142	70	7	ds	ds	PROPN
ap-6142	70	8	+	+	CCONJ
ap-6142	70	9	∫	∫	PROPN
ap-6142	70	10	ω	ω	PROPN
ap-6142	70	11	f	f	PROPN
ap-6142	70	12	·	·	PUNCT
ap-6142	70	13	φ	φ	PROPN
ap-6142	70	14	dx	dx	PROPN
ap-6142	70	15	,	,	PUNCT
ap-6142	70	16	b	b	PROPN
ap-6142	70	17	)	)	PUNCT
ap-6142	70	18	∫	∫	PROPN
ap-6142	71	1	ω	ω	PROPN
ap-6142	71	2	[	[	PUNCT
ap-6142	71	3	v	v	NOUN
ap-6142	71	4	·	·	PUNCT
ap-6142	71	5	∇v	∇v	NOUN
ap-6142	71	6	·	·	PUNCT
ap-6142	71	7	φ+	φ+	NOUN
ap-6142	71	8	ν	ν	X
ap-6142	71	9	(	(	PUNCT
ap-6142	71	10	∇v	∇v	PROPN
ap-6142	71	11	+	+	CCONJ
ap-6142	71	12	(	(	PUNCT
ap-6142	71	13	∇v)t	∇v)t	X
ap-6142	71	14	)	)	PUNCT
ap-6142	71	15	:	:	PUNCT
ap-6142	72	1	∇φ	∇φ	ADJ
ap-6142	72	2	]	]	PUNCT
ap-6142	72	3	dx	dx	PROPN
ap-6142	72	4	=	=	SYM
ap-6142	72	5	∫	∫	PROPN
ap-6142	72	6	γ2	γ2	PROPN
ap-6142	72	7	g	g	PROPN
ap-6142	72	8	·	·	PUNCT
ap-6142	72	9	φ	φ	PROPN
ap-6142	72	10	ds	ds	PROPN
ap-6142	72	11	+	+	CCONJ
ap-6142	72	12	∫	∫	PROPN
ap-6142	72	13	ω	ω	PROPN
ap-6142	72	14	f	f	PROPN
ap-6142	72	15	·	·	PUNCT
ap-6142	72	16	φ	φ	PROPN
ap-6142	72	17	dx	dx	PROPN
ap-6142	72	18	,	,	PUNCT
ap-6142	72	19	c	c	NOUN
ap-6142	72	20	)	)	PUNCT
ap-6142	72	21	∫	∫	PROPN
ap-6142	73	1	ω	ω	PROPN
ap-6142	73	2	[	[	PUNCT
ap-6142	73	3	v	v	NOUN
ap-6142	73	4	·	·	PUNCT
ap-6142	73	5	∇v	∇v	NOUN
ap-6142	73	6	·	·	PUNCT
ap-6142	73	7	φ+	φ+	NOUN
ap-6142	73	8	ν	ν	X
ap-6142	73	9	curlv	curlv	X
ap-6142	73	10	·	·	PUNCT
ap-6142	73	11	curlφ	curlφ	PROPN
ap-6142	73	12	]	]	PUNCT
ap-6142	73	13	dx	dx	PROPN
ap-6142	74	1	=	=	SYM
ap-6142	74	2	∫	∫	PROPN
ap-6142	74	3	γ2	γ2	PROPN
ap-6142	74	4	g	g	PROPN
ap-6142	74	5	·	·	PUNCT
ap-6142	74	6	φ	φ	PROPN
ap-6142	74	7	ds	ds	PROPN
ap-6142	74	8	+	+	CCONJ
ap-6142	74	9	∫	∫	PROPN
ap-6142	74	10	ω	ω	PROPN
ap-6142	74	11	f	f	PROPN
ap-6142	74	12	·	·	PUNCT
ap-6142	74	13	φ	φ	PROPN
ap-6142	74	14	dx	dx	PROPN
ap-6142	74	15	.	.	PROPN
ap-6142	74	16			NOUN
ap-6142	74	17	(	(	PUNCT
ap-6142	74	18	8)	8)	NUM
ap-6142	74	19	the	the	DET
ap-6142	74	20	equations	equation	NOUN
ap-6142	74	21	should	should	AUX
ap-6142	74	22	satisfy	satisfy	VERB
ap-6142	74	23	all	all	DET
ap-6142	74	24	functions	function	NOUN
ap-6142	74	25	φ	φ	VERB
ap-6142	74	26	with	with	ADP
ap-6142	74	27	the	the	DET
ap-6142	74	28	aforementioned	aforementioned	ADJ
ap-6142	74	29	properties	property	NOUN
ap-6142	74	30	and	and	CCONJ
ap-6142	74	31	v	v	NOUN
ap-6142	74	32	should	should	AUX
ap-6142	74	33	also	also	ADV
ap-6142	74	34	satisfy	satisfy	VERB
ap-6142	74	35	the	the	DET
ap-6142	74	36	boundary	boundary	ADJ
ap-6142	74	37	conditions	condition	NOUN
ap-6142	74	38	(	(	PUNCT
ap-6142	74	39	3	3	NUM
ap-6142	74	40	)	)	PUNCT
ap-6142	74	41	and	and	CCONJ
ap-6142	74	42	(	(	PUNCT
ap-6142	74	43	4	4	NUM
ap-6142	74	44	)	)	PUNCT
ap-6142	74	45	.	.	PUNCT
ap-6142	75	1	if	if	SCONJ
ap-6142	75	2	a	a	DET
ap-6142	75	3	weak	weak	ADJ
ap-6142	75	4	solution	solution	NOUN
ap-6142	75	5	v	v	NOUN
ap-6142	75	6	exists	exist	VERB
ap-6142	75	7	and	and	CCONJ
ap-6142	75	8	is	be	AUX
ap-6142	75	9	sufficiently	sufficiently	ADV
ap-6142	75	10	smooth	smooth	ADJ
ap-6142	75	11	then	then	ADV
ap-6142	75	12	,	,	PUNCT
ap-6142	75	13	by	by	ADP
ap-6142	75	14	a	a	DET
ap-6142	75	15	reverse	reverse	ADJ
ap-6142	75	16	integration	integration	NOUN
ap-6142	75	17	by	by	ADP
ap-6142	75	18	parts	part	NOUN
ap-6142	75	19	,	,	PUNCT
ap-6142	75	20	one	one	PRON
ap-6142	75	21	can	can	AUX
ap-6142	75	22	prove	prove	VERB
ap-6142	75	23	that	that	SCONJ
ap-6142	75	24	there	there	PRON
ap-6142	75	25	exists	exist	VERB
ap-6142	75	26	an	an	DET
ap-6142	75	27	appropriate	appropriate	ADJ
ap-6142	75	28	associated	associated	ADJ
ap-6142	75	29	pressure	pressure	NOUN
ap-6142	75	30	p	p	NOUN
ap-6142	75	31	and	and	CCONJ
ap-6142	75	32	show	show	VERB
ap-6142	75	33	that	that	SCONJ
ap-6142	75	34	v	v	NOUN
ap-6142	75	35	and	and	CCONJ
ap-6142	75	36	p	p	NOUN
ap-6142	75	37	satisfy	satisfy	VERB
ap-6142	75	38	the	the	DET
ap-6142	75	39	boundary	boundary	ADJ
ap-6142	75	40	conditions	condition	NOUN
ap-6142	75	41	a	a	PRON
ap-6142	75	42	)	)	PUNCT
ap-6142	76	1	−pn+	−pn+	NOUN
ap-6142	76	2	ν∇v	ν∇v	X
ap-6142	76	3	·	·	PUNCT
ap-6142	76	4	n	n	NOUN
ap-6142	76	5	=	=	SYM
ap-6142	76	6	g	g	PROPN
ap-6142	76	7	,	,	PUNCT
ap-6142	76	8	b	b	NOUN
ap-6142	76	9	)	)	PUNCT
ap-6142	76	10	−pn+	−pn+	NOUN
ap-6142	76	11	ν	ν	X
ap-6142	77	1	[	[	X
ap-6142	77	2	∇v	∇v	PROPN
ap-6142	77	3	+	+	CCONJ
ap-6142	77	4	(	(	PUNCT
ap-6142	77	5	∇v)t	∇v)t	X
ap-6142	77	6	]	]	PUNCT
ap-6142	77	7	·	·	PUNCT
ap-6142	77	8	n	n	X
ap-6142	77	9	=	=	SYM
ap-6142	77	10	g	g	NOUN
ap-6142	77	11	,	,	PUNCT
ap-6142	77	12	c	c	NOUN
ap-6142	77	13	)	)	PUNCT
ap-6142	77	14	−pn−	−pn−	X
ap-6142	77	15	ν	ν	X
ap-6142	77	16	curlv	curlv	PROPN
ap-6142	77	17	×	×	PROPN
ap-6142	77	18	n	n	NOUN
ap-6142	77	19	=	=	SYM
ap-6142	77	20	g	g	PROPN
ap-6142	77	21	,	,	PUNCT
ap-6142	77	22			X
ap-6142	77	23	(	(	PUNCT
ap-6142	77	24	9	9	NUM
ap-6142	77	25	)	)	SYM
ap-6142	77	26	90	90	NUM
ap-6142	77	27	vol	vol	NOUN
ap-6142	77	28	.	.	PUNCT
ap-6142	78	1	61	61	NUM
ap-6142	78	2	special	special	ADJ
ap-6142	78	3	issue/2021	issue/2021	NOUN
ap-6142	78	4	modeling	modeling	NOUN
ap-6142	78	5	of	of	ADP
ap-6142	78	6	flows	flow	NOUN
ap-6142	78	7	through	through	ADP
ap-6142	78	8	a	a	DET
ap-6142	78	9	channel	channel	NOUN
ap-6142	78	10	respectively	respectively	ADV
ap-6142	78	11	,	,	PUNCT
ap-6142	78	12	on	on	ADP
ap-6142	78	13	γ2	γ2	NOUN
ap-6142	78	14	.	.	PUNCT
ap-6142	79	1	it	it	PRON
ap-6142	79	2	is	be	AUX
ap-6142	79	3	well	well	ADV
ap-6142	79	4	known	know	VERB
ap-6142	79	5	that	that	SCONJ
ap-6142	79	6	the	the	DET
ap-6142	79	7	pressure	pressure	NOUN
ap-6142	79	8	p	p	NOUN
ap-6142	79	9	in	in	ADP
ap-6142	79	10	equation	equation	NOUN
ap-6142	79	11	(	(	PUNCT
ap-6142	79	12	1	1	X
ap-6142	79	13	)	)	PUNCT
ap-6142	79	14	is	be	AUX
ap-6142	79	15	not	not	PART
ap-6142	79	16	unique	unique	ADJ
ap-6142	79	17	,	,	PUNCT
ap-6142	79	18	because	because	SCONJ
ap-6142	79	19	p+	p+	VERB
ap-6142	79	20	c	c	X
ap-6142	79	21	,	,	PUNCT
ap-6142	79	22	where	where	SCONJ
ap-6142	79	23	c	c	PROPN
ap-6142	79	24	is	be	AUX
ap-6142	79	25	an	an	DET
ap-6142	79	26	arbitrary	arbitrary	ADJ
ap-6142	79	27	additional	additional	ADJ
ap-6142	79	28	constant	constant	ADJ
ap-6142	79	29	(	(	PUNCT
ap-6142	79	30	or	or	CCONJ
ap-6142	79	31	a	a	DET
ap-6142	79	32	function	function	NOUN
ap-6142	79	33	of	of	ADP
ap-6142	79	34	time	time	NOUN
ap-6142	79	35	)	)	PUNCT
ap-6142	79	36	,	,	PUNCT
ap-6142	79	37	also	also	ADV
ap-6142	79	38	satisfies	satisfy	VERB
ap-6142	79	39	the	the	DET
ap-6142	79	40	same	same	ADJ
ap-6142	79	41	equation	equation	NOUN
ap-6142	79	42	.	.	PUNCT
ap-6142	80	1	however	however	ADV
ap-6142	80	2	,	,	PUNCT
ap-6142	80	3	the	the	DET
ap-6142	80	4	same	same	ADJ
ap-6142	80	5	consideration	consideration	NOUN
ap-6142	80	6	is	be	AUX
ap-6142	80	7	not	not	PART
ap-6142	80	8	possible	possible	ADJ
ap-6142	80	9	in	in	ADP
ap-6142	80	10	the	the	DET
ap-6142	80	11	boundary	boundary	ADJ
ap-6142	80	12	conditions	condition	NOUN
ap-6142	80	13	a	a	X
ap-6142	80	14	)	)	PUNCT
ap-6142	80	15	–	–	PUNCT
ap-6142	80	16	c	c	X
ap-6142	80	17	)	)	PUNCT
ap-6142	80	18	in	in	ADP
ap-6142	80	19	(	(	PUNCT
ap-6142	80	20	9	9	NUM
ap-6142	80	21	)	)	PUNCT
ap-6142	80	22	.	.	PUNCT
ap-6142	81	1	here	here	ADV
ap-6142	81	2	,	,	PUNCT
ap-6142	81	3	it	it	PRON
ap-6142	81	4	only	only	ADV
ap-6142	81	5	follows	follow	VERB
ap-6142	81	6	from	from	ADP
ap-6142	81	7	the	the	DET
ap-6142	81	8	variational	variational	ADJ
ap-6142	81	9	formulation	formulation	NOUN
ap-6142	81	10	that	that	SCONJ
ap-6142	81	11	,	,	PUNCT
ap-6142	81	12	one	one	PRON
ap-6142	81	13	can	can	AUX
ap-6142	81	14	choose	choose	VERB
ap-6142	81	15	only	only	ADV
ap-6142	81	16	one	one	NUM
ap-6142	81	17	pressure	pressure	NOUN
ap-6142	81	18	p	p	NOUN
ap-6142	81	19	from	from	ADP
ap-6142	81	20	all	all	DET
ap-6142	81	21	associated	associated	ADJ
ap-6142	81	22	pressures	pressure	NOUN
ap-6142	81	23	,	,	PUNCT
ap-6142	81	24	that	that	PRON
ap-6142	81	25	satisfies	satisfy	VERB
ap-6142	81	26	the	the	DET
ap-6142	81	27	boundary	boundary	ADJ
ap-6142	81	28	condition	condition	NOUN
ap-6142	81	29	.	.	PUNCT
ap-6142	82	1	2.3	2.3	NUM
ap-6142	82	2	.	.	PUNCT
ap-6142	83	1	the	the	DET
ap-6142	83	2	momentum	momentum	NOUN
ap-6142	83	3	equation	equation	NOUN
ap-6142	83	4	with	with	ADP
ap-6142	83	5	the	the	DET
ap-6142	83	6	bernoulli	bernoulli	NOUN
ap-6142	83	7	pressure	pressure	NOUN
ap-6142	83	8	none	none	NOUN
ap-6142	83	9	of	of	ADP
ap-6142	83	10	the	the	DET
ap-6142	83	11	conditions	condition	NOUN
ap-6142	83	12	a	a	X
ap-6142	83	13	)	)	PUNCT
ap-6142	83	14	–	–	PUNCT
ap-6142	83	15	c	c	X
ap-6142	83	16	)	)	PUNCT
ap-6142	83	17	in	in	ADP
ap-6142	83	18	(	(	PUNCT
ap-6142	83	19	9	9	X
ap-6142	83	20	)	)	PUNCT
ap-6142	83	21	excludes	exclude	VERB
ap-6142	83	22	a	a	DET
ap-6142	83	23	possible	possible	ADJ
ap-6142	83	24	reverse	reverse	ADJ
ap-6142	83	25	flow	flow	NOUN
ap-6142	83	26	on	on	ADP
ap-6142	83	27	γ2	γ2	NOUN
ap-6142	83	28	that	that	PRON
ap-6142	83	29	could	could	AUX
ap-6142	83	30	hypothetically	hypothetically	ADV
ap-6142	83	31	bring	bring	VERB
ap-6142	83	32	an	an	DET
ap-6142	83	33	arbitrarily	arbitrarily	ADV
ap-6142	83	34	large	large	ADJ
ap-6142	83	35	amount	amount	NOUN
ap-6142	83	36	of	of	ADP
ap-6142	83	37	the	the	DET
ap-6142	83	38	kinetic	kinetic	ADJ
ap-6142	83	39	energy	energy	NOUN
ap-6142	83	40	back	back	ADV
ap-6142	83	41	to	to	ADP
ap-6142	83	42	ω	ω	PROPN
ap-6142	83	43	.	.	PUNCT
ap-6142	84	1	one	one	NOUN
ap-6142	84	2	usually	usually	ADV
ap-6142	84	3	derives	derive	VERB
ap-6142	84	4	an	an	DET
ap-6142	84	5	a	a	DET
ap-6142	84	6	priori	priori	X
ap-6142	84	7	energy	energy	NOUN
ap-6142	84	8	inequality	inequality	NOUN
ap-6142	84	9	so	so	SCONJ
ap-6142	84	10	that	that	SCONJ
ap-6142	84	11	the	the	DET
ap-6142	84	12	momentum	momentum	NOUN
ap-6142	84	13	equation	equation	NOUN
ap-6142	84	14	(	(	PUNCT
ap-6142	84	15	1	1	X
ap-6142	84	16	)	)	PUNCT
ap-6142	84	17	is	be	AUX
ap-6142	84	18	multiplied	multiply	VERB
ap-6142	84	19	by	by	ADP
ap-6142	84	20	v	v	NOUN
ap-6142	84	21	and	and	CCONJ
ap-6142	84	22	integrated	integrate	VERB
ap-6142	84	23	over	over	ADP
ap-6142	84	24	ω	ω	PROPN
ap-6142	84	25	.	.	PUNCT
ap-6142	85	1	then	then	ADV
ap-6142	85	2	the	the	DET
ap-6142	85	3	flow	flow	NOUN
ap-6142	85	4	of	of	ADP
ap-6142	85	5	the	the	DET
ap-6142	85	6	kinetic	kinetic	ADJ
ap-6142	85	7	energy	energy	NOUN
ap-6142	85	8	through	through	ADP
ap-6142	85	9	γ2	γ2	PROPN
ap-6142	85	10	comes	come	VERB
ap-6142	85	11	from	from	ADP
ap-6142	85	12	the	the	DET
ap-6142	85	13	integral	integral	ADJ
ap-6142	85	14	of	of	ADP
ap-6142	85	15	(	(	PUNCT
ap-6142	85	16	v·∇v)·v	v·∇v)·v	NOUN
ap-6142	85	17	.	.	PUNCT
ap-6142	86	1	applying	apply	VERB
ap-6142	86	2	the	the	DET
ap-6142	86	3	integration	integration	NOUN
ap-6142	86	4	by	by	ADP
ap-6142	86	5	parts	part	NOUN
ap-6142	86	6	,	,	PUNCT
ap-6142	86	7	we	we	PRON
ap-6142	86	8	can	can	AUX
ap-6142	86	9	express	express	VERB
ap-6142	86	10	this	this	DET
ap-6142	86	11	integral	integral	ADJ
ap-6142	86	12	as	as	ADP
ap-6142	86	13	follows:∫	follows:∫	PROPN
ap-6142	86	14	ω	ω	NUM
ap-6142	86	15	(	(	PUNCT
ap-6142	86	16	v	v	NOUN
ap-6142	86	17	·	·	PUNCT
ap-6142	86	18	∇v	∇v	NOUN
ap-6142	86	19	)	)	PUNCT
ap-6142	86	20	·	·	PUNCT
ap-6142	87	1	v	v	X
ap-6142	87	2	dx	dx	PROPN
ap-6142	87	3	=	=	SYM
ap-6142	87	4	∫	∫	PROPN
ap-6142	87	5	∂ω	∂ω	PROPN
ap-6142	87	6	(	(	PUNCT
ap-6142	87	7	v	v	NOUN
ap-6142	87	8	·	·	PUNCT
ap-6142	87	9	n	n	CCONJ
ap-6142	87	10	)	)	PUNCT
ap-6142	87	11	1	1	NUM
ap-6142	87	12	2	2	NUM
ap-6142	87	13	|v|	|v|	NUM
ap-6142	87	14	2	2	NUM
ap-6142	87	15	ds	ds	NOUN
ap-6142	87	16	=	=	PUNCT
ap-6142	87	17	∫	∫	PROPN
ap-6142	87	18	γ1	γ1	PROPN
ap-6142	87	19	(	(	PUNCT
ap-6142	87	20	v∗	v∗	PROPN
ap-6142	87	21	·	·	PUNCT
ap-6142	87	22	n	n	CCONJ
ap-6142	87	23	)	)	PUNCT
ap-6142	87	24	1	1	NUM
ap-6142	87	25	2	2	NUM
ap-6142	87	26	|v	|v	X
ap-6142	87	27	∗|2	∗|2	X
ap-6142	87	28	ds	ds	PROPN
ap-6142	87	29	+	+	CCONJ
ap-6142	87	30	∫	∫	PROPN
ap-6142	87	31	γ2	γ2	PROPN
ap-6142	87	32	(	(	PUNCT
ap-6142	87	33	v	v	NOUN
ap-6142	87	34	·	·	PUNCT
ap-6142	87	35	n	n	CCONJ
ap-6142	87	36	)	)	PUNCT
ap-6142	87	37	1	1	NUM
ap-6142	87	38	2	2	NUM
ap-6142	87	39	|v|	|v|	NUM
ap-6142	87	40	2	2	NUM
ap-6142	87	41	ds	ds	NOUN
ap-6142	87	42	.	.	PUNCT
ap-6142	87	43	(	(	PUNCT
ap-6142	87	44	10	10	NUM
ap-6142	87	45	)	)	PUNCT
ap-6142	87	46	the	the	DET
ap-6142	87	47	last	last	ADJ
ap-6142	87	48	integral	integral	NOUN
ap-6142	87	49	can	can	AUX
ap-6142	87	50	hypothetically	hypothetically	ADV
ap-6142	87	51	take	take	VERB
ap-6142	87	52	an	an	DET
ap-6142	87	53	arbitrarily	arbitrarily	ADV
ap-6142	87	54	large	large	ADJ
ap-6142	87	55	value	value	NOUN
ap-6142	87	56	if	if	SCONJ
ap-6142	87	57	v	v	X
ap-6142	87	58	·	·	PUNCT
ap-6142	87	59	n	n	X
ap-6142	87	60	<	<	X
ap-6142	87	61	0	0	NUM
ap-6142	87	62	on	on	ADP
ap-6142	87	63	the	the	DET
ap-6142	87	64	part	part	NOUN
ap-6142	87	65	of	of	ADP
ap-6142	87	66	γ2	γ2	ADJ
ap-6142	87	67	,	,	PUNCT
ap-6142	87	68	i.e.	i.e.	X
ap-6142	87	69	in	in	ADP
ap-6142	87	70	the	the	DET
ap-6142	87	71	case	case	NOUN
ap-6142	87	72	of	of	ADP
ap-6142	87	73	a	a	DET
ap-6142	87	74	reverse	reverse	ADJ
ap-6142	87	75	flow	flow	NOUN
ap-6142	87	76	.	.	PUNCT
ap-6142	88	1	the	the	DET
ap-6142	88	2	situation	situation	NOUN
ap-6142	88	3	is	be	AUX
ap-6142	88	4	different	different	ADJ
ap-6142	88	5	if	if	SCONJ
ap-6142	88	6	the	the	DET
ap-6142	88	7	nonlinear	nonlinear	ADJ
ap-6142	88	8	term	term	NOUN
ap-6142	88	9	in	in	ADP
ap-6142	88	10	equation	equation	NOUN
ap-6142	88	11	(	(	PUNCT
ap-6142	88	12	1	1	X
ap-6142	88	13	)	)	PUNCT
ap-6142	88	14	is	be	AUX
ap-6142	88	15	considered	consider	VERB
ap-6142	88	16	in	in	ADP
ap-6142	88	17	the	the	DET
ap-6142	88	18	form	form	NOUN
ap-6142	88	19	curlv	curlv	X
ap-6142	88	20	×	×	PROPN
ap-6142	88	21	v	v	NOUN
ap-6142	88	22	+	+	CCONJ
ap-6142	88	23	∇	∇	X
ap-6142	88	24	1	1	NUM
ap-6142	88	25	2	2	NUM
ap-6142	88	26	|v|	|v|	NUM
ap-6142	88	27	2	2	NUM
ap-6142	88	28	and	and	CCONJ
ap-6142	88	29	one	one	NUM
ap-6142	88	30	involves	involve	VERB
ap-6142	88	31	∇	∇	X
ap-6142	88	32	1	1	NUM
ap-6142	88	33	2	2	NUM
ap-6142	88	34	|v|	|v|	NUM
ap-6142	88	35	2	2	NUM
ap-6142	88	36	and	and	CCONJ
ap-6142	88	37	p	p	NOUN
ap-6142	88	38	to	to	ADP
ap-6142	88	39	the	the	DET
ap-6142	88	40	so	so	ADV
ap-6142	88	41	called	call	VERB
ap-6142	88	42	bernoulli	bernoulli	PROPN
ap-6142	88	43	pressure	pressure	NOUN
ap-6142	88	44	q	q	NOUN
ap-6142	89	1	:	:	PUNCT
ap-6142	89	2	=	=	SYM
ap-6142	89	3	p	p	X
ap-6142	89	4	+	+	NOUN
ap-6142	89	5	1	1	NUM
ap-6142	89	6	2	2	NUM
ap-6142	89	7	|v|	|v|	NUM
ap-6142	89	8	2	2	NUM
ap-6142	89	9	.	.	PUNCT
ap-6142	90	1	then	then	ADV
ap-6142	90	2	,	,	PUNCT
ap-6142	90	3	instead	instead	ADV
ap-6142	90	4	of	of	ADP
ap-6142	90	5	(	(	PUNCT
ap-6142	90	6	9	9	NUM
ap-6142	90	7	)	)	PUNCT
ap-6142	90	8	,	,	PUNCT
ap-6142	90	9	one	one	NUM
ap-6142	90	10	obtains	obtain	VERB
ap-6142	90	11	from	from	ADP
ap-6142	90	12	the	the	DET
ap-6142	90	13	integral	integral	ADJ
ap-6142	90	14	equations	equation	NOUN
ap-6142	90	15	(	(	PUNCT
ap-6142	90	16	8)	8)	NUM
ap-6142	90	17	the	the	DET
ap-6142	90	18	boundary	boundary	ADJ
ap-6142	90	19	conditions	condition	NOUN
ap-6142	90	20	a	a	PRON
ap-6142	90	21	)	)	PUNCT
ap-6142	90	22	−qn+	−qn+	PROPN
ap-6142	90	23	ν∇v	ν∇v	PROPN
ap-6142	90	24	·	·	PUNCT
ap-6142	90	25	n	n	NOUN
ap-6142	90	26	=	=	SYM
ap-6142	90	27	g	g	PROPN
ap-6142	90	28	,	,	PUNCT
ap-6142	90	29	b	b	NOUN
ap-6142	90	30	)	)	PUNCT
ap-6142	90	31	−qn+	−qn+	PUNCT
ap-6142	91	1	ν	ν	X
ap-6142	92	1	[	[	X
ap-6142	92	2	∇v	∇v	PROPN
ap-6142	92	3	+	+	CCONJ
ap-6142	92	4	(	(	PUNCT
ap-6142	92	5	∇v)t	∇v)t	X
ap-6142	92	6	]	]	PUNCT
ap-6142	92	7	·	·	PUNCT
ap-6142	92	8	n	n	X
ap-6142	92	9	=	=	SYM
ap-6142	92	10	g	g	NOUN
ap-6142	92	11	,	,	PUNCT
ap-6142	92	12	c	c	NOUN
ap-6142	92	13	)	)	PUNCT
ap-6142	92	14	−qn−	−qn−	NUM
ap-6142	92	15	ν	ν	X
ap-6142	92	16	curlv	curlv	X
ap-6142	92	17	×	×	PROPN
ap-6142	92	18	n	n	PROPN
ap-6142	92	19	=	=	SYM
ap-6142	92	20	g.	g.	PROPN
ap-6142	92	21			PROPN
ap-6142	92	22	(	(	PUNCT
ap-6142	92	23	11	11	NUM
ap-6142	92	24	)	)	PUNCT
ap-6142	92	25	now	now	ADV
ap-6142	92	26	,	,	PUNCT
ap-6142	92	27	the	the	DET
ap-6142	92	28	nonlinear	nonlinear	ADJ
ap-6142	92	29	term	term	NOUN
ap-6142	92	30	in	in	ADP
ap-6142	92	31	equation	equation	NOUN
ap-6142	92	32	(	(	PUNCT
ap-6142	92	33	1	1	X
ap-6142	92	34	)	)	PUNCT
ap-6142	92	35	is	be	AUX
ap-6142	92	36	just	just	ADV
ap-6142	92	37	curlv	curlv	ADJ
ap-6142	92	38	×	×	PROPN
ap-6142	92	39	v	v	NOUN
ap-6142	92	40	(	(	PUNCT
ap-6142	92	41	instead	instead	ADV
ap-6142	92	42	of	of	ADP
ap-6142	92	43	v	v	NOUN
ap-6142	92	44	·	·	PUNCT
ap-6142	92	45	∇v	∇v	NOUN
ap-6142	92	46	)	)	PUNCT
ap-6142	92	47	,	,	PUNCT
ap-6142	92	48	which	which	PRON
ap-6142	92	49	yields	yield	VERB
ap-6142	92	50	the	the	DET
ap-6142	92	51	term∫	term∫	PROPN
ap-6142	92	52	ω	ω	PROPN
ap-6142	92	53	curlv	curlv	PROPN
ap-6142	92	54	×	×	PROPN
ap-6142	92	55	v	v	PROPN
ap-6142	92	56	·	·	PUNCT
ap-6142	92	57	φ	φ	NUM
ap-6142	92	58	dx	dx	PROPN
ap-6142	92	59	in	in	ADP
ap-6142	92	60	the	the	DET
ap-6142	92	61	variational	variational	ADJ
ap-6142	92	62	formulation	formulation	NOUN
ap-6142	92	63	.	.	PUNCT
ap-6142	93	1	if	if	SCONJ
ap-6142	93	2	one	one	PRON
ap-6142	93	3	formally	formally	ADV
ap-6142	93	4	multiplies	multiply	VERB
ap-6142	93	5	equation	equation	NOUN
ap-6142	93	6	(	(	PUNCT
ap-6142	93	7	1	1	NUM
ap-6142	93	8	)	)	PUNCT
ap-6142	93	9	by	by	ADP
ap-6142	93	10	the	the	DET
ap-6142	93	11	velocity	velocity	NOUN
ap-6142	93	12	v	v	ADP
ap-6142	93	13	then	then	ADV
ap-6142	93	14	the	the	DET
ap-6142	93	15	nonlinear	nonlinear	ADJ
ap-6142	93	16	term	term	NOUN
ap-6142	93	17	vanishes	vanish	VERB
ap-6142	93	18	,	,	PUNCT
ap-6142	93	19	because	because	SCONJ
ap-6142	93	20	(	(	PUNCT
ap-6142	93	21	curlv	curlv	INTJ
ap-6142	93	22	×	×	PROPN
ap-6142	93	23	v	v	NOUN
ap-6142	93	24	)	)	PUNCT
ap-6142	93	25	·	·	PUNCT
ap-6142	94	1	v	v	X
ap-6142	94	2	=	=	SYM
ap-6142	94	3	0	0	PROPN
ap-6142	94	4	.	.	PUNCT
ap-6142	95	1	this	this	PRON
ap-6142	95	2	has	have	VERB
ap-6142	95	3	the	the	DET
ap-6142	95	4	following	follow	VERB
ap-6142	95	5	consequences	consequence	NOUN
ap-6142	95	6	:	:	PUNCT
ap-6142	95	7	1	1	X
ap-6142	95	8	)	)	PUNCT
ap-6142	95	9	the	the	DET
ap-6142	95	10	nonlinear	nonlinear	ADJ
ap-6142	95	11	term	term	NOUN
ap-6142	95	12	curlv×	curlv×	PROPN
ap-6142	95	13	v	v	NOUN
ap-6142	95	14	generates	generate	VERB
ap-6142	95	15	no	no	DET
ap-6142	95	16	backward	backward	ADJ
ap-6142	95	17	inflow	inflow	NOUN
ap-6142	95	18	of	of	ADP
ap-6142	95	19	kinetic	kinetic	ADJ
ap-6142	95	20	energy	energy	NOUN
ap-6142	95	21	to	to	ADP
ap-6142	95	22	ω	ω	PROPN
ap-6142	95	23	through	through	ADP
ap-6142	95	24	the	the	DET
ap-6142	95	25	surface	surface	NOUN
ap-6142	95	26	γ2	γ2	NOUN
ap-6142	95	27	,	,	PUNCT
ap-6142	95	28	2	2	NUM
ap-6142	95	29	)	)	PUNCT
ap-6142	95	30	the	the	DET
ap-6142	95	31	usual	usual	ADJ
ap-6142	95	32	energy	energy	NOUN
ap-6142	95	33	–	–	PUNCT
ap-6142	95	34	type	type	NOUN
ap-6142	95	35	inequality	inequality	NOUN
ap-6142	95	36	can	can	AUX
ap-6142	95	37	be	be	AUX
ap-6142	95	38	derived	derive	VERB
ap-6142	95	39	,	,	PUNCT
ap-6142	95	40	3	3	X
ap-6142	95	41	)	)	PUNCT
ap-6142	95	42	the	the	DET
ap-6142	95	43	existence	existence	NOUN
ap-6142	95	44	of	of	ADP
ap-6142	95	45	a	a	DET
ap-6142	95	46	weak	weak	ADJ
ap-6142	95	47	solution	solution	NOUN
ap-6142	95	48	on	on	ADP
ap-6142	95	49	an	an	DET
ap-6142	95	50	arbitrarily	arbitrarily	ADV
ap-6142	95	51	long	long	ADJ
ap-6142	95	52	time	time	NOUN
ap-6142	95	53	interval	interval	NOUN
ap-6142	95	54	can	can	AUX
ap-6142	95	55	be	be	AUX
ap-6142	95	56	proven	prove	VERB
ap-6142	95	57	by	by	ADP
ap-6142	95	58	similar	similar	ADJ
ap-6142	95	59	methods	method	NOUN
ap-6142	95	60	,	,	PUNCT
ap-6142	95	61	as	as	SCONJ
ap-6142	95	62	if	if	SCONJ
ap-6142	95	63	one	one	PRON
ap-6142	95	64	considers	consider	VERB
ap-6142	95	65	the	the	DET
ap-6142	95	66	homogeneous	homogeneous	ADJ
ap-6142	95	67	or	or	CCONJ
ap-6142	95	68	inhomogeneous	inhomogeneous	ADJ
ap-6142	95	69	dirichlet	dirichlet	PROPN
ap-6142	95	70	boundary	boundary	ADJ
ap-6142	95	71	condition	condition	NOUN
ap-6142	95	72	on	on	ADP
ap-6142	95	73	the	the	DET
ap-6142	95	74	whole	whole	ADJ
ap-6142	95	75	boundary	boundary	ADJ
ap-6142	95	76	∂ω	∂ω	PROPN
ap-6142	95	77	(	(	PUNCT
ap-6142	95	78	see	see	VERB
ap-6142	96	1	e.g.	e.g.	ADV
ap-6142	96	2	[	[	X
ap-6142	96	3	18	18	NUM
ap-6142	96	4	]	]	NUM
ap-6142	96	5	)	)	PUNCT
ap-6142	96	6	.	.	PUNCT
ap-6142	97	1	2.4	2.4	NUM
ap-6142	97	2	.	.	X
ap-6142	98	1	which	which	DET
ap-6142	98	2	artificial	artificial	ADJ
ap-6142	98	3	boundary	boundary	ADJ
ap-6142	98	4	condition	condition	NOUN
ap-6142	98	5	is	be	AUX
ap-6142	98	6	the	the	DET
ap-6142	98	7	best	good	ADJ
ap-6142	98	8	?	?	PUNCT
ap-6142	99	1	there	there	PRON
ap-6142	99	2	arises	arise	VERB
ap-6142	99	3	a	a	DET
ap-6142	99	4	natural	natural	ADJ
ap-6142	99	5	question	question	NOUN
ap-6142	99	6	:	:	PUNCT
ap-6142	99	7	which	which	PRON
ap-6142	99	8	of	of	ADP
ap-6142	99	9	the	the	DET
ap-6142	99	10	formulated	formulated	ADJ
ap-6142	99	11	boundary	boundary	ADJ
ap-6142	99	12	conditions	condition	NOUN
ap-6142	99	13	a	a	NOUN
ap-6142	99	14	)	)	PUNCT
ap-6142	99	15	–	–	PUNCT
ap-6142	99	16	c	c	X
ap-6142	99	17	)	)	PUNCT
ap-6142	99	18	in	in	ADP
ap-6142	99	19	(	(	PUNCT
ap-6142	99	20	9	9	NUM
ap-6142	99	21	)	)	PUNCT
ap-6142	99	22	and	and	CCONJ
ap-6142	99	23	a	a	X
ap-6142	99	24	)	)	PUNCT
ap-6142	99	25	–	–	PUNCT
ap-6142	99	26	c	c	X
ap-6142	99	27	)	)	PUNCT
ap-6142	99	28	in	in	ADP
ap-6142	99	29	(	(	PUNCT
ap-6142	99	30	11	11	NUM
ap-6142	99	31	)	)	PUNCT
ap-6142	99	32	on	on	ADP
ap-6142	99	33	γ2	γ2	PROPN
ap-6142	99	34	is	be	AUX
ap-6142	99	35	most	most	ADV
ap-6142	99	36	appropriate	appropriate	ADJ
ap-6142	99	37	?	?	PUNCT
ap-6142	100	1	the	the	DET
ap-6142	100	2	advantage	advantage	NOUN
ap-6142	100	3	of	of	ADP
ap-6142	100	4	all	all	DET
ap-6142	100	5	the	the	DET
ap-6142	100	6	conditions	condition	NOUN
ap-6142	100	7	in	in	ADP
ap-6142	100	8	(	(	PUNCT
ap-6142	100	9	11	11	NUM
ap-6142	100	10	)	)	PUNCT
ap-6142	100	11	is	be	AUX
ap-6142	100	12	that	that	SCONJ
ap-6142	100	13	,	,	PUNCT
ap-6142	100	14	in	in	ADP
ap-6142	100	15	contrast	contrast	NOUN
ap-6142	100	16	to	to	ADP
ap-6142	100	17	the	the	DET
ap-6142	100	18	conditions	condition	NOUN
ap-6142	100	19	from	from	ADP
ap-6142	100	20	(	(	PUNCT
ap-6142	100	21	9	9	NUM
ap-6142	100	22	)	)	PUNCT
ap-6142	100	23	,	,	PUNCT
ap-6142	100	24	they	they	PRON
ap-6142	100	25	enable	enable	VERB
ap-6142	100	26	one	one	NUM
ap-6142	100	27	to	to	PART
ap-6142	100	28	prove	prove	VERB
ap-6142	100	29	the	the	DET
ap-6142	100	30	existence	existence	NOUN
ap-6142	100	31	of	of	ADP
ap-6142	100	32	a	a	DET
ap-6142	100	33	weak	weak	ADJ
ap-6142	100	34	solution	solution	NOUN
ap-6142	100	35	.	.	PUNCT
ap-6142	101	1	on	on	ADP
ap-6142	101	2	the	the	DET
ap-6142	101	3	other	other	ADJ
ap-6142	101	4	hand	hand	NOUN
ap-6142	101	5	,	,	PUNCT
ap-6142	101	6	the	the	DET
ap-6142	101	7	condition	condition	NOUN
ap-6142	101	8	a	a	X
ap-6142	101	9	)	)	PUNCT
ap-6142	101	10	from	from	ADP
ap-6142	101	11	(	(	PUNCT
ap-6142	101	12	9	9	NUM
ap-6142	101	13	)	)	PUNCT
ap-6142	101	14	is	be	AUX
ap-6142	101	15	fulfilled	fulfil	VERB
ap-6142	101	16	(	(	PUNCT
ap-6142	101	17	with	with	ADP
ap-6142	101	18	g	g	PROPN
ap-6142	101	19	=	=	SYM
ap-6142	101	20	0	0	NUM
ap-6142	101	21	)	)	PUNCT
ap-6142	101	22	by	by	ADP
ap-6142	101	23	the	the	DET
ap-6142	101	24	poiseuille	poiseuille	NOUN
ap-6142	101	25	flow	flow	NOUN
ap-6142	101	26	in	in	ADP
ap-6142	101	27	a	a	DET
ap-6142	101	28	circular	circular	ADJ
ap-6142	101	29	pipe	pipe	NOUN
ap-6142	101	30	.	.	PUNCT
ap-6142	102	1	this	this	PRON
ap-6142	102	2	is	be	AUX
ap-6142	102	3	mainly	mainly	ADV
ap-6142	102	4	why	why	SCONJ
ap-6142	102	5	this	this	DET
ap-6142	102	6	condition	condition	NOUN
ap-6142	102	7	is	be	AUX
ap-6142	102	8	usually	usually	ADV
ap-6142	102	9	considered	consider	VERB
ap-6142	102	10	as	as	ADP
ap-6142	102	11	the	the	DET
ap-6142	102	12	best	good	ADJ
ap-6142	102	13	from	from	ADP
ap-6142	102	14	a	a	DET
ap-6142	102	15	physical	physical	ADJ
ap-6142	102	16	point	point	NOUN
ap-6142	102	17	of	of	ADP
ap-6142	102	18	view	view	NOUN
ap-6142	102	19	.	.	PUNCT
ap-6142	103	1	on	on	ADP
ap-6142	103	2	the	the	DET
ap-6142	103	3	other	other	ADJ
ap-6142	103	4	hand	hand	NOUN
ap-6142	103	5	,	,	PUNCT
ap-6142	103	6	in	in	ADP
ap-6142	103	7	any	any	PRON
ap-6142	103	8	of	of	ADP
ap-6142	103	9	the	the	DET
ap-6142	103	10	formulated	formulated	ADJ
ap-6142	103	11	boundary	boundary	ADJ
ap-6142	103	12	conditions	condition	NOUN
ap-6142	103	13	,	,	PUNCT
ap-6142	103	14	one	one	PRON
ap-6142	103	15	can	can	AUX
ap-6142	103	16	always	always	ADV
ap-6142	103	17	calculate	calculate	VERB
ap-6142	103	18	an	an	DET
ap-6142	103	19	appropriate	appropriate	ADJ
ap-6142	103	20	function	function	NOUN
ap-6142	103	21	g	g	NOUN
ap-6142	103	22	so	so	SCONJ
ap-6142	103	23	that	that	SCONJ
ap-6142	103	24	the	the	DET
ap-6142	103	25	poiseuille	poiseuille	NOUN
ap-6142	103	26	flow	flow	NOUN
ap-6142	103	27	satisfies	satisfy	VERB
ap-6142	103	28	the	the	DET
ap-6142	103	29	considered	consider	VERB
ap-6142	103	30	condition	condition	NOUN
ap-6142	103	31	with	with	ADP
ap-6142	103	32	this	this	DET
ap-6142	103	33	concrete	concrete	ADJ
ap-6142	103	34	function	function	NOUN
ap-6142	103	35	g.	g.	PROPN
ap-6142	103	36	thus	thus	ADV
ap-6142	103	37	,	,	PUNCT
ap-6142	103	38	the	the	DET
ap-6142	103	39	suitability	suitability	NOUN
ap-6142	103	40	of	of	ADP
ap-6142	103	41	the	the	DET
ap-6142	103	42	chosen	choose	VERB
ap-6142	103	43	boundary	boundary	ADJ
ap-6142	103	44	condition	condition	NOUN
ap-6142	103	45	probably	probably	ADV
ap-6142	103	46	depends	depend	VERB
ap-6142	103	47	only	only	ADV
ap-6142	103	48	on	on	ADP
ap-6142	103	49	a	a	DET
ap-6142	103	50	particular	particular	ADJ
ap-6142	103	51	situation	situation	NOUN
ap-6142	103	52	.	.	PUNCT
ap-6142	104	1	moreover	moreover	ADV
ap-6142	104	2	,	,	PUNCT
ap-6142	104	3	in	in	ADP
ap-6142	104	4	our	our	PRON
ap-6142	104	5	opinion	opinion	NOUN
ap-6142	104	6	,	,	PUNCT
ap-6142	104	7	it	it	PRON
ap-6142	104	8	would	would	AUX
ap-6142	104	9	be	be	AUX
ap-6142	104	10	very	very	ADV
ap-6142	104	11	useful	useful	ADJ
ap-6142	104	12	to	to	PART
ap-6142	104	13	perform	perform	VERB
ap-6142	104	14	numerical	numerical	ADJ
ap-6142	104	15	calculations	calculation	NOUN
ap-6142	104	16	with	with	ADP
ap-6142	104	17	various	various	ADJ
ap-6142	104	18	boundary	boundary	ADJ
ap-6142	104	19	conditions	condition	NOUN
ap-6142	104	20	so	so	SCONJ
ap-6142	104	21	that	that	SCONJ
ap-6142	104	22	one	one	PRON
ap-6142	104	23	could	could	AUX
ap-6142	104	24	compare	compare	VERB
ap-6142	104	25	the	the	DET
ap-6142	104	26	results	result	NOUN
ap-6142	104	27	among	among	ADP
ap-6142	104	28	themselves	themselves	PRON
ap-6142	104	29	and	and	CCONJ
ap-6142	104	30	also	also	ADV
ap-6142	104	31	with	with	ADP
ap-6142	104	32	physical	physical	ADJ
ap-6142	104	33	measurements	measurement	NOUN
ap-6142	104	34	.	.	PUNCT
ap-6142	105	1	3	3	X
ap-6142	105	2	.	.	X
ap-6142	105	3	the	the	DET
ap-6142	105	4	navier	navier	NOUN
ap-6142	105	5	–	–	PUNCT
ap-6142	105	6	stokes	stoke	VERB
ap-6142	105	7	inequality	inequality	NOUN
ap-6142	105	8	–	–	PUNCT
ap-6142	105	9	the	the	DET
ap-6142	105	10	non	non	ADJ
ap-6142	105	11	-	-	ADJ
ap-6142	105	12	steady	steady	ADJ
ap-6142	105	13	case	case	NOUN
ap-6142	105	14	in	in	ADP
ap-6142	105	15	this	this	DET
ap-6142	105	16	section	section	NOUN
ap-6142	105	17	,	,	PUNCT
ap-6142	105	18	we	we	PRON
ap-6142	105	19	deal	deal	VERB
ap-6142	105	20	with	with	ADP
ap-6142	105	21	the	the	DET
ap-6142	105	22	navier	navier	NOUN
ap-6142	105	23	–	–	PUNCT
ap-6142	105	24	stokes	stoke	NOUN
ap-6142	105	25	problem	problem	NOUN
ap-6142	105	26	(	(	PUNCT
ap-6142	105	27	1)–(4	1)–(4	NUM
ap-6142	105	28	)	)	PUNCT
ap-6142	105	29	in	in	ADP
ap-6142	105	30	ω	ω	PROPN
ap-6142	105	31	with	with	ADP
ap-6142	105	32	the	the	DET
ap-6142	105	33	boundary	boundary	ADJ
ap-6142	105	34	condition	condition	NOUN
ap-6142	105	35	(	(	PUNCT
ap-6142	105	36	5	5	NUM
ap-6142	105	37	)	)	PUNCT
ap-6142	105	38	on	on	ADP
ap-6142	105	39	γ2	γ2	PROPN
ap-6142	105	40	.	.	PUNCT
ap-6142	106	1	due	due	ADP
ap-6142	106	2	to	to	ADP
ap-6142	106	3	the	the	DET
ap-6142	106	4	reasons	reason	NOUN
ap-6142	106	5	,	,	PUNCT
ap-6142	106	6	explained	explain	VERB
ap-6142	106	7	in	in	ADP
ap-6142	106	8	sections	section	NOUN
ap-6142	106	9	1	1	NUM
ap-6142	106	10	and	and	CCONJ
ap-6142	106	11	2	2	NUM
ap-6142	106	12	,	,	PUNCT
ap-6142	106	13	we	we	PRON
ap-6142	106	14	study	study	VERB
ap-6142	106	15	the	the	DET
ap-6142	106	16	problem	problem	NOUN
ap-6142	106	17	in	in	ADP
ap-6142	106	18	the	the	DET
ap-6142	106	19	form	form	NOUN
ap-6142	106	20	of	of	ADP
ap-6142	106	21	a	a	DET
ap-6142	106	22	variational	variational	ADJ
ap-6142	106	23	inequality	inequality	NOUN
ap-6142	106	24	.	.	PUNCT
ap-6142	107	1	3.1	3.1	NUM
ap-6142	107	2	.	.	PUNCT
ap-6142	107	3	notation	notation	NOUN
ap-6142	107	4	(	(	PUNCT
ap-6142	107	5	i	i	NOUN
ap-6142	107	6	)	)	PUNCT
ap-6142	107	7	we	we	PRON
ap-6142	107	8	use	use	VERB
ap-6142	107	9	the	the	DET
ap-6142	107	10	usual	usual	ADJ
ap-6142	107	11	notation	notation	NOUN
ap-6142	107	12	of	of	ADP
ap-6142	107	13	the	the	DET
ap-6142	107	14	norms	norm	NOUN
ap-6142	107	15	in	in	ADP
ap-6142	107	16	the	the	DET
ap-6142	107	17	lebesgue	lebesgue	NOUN
ap-6142	107	18	spaces	space	NOUN
ap-6142	107	19	:	:	PUNCT
ap-6142	107	20	‖	‖	ADJ
ap-6142	107	21	.	.	PUNCT
ap-6142	108	1	‖r	‖r	NOUN
ap-6142	108	2	is	be	AUX
ap-6142	108	3	the	the	DET
ap-6142	108	4	norm	norm	NOUN
ap-6142	108	5	in	in	ADP
ap-6142	108	6	lr(ω	lr(ω	NOUN
ap-6142	108	7	)	)	PUNCT
ap-6142	108	8	or	or	CCONJ
ap-6142	108	9	in	in	ADP
ap-6142	108	10	lr(ω	lr(ω	NOUN
ap-6142	108	11	)	)	PUNCT
ap-6142	108	12	(	(	PUNCT
ap-6142	108	13	the	the	DET
ap-6142	108	14	space	space	NOUN
ap-6142	108	15	of	of	ADP
ap-6142	108	16	vector	vector	NOUN
ap-6142	108	17	functions	function	NOUN
ap-6142	108	18	)	)	PUNCT
ap-6142	108	19	or	or	CCONJ
ap-6142	108	20	in	in	ADP
ap-6142	108	21	lr(ω)3×3	lr(ω)3×3	PROPN
ap-6142	108	22	(	(	PUNCT
ap-6142	108	23	the	the	DET
ap-6142	108	24	space	space	NOUN
ap-6142	108	25	of	of	ADP
ap-6142	108	26	tensorial	tensorial	ADJ
ap-6142	108	27	functions	function	NOUN
ap-6142	108	28	)	)	PUNCT
ap-6142	108	29	.	.	PUNCT
ap-6142	109	1	by	by	ADP
ap-6142	109	2	analogy	analogy	NOUN
ap-6142	109	3	,	,	PUNCT
ap-6142	109	4	‖	‖	PROPN
ap-6142	109	5	.	.	PUNCT
ap-6142	109	6	‖k	‖k	NOUN
ap-6142	109	7	,	,	PUNCT
ap-6142	109	8	r	r	NOUN
ap-6142	109	9	denotes	denote	VERB
ap-6142	109	10	the	the	DET
ap-6142	109	11	norm	norm	NOUN
ap-6142	109	12	in	in	ADP
ap-6142	109	13	the	the	DET
ap-6142	109	14	sobolev	sobolev	NOUN
ap-6142	109	15	spacew	spacew	NOUN
ap-6142	109	16	k	k	PROPN
ap-6142	109	17	,	,	PUNCT
ap-6142	109	18	r(ω	r(ω	ADJ
ap-6142	109	19	)	)	PUNCT
ap-6142	109	20	orw	orw	VERB
ap-6142	109	21	k	k	NOUN
ap-6142	109	22	,	,	PUNCT
ap-6142	109	23	r(ω	r(ω	ADJ
ap-6142	109	24	)	)	PUNCT
ap-6142	109	25	orw	orw	VERB
ap-6142	109	26	k	k	NOUN
ap-6142	109	27	,	,	PUNCT
ap-6142	109	28	r(ω)3×3	r(ω)3×3	PROPN
ap-6142	109	29	.	.	PUNCT
ap-6142	110	1	if	if	SCONJ
ap-6142	110	2	the	the	DET
ap-6142	110	3	norm	norm	NOUN
ap-6142	110	4	is	be	AUX
ap-6142	110	5	related	relate	VERB
ap-6142	110	6	to	to	ADP
ap-6142	110	7	another	another	DET
ap-6142	110	8	set	set	NOUN
ap-6142	110	9	than	than	ADP
ap-6142	110	10	ω	ω	PROPN
ap-6142	110	11	then	then	ADV
ap-6142	110	12	we	we	PRON
ap-6142	110	13	denote	denote	VERB
ap-6142	110	14	it	it	PRON
ap-6142	110	15	e.g.	e.g.	ADV
ap-6142	110	16	by	by	ADP
ap-6142	110	17	‖	‖	PROPN
ap-6142	110	18	.	.	PUNCT
ap-6142	111	1	‖r	‖r	NOUN
ap-6142	111	2	;	;	PUNCT
ap-6142	111	3	γ2	γ2	NOUN
ap-6142	111	4	,	,	PUNCT
ap-6142	111	5	etc	etc	X
ap-6142	111	6	.	.	X
ap-6142	111	7	(	(	PUNCT
ap-6142	111	8	ii	ii	X
ap-6142	111	9	)	)	PUNCT
ap-6142	111	10	we	we	PRON
ap-6142	111	11	assume	assume	VERB
ap-6142	111	12	that	that	SCONJ
ap-6142	111	13	v∗	v∗	PROPN
ap-6142	111	14	is	be	AUX
ap-6142	111	15	a	a	DET
ap-6142	111	16	given	give	VERB
ap-6142	111	17	function	function	NOUN
ap-6142	111	18	on	on	ADP
ap-6142	111	19	γ1	γ1	PROPN
ap-6142	111	20	×	×	PROPN
ap-6142	111	21	(	(	PUNCT
ap-6142	111	22	0	0	NUM
ap-6142	111	23	,	,	PUNCT
ap-6142	111	24	t	t	PROPN
ap-6142	111	25	)	)	PUNCT
ap-6142	111	26	,	,	PUNCT
ap-6142	111	27	such	such	ADJ
ap-6142	111	28	that	that	SCONJ
ap-6142	111	29	1	1	NUM
ap-6142	111	30	2	2	NUM
ap-6142	111	31	∫	∫	NOUN
ap-6142	111	32	γ1	γ1	NOUN
ap-6142	111	33	[	[	X
ap-6142	111	34	v∗	v∗	PROPN
ap-6142	111	35	·	·	PUNCT
ap-6142	111	36	(	(	PUNCT
ap-6142	111	37	−n	−n	ADV
ap-6142	111	38	)	)	PUNCT
ap-6142	111	39	]	]	PUNCT
ap-6142	112	1	|v∗|2	|v∗|2	NUM
ap-6142	112	2	ds	ds	NOUN
ap-6142	112	3	(	(	PUNCT
ap-6142	112	4	the	the	DET
ap-6142	112	5	inflow	inflow	NOUN
ap-6142	112	6	of	of	ADP
ap-6142	112	7	the	the	DET
ap-6142	112	8	kinetic	kinetic	ADJ
ap-6142	112	9	energy	energy	NOUN
ap-6142	112	10	to	to	ADP
ap-6142	112	11	ω	ω	PROPN
ap-6142	112	12	through	through	ADP
ap-6142	112	13	γ1	γ1	NOUN
ap-6142	112	14	)	)	PUNCT
ap-6142	112	15	is	be	AUX
ap-6142	112	16	bounded	bound	VERB
ap-6142	112	17	,	,	PUNCT
ap-6142	112	18	as	as	ADP
ap-6142	112	19	a	a	DET
ap-6142	112	20	function	function	NOUN
ap-6142	112	21	of	of	ADP
ap-6142	112	22	t	t	PROPN
ap-6142	112	23	,	,	PUNCT
ap-6142	112	24	for	for	ADP
ap-6142	112	25	t	t	PROPN
ap-6142	112	26	∈	∈	PROPN
ap-6142	112	27	(	(	PUNCT
ap-6142	112	28	0	0	NUM
ap-6142	112	29	,	,	PUNCT
ap-6142	112	30	t	t	NOUN
ap-6142	112	31	)	)	PUNCT
ap-6142	112	32	.	.	PUNCT
ap-6142	113	1	(	(	PUNCT
ap-6142	113	2	iii	iii	X
ap-6142	113	3	)	)	PUNCT
ap-6142	113	4	furthermore	furthermore	ADV
ap-6142	113	5	,	,	PUNCT
ap-6142	113	6	we	we	PRON
ap-6142	113	7	assume	assume	VERB
ap-6142	113	8	that	that	SCONJ
ap-6142	113	9	v∗	v∗	PROPN
ap-6142	113	10	can	can	AUX
ap-6142	113	11	be	be	AUX
ap-6142	113	12	extended	extend	VERB
ap-6142	113	13	to	to	ADP
ap-6142	113	14	ω×(0	ω×(0	PROPN
ap-6142	113	15	,	,	PUNCT
ap-6142	113	16	t	t	NOUN
ap-6142	113	17	)	)	PUNCT
ap-6142	113	18	so	so	SCONJ
ap-6142	113	19	that	that	SCONJ
ap-6142	113	20	the	the	DET
ap-6142	113	21	extended	extended	ADJ
ap-6142	113	22	function	function	NOUN
ap-6142	113	23	(	(	PUNCT
ap-6142	113	24	which	which	PRON
ap-6142	113	25	is	be	AUX
ap-6142	113	26	denoted	denote	VERB
ap-6142	113	27	by	by	ADP
ap-6142	113	28	v∗ext	v∗ext	PROPN
ap-6142	113	29	)	)	PUNCT
ap-6142	113	30	satisfies	satisfy	VERB
ap-6142	113	31	the	the	DET
ap-6142	113	32	boundary	boundary	ADJ
ap-6142	113	33	condition	condition	NOUN
ap-6142	113	34	(	(	PUNCT
ap-6142	113	35	3	3	NUM
ap-6142	113	36	)	)	PUNCT
ap-6142	113	37	on	on	ADP
ap-6142	113	38	γ0	γ0	PROPN
ap-6142	113	39	×	×	PROPN
ap-6142	113	40	(	(	PUNCT
ap-6142	113	41	0	0	NUM
ap-6142	113	42	,	,	PUNCT
ap-6142	113	43	t	t	PROPN
ap-6142	113	44	)	)	PUNCT
ap-6142	113	45	and	and	CCONJ
ap-6142	113	46	a	a	X
ap-6142	113	47	)	)	PUNCT
ap-6142	113	48	v∗ext	v∗ext	PROPN
ap-6142	113	49	∈	∈	PROPN
ap-6142	113	50	l∞	l∞	NOUN
ap-6142	113	51	(	(	PUNCT
ap-6142	113	52	0	0	NUM
ap-6142	113	53	,	,	PUNCT
ap-6142	113	54	t	t	NOUN
ap-6142	113	55	;	;	PUNCT
ap-6142	113	56	w	w	PROPN
ap-6142	113	57	1,2(ω	1,2(ω	NUM
ap-6142	113	58	)	)	PUNCT
ap-6142	113	59	)	)	PUNCT
ap-6142	113	60	and	and	CCONJ
ap-6142	113	61	∂tv∗ext	∂tv∗ext	PROPN
ap-6142	113	62	∈	∈	PROPN
ap-6142	113	63	l2(0	l2(0	NOUN
ap-6142	113	64	,	,	PUNCT
ap-6142	113	65	t	t	NOUN
ap-6142	113	66	;	;	PUNCT
ap-6142	113	67	w−1,2(ω	w−1,2(ω	ADJ
ap-6142	113	68	)	)	PUNCT
ap-6142	113	69	)	)	PUNCT
ap-6142	113	70	,	,	PUNCT
ap-6142	113	71	b	b	X
ap-6142	113	72	)	)	PUNCT
ap-6142	113	73	v∗ext	v∗ext	NOUN
ap-6142	113	74	is	be	AUX
ap-6142	113	75	divergence	divergence	ADJ
ap-6142	113	76	–	–	PUNCT
ap-6142	113	77	free	free	ADJ
ap-6142	113	78	.	.	PUNCT
ap-6142	114	1	(	(	PUNCT
ap-6142	114	2	here	here	ADV
ap-6142	114	3	,	,	PUNCT
ap-6142	114	4	we	we	PRON
ap-6142	114	5	denote	denote	VERB
ap-6142	114	6	by	by	ADP
ap-6142	114	7	w−1,2(ω	w−1,2(ω	NOUN
ap-6142	114	8	)	)	PUNCT
ap-6142	114	9	the	the	DET
ap-6142	114	10	dual	dual	ADJ
ap-6142	114	11	space	space	NOUN
ap-6142	114	12	to	to	ADP
ap-6142	114	13	w	w	PROPN
ap-6142	114	14	1,2(ω	1,2(ω	NUM
ap-6142	114	15	)	)	PUNCT
ap-6142	114	16	.	.	PUNCT
ap-6142	115	1	the	the	DET
ap-6142	115	2	duality	duality	NOUN
ap-6142	115	3	pairing	pair	VERB
ap-6142	115	4	between	between	ADP
ap-6142	115	5	w−1,2(ω	w−1,2(ω	NOUN
ap-6142	115	6	)	)	PUNCT
ap-6142	115	7	and	and	CCONJ
ap-6142	115	8	w	w	NOUN
ap-6142	115	9	1,2(ω	1,2(ω	NUM
ap-6142	115	10	)	)	PUNCT
ap-6142	115	11	is	be	AUX
ap-6142	115	12	denoted	denote	VERB
ap-6142	115	13	by	by	ADP
ap-6142	115	14	〈	〈	PROPN
ap-6142	115	15	.	.	PUNCT
ap-6142	116	1	,	,	PUNCT
ap-6142	116	2	.	.	PUNCT
ap-6142	117	1	〉	〉	NOUN
ap-6142	117	2	.	.	PUNCT
ap-6142	117	3	)	)	PUNCT
ap-6142	118	1	due	due	ADP
ap-6142	118	2	to	to	ADP
ap-6142	118	3	[	[	X
ap-6142	118	4	19	19	NUM
ap-6142	118	5	,	,	PUNCT
ap-6142	118	6	theorem	theorem	ADJ
ap-6142	118	7	i.3.1	i.3.1	NOUN
ap-6142	118	8	]	]	PUNCT
ap-6142	118	9	function	function	NOUN
ap-6142	118	10	v∗ext	v∗ext	PROPN
ap-6142	118	11	belongs	belong	VERB
ap-6142	118	12	to	to	ADP
ap-6142	118	13	c0([0	c0([0	PROPN
ap-6142	118	14	,	,	PUNCT
ap-6142	118	15	t	t	X
ap-6142	118	16	]	]	X
ap-6142	118	17	;	;	PUNCT
ap-6142	118	18	l2(ω	l2(ω	X
ap-6142	118	19	)	)	PUNCT
ap-6142	118	20	)	)	PUNCT
ap-6142	118	21	.	.	PUNCT
ap-6142	119	1	(	(	PUNCT
ap-6142	119	2	iv	iv	X
ap-6142	119	3	)	)	PUNCT
ap-6142	119	4	we	we	PRON
ap-6142	119	5	denote	denote	VERB
ap-6142	119	6	by	by	ADP
ap-6142	119	7	v	v	ADP
ap-6142	119	8	the	the	DET
ap-6142	119	9	linear	linear	ADJ
ap-6142	119	10	space	space	NOUN
ap-6142	119	11	of	of	ADP
ap-6142	119	12	all	all	DET
ap-6142	119	13	divergence	divergence	ADJ
ap-6142	119	14	–	–	PUNCT
ap-6142	119	15	free	free	ADJ
ap-6142	119	16	vector	vector	NOUN
ap-6142	119	17	functions	function	NOUN
ap-6142	119	18	φ	φ	PROPN
ap-6142	119	19	∈w	∈w	PROPN
ap-6142	119	20	1,2(ω	1,2(ω	NUM
ap-6142	119	21	)	)	PUNCT
ap-6142	119	22	,	,	PUNCT
ap-6142	119	23	such	such	ADJ
ap-6142	119	24	that	that	SCONJ
ap-6142	119	25	φ	φ	PROPN
ap-6142	119	26	=	=	SYM
ap-6142	119	27	0	0	NUM
ap-6142	119	28	on	on	ADP
ap-6142	119	29	γ0∪γ1	γ0∪γ1	NOUN
ap-6142	119	30	.	.	PUNCT
ap-6142	120	1	then	then	ADV
ap-6142	120	2	v∗ext(t)+v	v∗ext(t)+v	PROPN
ap-6142	120	3	(	(	PUNCT
ap-6142	120	4	for	for	ADP
ap-6142	120	5	a.a	a.a	PROPN
ap-6142	120	6	.	.	PROPN
ap-6142	120	7	t	t	PROPN
ap-6142	120	8	∈	∈	PROPN
ap-6142	120	9	(	(	PUNCT
ap-6142	120	10	0	0	NUM
ap-6142	120	11	,	,	PUNCT
ap-6142	120	12	t	t	NOUN
ap-6142	120	13	)	)	PUNCT
ap-6142	120	14	)	)	PUNCT
ap-6142	120	15	91	91	NUM
ap-6142	120	16	stanislav	stanislav	X
ap-6142	120	17	kračmar	kračmar	PROPN
ap-6142	120	18	,	,	PUNCT
ap-6142	120	19	jiří	jiří	NOUN
ap-6142	120	20	neustupa	neustupa	PROPN
ap-6142	120	21	acta	acta	PROPN
ap-6142	120	22	polytechnica	polytechnica	PROPN
ap-6142	120	23	is	be	AUX
ap-6142	120	24	the	the	DET
ap-6142	120	25	set	set	NOUN
ap-6142	120	26	of	of	ADP
ap-6142	120	27	all	all	DET
ap-6142	120	28	functions	function	NOUN
ap-6142	120	29	φ	φ	NUM
ap-6142	120	30	from	from	ADP
ap-6142	120	31	w	w	PROPN
ap-6142	120	32	1,2(ω	1,2(ω	NUM
ap-6142	120	33	)	)	PUNCT
ap-6142	120	34	,	,	PUNCT
ap-6142	120	35	such	such	ADJ
ap-6142	120	36	that	that	DET
ap-6142	120	37	divφ	divφ	NOUN
ap-6142	120	38	=	=	SYM
ap-6142	120	39	0	0	NUM
ap-6142	120	40	,	,	PUNCT
ap-6142	120	41	φ	φ	NOUN
ap-6142	120	42	=	=	SYM
ap-6142	120	43	0	0	NUM
ap-6142	120	44	on	on	ADP
ap-6142	120	45	γ0	γ0	NOUN
ap-6142	120	46	and	and	CCONJ
ap-6142	120	47	φ	φ	NOUN
ap-6142	120	48	=	=	SYM
ap-6142	120	49	v∗ext(t	v∗ext(t	PROPN
ap-6142	120	50	)	)	PUNCT
ap-6142	120	51	on	on	ADP
ap-6142	120	52	γ1	γ1	PROPN
ap-6142	120	53	.	.	PUNCT
ap-6142	121	1	(	(	PUNCT
ap-6142	121	2	v	v	NOUN
ap-6142	121	3	)	)	PUNCT
ap-6142	121	4	let	let	VERB
ap-6142	121	5	ε1	ε1	VERB
ap-6142	121	6	>	>	X
ap-6142	121	7	0	0	PUNCT
ap-6142	122	1	and	and	CCONJ
ap-6142	122	2	ζ	ζ	NOUN
ap-6142	122	3	∈	∈	PROPN
ap-6142	122	4	l∞(0	l∞(0	NOUN
ap-6142	122	5	,	,	PUNCT
ap-6142	122	6	t	t	PROPN
ap-6142	122	7	)	)	PUNCT
ap-6142	122	8	satisfy	satisfy	VERB
ap-6142	122	9	the	the	DET
ap-6142	122	10	inequality∥∥(v∗ext(t	inequality∥∥(v∗ext(t	NOUN
ap-6142	122	11	)	)	PUNCT
ap-6142	122	12	·	·	PUNCT
ap-6142	122	13	n	n	X
ap-6142	122	14	)	)	PUNCT
ap-6142	122	15	−	−	PROPN
ap-6142	122	16	|v	|v	PROPN
ap-6142	122	17	∗	∗	NOUN
ap-6142	122	18	ext(t)|2	ext(t)|2	NUM
ap-6142	122	19	∥∥	∥∥	PROPN
ap-6142	122	20	1	1	NUM
ap-6142	122	21	;	;	PUNCT
ap-6142	122	22	γ2	γ2	PROPN
ap-6142	122	23	+	+	CCONJ
ap-6142	122	24	ε1	ε1	PROPN
ap-6142	122	25	<	<	X
ap-6142	122	26	ζ(t	ζ(t	PROPN
ap-6142	122	27	)	)	PUNCT
ap-6142	122	28	(	(	PUNCT
ap-6142	122	29	12	12	NUM
ap-6142	122	30	)	)	PUNCT
ap-6142	122	31	for	for	ADP
ap-6142	122	32	a.a	a.a	PROPN
ap-6142	122	33	.	.	PROPN
ap-6142	122	34	t	t	PROPN
ap-6142	122	35	∈	∈	PROPN
ap-6142	122	36	(	(	PUNCT
ap-6142	122	37	0	0	NUM
ap-6142	122	38	,	,	PUNCT
ap-6142	122	39	t	t	NOUN
ap-6142	122	40	)	)	PUNCT
ap-6142	122	41	.	.	PUNCT
ap-6142	123	1	(	(	PUNCT
ap-6142	123	2	the	the	DET
ap-6142	123	3	subscript	subscript	NOUN
ap-6142	123	4	“	"	PUNCT
ap-6142	123	5	−	−	PROPN
ap-6142	123	6	”	"	PUNCT
ap-6142	123	7	denotes	denote	VERB
ap-6142	123	8	the	the	DET
ap-6142	123	9	negative	negative	ADJ
ap-6142	123	10	part	part	NOUN
ap-6142	123	11	.	.	PUNCT
ap-6142	123	12	)	)	PUNCT
ap-6142	124	1	such	such	ADJ
ap-6142	124	2	number	number	NOUN
ap-6142	124	3	ε1	ε1	VERB
ap-6142	124	4	and	and	CCONJ
ap-6142	124	5	function	function	VERB
ap-6142	124	6	ζ	ζ	NOUN
ap-6142	124	7	exist	exist	NOUN
ap-6142	124	8	,	,	PUNCT
ap-6142	124	9	because	because	SCONJ
ap-6142	124	10	the	the	DET
ap-6142	124	11	trace	trace	NOUN
ap-6142	124	12	of	of	ADP
ap-6142	124	13	v∗	v∗	NOUN
ap-6142	124	14	on	on	ADP
ap-6142	124	15	γ2×(0	γ2×(0	PROPN
ap-6142	124	16	,	,	PUNCT
ap-6142	124	17	t	t	PROPN
ap-6142	124	18	)	)	PUNCT
ap-6142	124	19	is	be	AUX
ap-6142	124	20	in	in	ADP
ap-6142	124	21	l∞	l∞	NOUN
ap-6142	124	22	(	(	PUNCT
ap-6142	124	23	0	0	NUM
ap-6142	124	24	,	,	PUNCT
ap-6142	124	25	t	t	PROPN
ap-6142	124	26	;	;	PUNCT
ap-6142	124	27	w	w	PROPN
ap-6142	124	28	1/2,2(γ2	1/2,2(γ2	NUM
ap-6142	124	29	)	)	PUNCT
ap-6142	124	30	)	)	PUNCT
ap-6142	125	1	and	and	CCONJ
ap-6142	125	2	this	this	DET
ap-6142	125	3	space	space	NOUN
ap-6142	125	4	is	be	AUX
ap-6142	125	5	continuously	continuously	ADV
ap-6142	125	6	imbedded	imbed	VERB
ap-6142	125	7	to	to	ADP
ap-6142	125	8	l∞	l∞	NOUN
ap-6142	125	9	(	(	PUNCT
ap-6142	125	10	0	0	NUM
ap-6142	125	11	,	,	PUNCT
ap-6142	125	12	t	t	PROPN
ap-6142	125	13	;	;	PUNCT
ap-6142	125	14	l4(γ2	l4(γ2	PROPN
ap-6142	125	15	)	)	PUNCT
ap-6142	125	16	)	)	PUNCT
ap-6142	125	17	.	.	PUNCT
ap-6142	126	1	we	we	PRON
ap-6142	126	2	denote	denote	VERB
ap-6142	126	3	by	by	ADP
ap-6142	126	4	kt	kt	PROPN
ap-6142	126	5	the	the	DET
ap-6142	126	6	set	set	NOUN
ap-6142	126	7	of	of	ADP
ap-6142	126	8	all	all	DET
ap-6142	126	9	functions	function	NOUN
ap-6142	126	10	φ	φ	X
ap-6142	126	11	∈	∈	PROPN
ap-6142	126	12	v∗ext(t	v∗ext(t	PROPN
ap-6142	126	13	)	)	PUNCT
ap-6142	127	1	+	+	CCONJ
ap-6142	127	2	v	v	ADP
ap-6142	127	3	such	such	ADJ
ap-6142	127	4	that∥∥(φ	that∥∥(φ	NUM
ap-6142	127	5	·	·	PUNCT
ap-6142	127	6	n)−	n)−	PROPN
ap-6142	127	7	|φ|2‖1	|φ|2‖1	PROPN
ap-6142	127	8	;	;	PUNCT
ap-6142	127	9	γ2	γ2	ADJ
ap-6142	127	10	≤	≤	NOUN
ap-6142	127	11	ζ(t	ζ(t	PROPN
ap-6142	127	12	)	)	PUNCT
ap-6142	127	13	for	for	ADP
ap-6142	127	14	a.a	a.a	PROPN
ap-6142	127	15	.	.	PROPN
ap-6142	127	16	t	t	PROPN
ap-6142	127	17	∈	∈	PROPN
ap-6142	127	18	(	(	PUNCT
ap-6142	127	19	0	0	NUM
ap-6142	127	20	,	,	PUNCT
ap-6142	127	21	t	t	NOUN
ap-6142	127	22	)	)	PUNCT
ap-6142	127	23	,	,	PUNCT
ap-6142	127	24	(	(	PUNCT
ap-6142	127	25	13	13	X
ap-6142	127	26	)	)	PUNCT
ap-6142	127	27	bykc	bykc	NOUN
ap-6142	127	28	t	t	PROPN
ap-6142	127	29	the	the	DET
ap-6142	127	30	convex	convex	PROPN
ap-6142	127	31	hull	hull	NOUN
ap-6142	127	32	ofkt	ofkt	PROPN
ap-6142	127	33	and	and	CCONJ
ap-6142	127	34	definekc	definekc	PROPN
ap-6142	127	35	t	t	PROPN
ap-6142	127	36	to	to	PART
ap-6142	127	37	be	be	AUX
ap-6142	127	38	the	the	DET
ap-6142	127	39	closure	closure	NOUN
ap-6142	127	40	of	of	ADP
ap-6142	127	41	kc	kc	PROPN
ap-6142	127	42	t	t	PROPN
ap-6142	127	43	.	.	PUNCT
ap-6142	128	1	set	set	VERB
ap-6142	128	2	kc	kc	PROPN
ap-6142	128	3	t	t	PROPN
ap-6142	128	4	is	be	AUX
ap-6142	128	5	the	the	DET
ap-6142	128	6	so	so	ADV
ap-6142	128	7	called	call	VERB
ap-6142	128	8	closed	closed	ADJ
ap-6142	128	9	convex	convex	PROPN
ap-6142	128	10	hull	hull	NOUN
ap-6142	128	11	ofkt	ofkt	NOUN
ap-6142	128	12	.	.	PUNCT
ap-6142	129	1	(	(	PUNCT
ap-6142	129	2	see	see	VERB
ap-6142	129	3	[	[	X
ap-6142	129	4	20	20	NUM
ap-6142	129	5	]	]	PUNCT
ap-6142	129	6	for	for	ADP
ap-6142	129	7	more	more	ADJ
ap-6142	129	8	properties	property	NOUN
ap-6142	129	9	of	of	ADP
ap-6142	129	10	the	the	DET
ap-6142	129	11	convex	convex	PROPN
ap-6142	129	12	hull	hull	NOUN
ap-6142	129	13	and	and	CCONJ
ap-6142	129	14	the	the	DET
ap-6142	129	15	closed	closed	ADJ
ap-6142	129	16	convex	convex	NOUN
ap-6142	129	17	hull	hull	NOUN
ap-6142	129	18	.	.	PUNCT
ap-6142	130	1	note	note	VERB
ap-6142	130	2	that	that	SCONJ
ap-6142	130	3	kc	kc	PROPN
ap-6142	130	4	t	t	PROPN
ap-6142	130	5	can	can	AUX
ap-6142	130	6	also	also	ADV
ap-6142	130	7	be	be	AUX
ap-6142	130	8	defined	define	VERB
ap-6142	130	9	as	as	ADP
ap-6142	130	10	the	the	DET
ap-6142	130	11	intersection	intersection	NOUN
ap-6142	130	12	of	of	ADP
ap-6142	130	13	all	all	DET
ap-6142	130	14	closed	closed	ADJ
ap-6142	130	15	convex	convex	NOUN
ap-6142	130	16	sets	set	NOUN
ap-6142	130	17	in	in	ADP
ap-6142	130	18	v∗ext(t	v∗ext(t	PROPN
ap-6142	130	19	)	)	PUNCT
ap-6142	131	1	+	+	NUM
ap-6142	131	2	v	v	NOUN
ap-6142	131	3	,	,	PUNCT
ap-6142	131	4	containing	contain	VERB
ap-6142	131	5	kt	kt	PROPN
ap-6142	131	6	.	.	PUNCT
ap-6142	131	7	)	)	PUNCT
ap-6142	132	1	we	we	PRON
ap-6142	132	2	assume	assume	VERB
ap-6142	132	3	that	that	SCONJ
ap-6142	132	4	the	the	DET
ap-6142	132	5	number	number	NOUN
ap-6142	132	6	ε1	ε1	PROPN
ap-6142	132	7	,	,	PUNCT
ap-6142	132	8	and	and	CCONJ
ap-6142	132	9	the	the	DET
ap-6142	132	10	functions	function	NOUN
ap-6142	132	11	v∗ext	v∗ext	PROPN
ap-6142	132	12	and	and	CCONJ
ap-6142	132	13	ζ	ζ	NOUN
ap-6142	132	14	are	be	AUX
ap-6142	132	15	fixed	fix	VERB
ap-6142	132	16	throughout	throughout	ADP
ap-6142	132	17	the	the	DET
ap-6142	132	18	whole	whole	ADJ
ap-6142	132	19	paper	paper	NOUN
ap-6142	132	20	.	.	PUNCT
ap-6142	133	1	using	use	VERB
ap-6142	133	2	the	the	DET
ap-6142	133	3	presence	presence	NOUN
ap-6142	133	4	of	of	ADP
ap-6142	133	5	ε1	ε1	PROPN
ap-6142	133	6	>	>	X
ap-6142	133	7	0	0	PUNCT
ap-6142	133	8	in	in	ADP
ap-6142	133	9	inequality	inequality	NOUN
ap-6142	133	10	(	(	PUNCT
ap-6142	133	11	12	12	NUM
ap-6142	133	12	)	)	PUNCT
ap-6142	133	13	,	,	PUNCT
ap-6142	133	14	one	one	PRON
ap-6142	133	15	can	can	AUX
ap-6142	133	16	also	also	ADV
ap-6142	133	17	show	show	VERB
ap-6142	133	18	that	that	SCONJ
ap-6142	133	19	there	there	PRON
ap-6142	133	20	exists	exist	VERB
ap-6142	133	21	ε2	ε2	ADV
ap-6142	133	22	>	>	X
ap-6142	133	23	0	0	NUM
ap-6142	133	24	such	such	ADJ
ap-6142	133	25	that	that	SCONJ
ap-6142	133	26	kc	kc	PROPN
ap-6142	133	27	t	t	PROPN
ap-6142	133	28	contains	contain	VERB
ap-6142	133	29	the	the	DET
ap-6142	133	30	ε2	ε2	ADJ
ap-6142	133	31	–	–	PUNCT
ap-6142	133	32	neighborhood	neighborhood	NOUN
ap-6142	133	33	of	of	ADP
ap-6142	133	34	v∗ext(t	v∗ext(t	PROPN
ap-6142	133	35	)	)	PUNCT
ap-6142	133	36	,	,	PUNCT
ap-6142	133	37	independently	independently	ADV
ap-6142	133	38	of	of	ADP
ap-6142	133	39	t.	t.	PROPN
ap-6142	133	40	(	(	PUNCT
ap-6142	133	41	vi	vi	NOUN
ap-6142	133	42	)	)	PUNCT
ap-6142	133	43	denote	denote	NOUN
ap-6142	133	44	by	by	ADP
ap-6142	133	45	w	w	PROPN
ap-6142	133	46	(	(	PUNCT
ap-6142	133	47	0	0	NUM
ap-6142	133	48	,	,	PUNCT
ap-6142	133	49	t	t	NOUN
ap-6142	133	50	)	)	PUNCT
ap-6142	133	51	the	the	DET
ap-6142	133	52	space	space	NOUN
ap-6142	133	53	{	{	PUNCT
ap-6142	133	54	w	w	PROPN
ap-6142	133	55	∈	∈	PROPN
ap-6142	133	56	l2(0	l2(0	NOUN
ap-6142	133	57	,	,	PUNCT
ap-6142	133	58	t	t	NOUN
ap-6142	133	59	;	;	PUNCT
ap-6142	133	60	w	w	PROPN
ap-6142	133	61	1,2(ω	1,2(ω	NUM
ap-6142	133	62	)	)	PUNCT
ap-6142	133	63	)	)	PUNCT
ap-6142	133	64	;	;	PUNCT
ap-6142	134	1	∂tw	∂tw	PROPN
ap-6142	134	2	∈	∈	PROPN
ap-6142	134	3	l2(0	l2(0	PROPN
ap-6142	134	4	,	,	PUNCT
ap-6142	134	5	t	t	NOUN
ap-6142	134	6	;	;	PUNCT
ap-6142	134	7	w−1,2(ω	w−1,2(ω	ADJ
ap-6142	134	8	)	)	PUNCT
ap-6142	134	9	)	)	PUNCT
ap-6142	134	10	}	}	PUNCT
ap-6142	134	11	with	with	ADP
ap-6142	134	12	the	the	DET
ap-6142	134	13	norm	norm	NOUN
ap-6142	134	14	|||w|||	|||w|||	NOUN
ap-6142	134	15	:	:	PUNCT
ap-6142	134	16	=	=	SYM
ap-6142	134	17	(	(	PUNCT
ap-6142	134	18	∫	∫	PROPN
ap-6142	134	19	t	t	PROPN
ap-6142	134	20	0	0	NUM
ap-6142	134	21	‖w‖21,2	‖w‖21,2	PROPN
ap-6142	134	22	dt+	dt+	NOUN
ap-6142	134	23	∫	∫	PROPN
ap-6142	134	24	t	t	NOUN
ap-6142	134	25	0	0	NUM
ap-6142	134	26	‖∂tw‖2−1,2	‖∂tw‖2−1,2	NUM
ap-6142	134	27	dt	dt	NOUN
ap-6142	134	28	)	)	PUNCT
ap-6142	134	29	1/2	1/2	NUM
ap-6142	134	30	.	.	PUNCT
ap-6142	135	1	using	use	VERB
ap-6142	135	2	[	[	X
ap-6142	135	3	19	19	NUM
ap-6142	135	4	,	,	PUNCT
ap-6142	135	5	theorem	theorem	VERB
ap-6142	135	6	i.3.1	i.3.1	PROPN
ap-6142	135	7	]	]	PUNCT
ap-6142	135	8	,	,	PUNCT
ap-6142	135	9	one	one	PRON
ap-6142	135	10	can	can	AUX
ap-6142	135	11	show	show	VERB
ap-6142	135	12	that	that	SCONJ
ap-6142	135	13	w	w	NOUN
ap-6142	135	14	(	(	PUNCT
ap-6142	135	15	0	0	NUM
ap-6142	135	16	,	,	PUNCT
ap-6142	135	17	t	t	NOUN
ap-6142	135	18	)	)	PUNCT
ap-6142	136	1	⊂	⊂	PROPN
ap-6142	136	2	c0([0	c0([0	PROPN
ap-6142	136	3	,	,	PUNCT
ap-6142	136	4	t	t	X
ap-6142	136	5	]	]	PUNCT
ap-6142	136	6	;	;	PUNCT
ap-6142	136	7	l2(ω	l2(ω	X
ap-6142	136	8	)	)	PUNCT
ap-6142	136	9	)	)	PUNCT
ap-6142	136	10	.	.	PUNCT
ap-6142	137	1	(	(	PUNCT
ap-6142	137	2	vii	vii	PROPN
ap-6142	137	3	)	)	PUNCT
ap-6142	137	4	put	put	VERB
ap-6142	137	5	k	k	PROPN
ap-6142	137	6	c(0	c(0	PROPN
ap-6142	137	7	,	,	PUNCT
ap-6142	137	8	t	t	NOUN
ap-6142	137	9	)	)	PUNCT
ap-6142	137	10	:	:	PUNCT
ap-6142	138	1	=	=	PRON
ap-6142	138	2	{	{	PUNCT
ap-6142	138	3	w	w	PROPN
ap-6142	138	4	∈	∈	PROPN
ap-6142	138	5	w	w	PROPN
ap-6142	138	6	(	(	PUNCT
ap-6142	138	7	0	0	NUM
ap-6142	138	8	,	,	PUNCT
ap-6142	138	9	t	t	NOUN
ap-6142	138	10	)	)	PUNCT
ap-6142	138	11	;	;	PUNCT
ap-6142	138	12	w(t	w(t	X
ap-6142	138	13	)	)	PUNCT
ap-6142	138	14	∈	∈	PROPN
ap-6142	138	15	kc	kc	PROPN
ap-6142	138	16	t	t	PROPN
ap-6142	138	17	for	for	ADP
ap-6142	138	18	a.a	a.a	PROPN
ap-6142	138	19	.	.	PROPN
ap-6142	138	20	t	t	PROPN
ap-6142	138	21	∈	∈	PROPN
ap-6142	138	22	(	(	PUNCT
ap-6142	138	23	0	0	NUM
ap-6142	138	24	,	,	PUNCT
ap-6142	138	25	t	t	NOUN
ap-6142	138	26	)	)	PUNCT
ap-6142	138	27	}	}	PUNCT
ap-6142	138	28	.	.	PUNCT
ap-6142	139	1	3.2	3.2	NUM
ap-6142	139	2	.	.	PUNCT
ap-6142	140	1	a	a	DET
ap-6142	140	2	formal	formal	ADJ
ap-6142	140	3	derivation	derivation	NOUN
ap-6142	140	4	of	of	ADP
ap-6142	140	5	the	the	DET
ap-6142	140	6	variational	variational	ADJ
ap-6142	140	7	inequality	inequality	NOUN
ap-6142	140	8	suppose	suppose	VERB
ap-6142	140	9	that	that	SCONJ
ap-6142	140	10	v	v	NOUN
ap-6142	140	11	,	,	PUNCT
ap-6142	140	12	p	p	NOUN
ap-6142	140	13	is	be	AUX
ap-6142	140	14	a	a	DET
ap-6142	140	15	sufficiently	sufficiently	ADV
ap-6142	140	16	smooth	smooth	ADJ
ap-6142	140	17	solution	solution	NOUN
ap-6142	140	18	of	of	ADP
ap-6142	140	19	the	the	DET
ap-6142	140	20	problem	problem	NOUN
ap-6142	140	21	(	(	PUNCT
ap-6142	140	22	1)–(6	1)–(6	X
ap-6142	140	23	)	)	PUNCT
ap-6142	140	24	and	and	CCONJ
ap-6142	140	25	w	w	PROPN
ap-6142	140	26	is	be	AUX
ap-6142	140	27	a	a	DET
ap-6142	140	28	sufficiently	sufficiently	ADV
ap-6142	140	29	smooth	smooth	ADJ
ap-6142	140	30	function	function	NOUN
ap-6142	140	31	from	from	ADP
ap-6142	140	32	[	[	X
ap-6142	140	33	0	0	NUM
ap-6142	140	34	,	,	PUNCT
ap-6142	140	35	t	t	X
ap-6142	140	36	]	]	PUNCT
ap-6142	140	37	such	such	ADJ
ap-6142	140	38	that	that	SCONJ
ap-6142	140	39	w(t	w(t	PROPN
ap-6142	140	40	)	)	PUNCT
ap-6142	140	41	∈	∈	PROPN
ap-6142	140	42	kc	kc	PROPN
ap-6142	140	43	t	t	PROPN
ap-6142	140	44	for	for	ADP
ap-6142	140	45	a.a	a.a	PROPN
ap-6142	140	46	.	.	PROPN
ap-6142	140	47	t	t	PROPN
ap-6142	140	48	∈	∈	PROPN
ap-6142	141	1	[	[	X
ap-6142	141	2	0	0	NUM
ap-6142	141	3	,	,	PUNCT
ap-6142	141	4	t	t	X
ap-6142	141	5	]	]	PUNCT
ap-6142	141	6	.	.	PUNCT
ap-6142	142	1	using	use	VERB
ap-6142	142	2	the	the	DET
ap-6142	142	3	form	form	NOUN
ap-6142	142	4	a	a	NOUN
ap-6142	142	5	)	)	PUNCT
ap-6142	142	6	of	of	ADP
ap-6142	142	7	the	the	DET
ap-6142	142	8	divergence	divergence	NOUN
ap-6142	142	9	of	of	ADP
ap-6142	142	10	the	the	DET
ap-6142	142	11	dynamic	dynamic	ADJ
ap-6142	142	12	stress	stress	NOUN
ap-6142	142	13	tensor	tensor	NOUN
ap-6142	142	14	in	in	ADP
ap-6142	142	15	(	(	PUNCT
ap-6142	142	16	7	7	NUM
ap-6142	142	17	)	)	PUNCT
ap-6142	142	18	,	,	PUNCT
ap-6142	142	19	multiplying	multiply	VERB
ap-6142	142	20	equation	equation	NOUN
ap-6142	142	21	(	(	PUNCT
ap-6142	142	22	1	1	NUM
ap-6142	142	23	)	)	PUNCT
ap-6142	142	24	by	by	ADP
ap-6142	142	25	the	the	DET
ap-6142	142	26	difference	difference	NOUN
ap-6142	142	27	w	w	ADP
ap-6142	142	28	−	−	PROPN
ap-6142	142	29	v	v	NOUN
ap-6142	142	30	,	,	PUNCT
ap-6142	142	31	integrating	integrate	VERB
ap-6142	142	32	in	in	ADP
ap-6142	142	33	ω×(0	ω×(0	PROPN
ap-6142	142	34	,	,	PUNCT
ap-6142	142	35	t	t	PROPN
ap-6142	142	36	)	)	PUNCT
ap-6142	142	37	,	,	PUNCT
ap-6142	142	38	applying	apply	VERB
ap-6142	142	39	the	the	DET
ap-6142	142	40	integration	integration	NOUN
ap-6142	142	41	by	by	ADP
ap-6142	142	42	parts	part	NOUN
ap-6142	142	43	and	and	CCONJ
ap-6142	142	44	using	use	VERB
ap-6142	142	45	the	the	DET
ap-6142	142	46	equality	equality	NOUN
ap-6142	142	47	w	w	ADP
ap-6142	142	48	−	−	PROPN
ap-6142	142	49	v	v	NOUN
ap-6142	142	50	=	=	SYM
ap-6142	142	51	0	0	NUM
ap-6142	142	52	on	on	ADP
ap-6142	142	53	γ0	γ0	PROPN
ap-6142	142	54	∪	∪	X
ap-6142	142	55	γ1	γ1	PROPN
ap-6142	142	56	×	×	PROPN
ap-6142	142	57	(	(	PUNCT
ap-6142	142	58	0	0	NUM
ap-6142	142	59	,	,	PUNCT
ap-6142	142	60	t	t	PROPN
ap-6142	142	61	)	)	PUNCT
ap-6142	142	62	and	and	CCONJ
ap-6142	142	63	the	the	DET
ap-6142	142	64	boundary	boundary	ADJ
ap-6142	142	65	condition	condition	NOUN
ap-6142	142	66	(	(	PUNCT
ap-6142	142	67	5	5	NUM
ap-6142	142	68	)	)	PUNCT
ap-6142	142	69	,	,	PUNCT
ap-6142	142	70	we	we	PRON
ap-6142	142	71	get∫	get∫	VERB
ap-6142	142	72	t	t	PROPN
ap-6142	142	73	0	0	NUM
ap-6142	142	74	∫	∫	PROPN
ap-6142	142	75	ω	ω	PROPN
ap-6142	143	1	[	[	X
ap-6142	143	2	∂tv	∂tv	PROPN
ap-6142	143	3	+	+	CCONJ
ap-6142	143	4	v	v	NOUN
ap-6142	143	5	·	·	PUNCT
ap-6142	143	6	∇v	∇v	ADV
ap-6142	143	7	]	]	PUNCT
ap-6142	143	8	·	·	PUNCT
ap-6142	143	9	(	(	PUNCT
ap-6142	143	10	w	w	NOUN
ap-6142	143	11	−	−	PROPN
ap-6142	143	12	v	v	NOUN
ap-6142	143	13	)	)	PUNCT
ap-6142	143	14	dx	dx	PROPN
ap-6142	143	15	dt	dt	PROPN
ap-6142	144	1	+	+	CCONJ
ap-6142	144	2	∫	∫	PROPN
ap-6142	144	3	t	t	PROPN
ap-6142	144	4	0	0	NUM
ap-6142	144	5	∫	∫	PROPN
ap-6142	145	1	ω	ω	PROPN
ap-6142	145	2	ν∇v	ν∇v	NOUN
ap-6142	145	3	:	:	PUNCT
ap-6142	145	4	∇(w	∇(w	ADJ
ap-6142	145	5	−	−	PROPN
ap-6142	145	6	v	v	NOUN
ap-6142	145	7	)	)	PUNCT
ap-6142	145	8	dx	dx	PROPN
ap-6142	145	9	dt	dt	X
ap-6142	146	1	=	=	SYM
ap-6142	146	2	∫	∫	PROPN
ap-6142	146	3	t	t	PROPN
ap-6142	146	4	0	0	NUM
ap-6142	147	1	∫	∫	PROPN
ap-6142	147	2	ω	ω	NUM
ap-6142	147	3	f	f	X
ap-6142	147	4	·	·	PUNCT
ap-6142	147	5	(	(	PUNCT
ap-6142	147	6	w	w	NOUN
ap-6142	147	7	−	−	PROPN
ap-6142	147	8	v	v	NOUN
ap-6142	147	9	)	)	PUNCT
ap-6142	147	10	dx	dx	PROPN
ap-6142	148	1	dt	dt	PROPN
ap-6142	149	1	+	+	CCONJ
ap-6142	149	2	∫	∫	PROPN
ap-6142	149	3	t	t	PROPN
ap-6142	149	4	0	0	NUM
ap-6142	149	5	∫	∫	PROPN
ap-6142	149	6	γ2	γ2	PROPN
ap-6142	149	7	g	g	PROPN
ap-6142	149	8	·	·	PUNCT
ap-6142	149	9	(	(	PUNCT
ap-6142	149	10	w	w	NOUN
ap-6142	149	11	−	−	PROPN
ap-6142	149	12	v	v	NOUN
ap-6142	149	13	)	)	PUNCT
ap-6142	149	14	ds	ds	ADJ
ap-6142	149	15	dt	dt	NOUN
ap-6142	149	16	.	.	PUNCT
ap-6142	150	1	(	(	PUNCT
ap-6142	150	2	14	14	NUM
ap-6142	150	3	)	)	PUNCT
ap-6142	150	4	the	the	DET
ap-6142	150	5	term	term	NOUN
ap-6142	150	6	,	,	PUNCT
ap-6142	150	7	which	which	PRON
ap-6142	150	8	contains	contain	VERB
ap-6142	150	9	the	the	DET
ap-6142	150	10	derivative	derivative	ADJ
ap-6142	150	11	∂tv	∂tv	PROPN
ap-6142	150	12	,	,	PUNCT
ap-6142	150	13	satisfies∫	satisfies∫	X
ap-6142	150	14	t	t	NOUN
ap-6142	150	15	0	0	NUM
ap-6142	150	16	∫	∫	PROPN
ap-6142	151	1	ω	ω	NUM
ap-6142	151	2	∂tv	∂tv	PROPN
ap-6142	151	3	·	·	PUNCT
ap-6142	151	4	(	(	PUNCT
ap-6142	151	5	w	w	NOUN
ap-6142	151	6	−	−	PROPN
ap-6142	151	7	v	v	NOUN
ap-6142	151	8	)	)	PUNCT
ap-6142	151	9	dx	dx	PROPN
ap-6142	152	1	dt	dt	X
ap-6142	153	1	=	=	SYM
ap-6142	153	2	∫	∫	PROPN
ap-6142	153	3	t	t	PROPN
ap-6142	153	4	0	0	NUM
ap-6142	153	5	∫	∫	PROPN
ap-6142	153	6	ω	ω	PROPN
ap-6142	153	7	∂t(v	∂t(v	PROPN
ap-6142	153	8	−w	−w	NOUN
ap-6142	153	9	)	)	PUNCT
ap-6142	153	10	·	·	PUNCT
ap-6142	154	1	(	(	PUNCT
ap-6142	154	2	w	w	NOUN
ap-6142	154	3	−	−	PROPN
ap-6142	154	4	v	v	NOUN
ap-6142	154	5	)	)	PUNCT
ap-6142	154	6	dx	dx	PROPN
ap-6142	155	1	dt	dt	PROPN
ap-6142	156	1	+	+	CCONJ
ap-6142	156	2	∫	∫	PROPN
ap-6142	156	3	t	t	PROPN
ap-6142	156	4	0	0	NUM
ap-6142	156	5	∫	∫	PROPN
ap-6142	157	1	ω	ω	NUM
ap-6142	157	2	∂tw	∂tw	PROPN
ap-6142	157	3	·	·	PUNCT
ap-6142	157	4	(	(	PUNCT
ap-6142	157	5	w	w	NOUN
ap-6142	157	6	−	−	PROPN
ap-6142	157	7	v	v	NOUN
ap-6142	157	8	)	)	PUNCT
ap-6142	157	9	dx	dx	PROPN
ap-6142	157	10	dt	dt	NOUN
ap-6142	158	1	=	=	NOUN
ap-6142	158	2	1	1	NUM
ap-6142	158	3	2	2	NUM
ap-6142	158	4	‖w(0)−	‖w(0)−	NOUN
ap-6142	158	5	v(0)‖22	v(0)‖22	NOUN
ap-6142	158	6	−	−	NOUN
ap-6142	158	7	1	1	NUM
ap-6142	158	8	2	2	NUM
ap-6142	158	9	‖w(t	‖w(t	NUM
ap-6142	158	10	)	)	PUNCT
ap-6142	158	11	−	−	PROPN
ap-6142	158	12	v(t	v(t	NOUN
ap-6142	158	13	)	)	PUNCT
ap-6142	158	14	‖22	‖22	PROPN
ap-6142	159	1	+	+	CCONJ
ap-6142	160	1	∫	∫	PROPN
ap-6142	160	2	t	t	PROPN
ap-6142	160	3	0	0	NUM
ap-6142	160	4	∫	∫	PROPN
ap-6142	161	1	ω	ω	NUM
ap-6142	161	2	∂tw	∂tw	PROPN
ap-6142	161	3	·	·	PUNCT
ap-6142	161	4	(	(	PUNCT
ap-6142	161	5	w	w	NOUN
ap-6142	161	6	−	−	PROPN
ap-6142	161	7	v	v	NOUN
ap-6142	161	8	)	)	PUNCT
ap-6142	161	9	dx	dx	PROPN
ap-6142	161	10	dt	dt	PROPN
ap-6142	162	1	≤	≤	NUM
ap-6142	162	2	1	1	NUM
ap-6142	162	3	2	2	NUM
ap-6142	162	4	‖w(0)−	‖w(0)−	NUM
ap-6142	162	5	v0‖22	v0‖22	NOUN
ap-6142	162	6	+	+	CCONJ
ap-6142	163	1	∫	∫	PROPN
ap-6142	163	2	t	t	PROPN
ap-6142	163	3	0	0	NUM
ap-6142	163	4	∫	∫	PROPN
ap-6142	164	1	ω	ω	NUM
ap-6142	164	2	∂tw	∂tw	PROPN
ap-6142	164	3	·	·	PUNCT
ap-6142	164	4	(	(	PUNCT
ap-6142	164	5	w	w	NOUN
ap-6142	164	6	−	−	PROPN
ap-6142	164	7	v	v	NOUN
ap-6142	164	8	)	)	PUNCT
ap-6142	164	9	dx	dx	PROPN
ap-6142	165	1	dt	dt	PROPN
ap-6142	165	2	.	.	PUNCT
ap-6142	166	1	(	(	PUNCT
ap-6142	166	2	15	15	X
ap-6142	166	3	)	)	PUNCT
ap-6142	166	4	let	let	VERB
ap-6142	166	5	w	w	PROPN
ap-6142	166	6	∈	∈	PROPN
ap-6142	166	7	k	k	PROPN
ap-6142	166	8	c(0	c(0	PROPN
ap-6142	166	9	,	,	PUNCT
ap-6142	166	10	t	t	NOUN
ap-6142	166	11	)	)	PUNCT
ap-6142	166	12	further	far	ADV
ap-6142	166	13	on	on	ADV
ap-6142	166	14	.	.	PUNCT
ap-6142	167	1	since∫	since∫	VERB
ap-6142	167	2	ω	ω	PROPN
ap-6142	167	3	∂tw	∂tw	PROPN
ap-6142	167	4	·	·	PUNCT
ap-6142	167	5	(	(	PUNCT
ap-6142	167	6	w	w	NOUN
ap-6142	167	7	−	−	PROPN
ap-6142	167	8	v	v	NOUN
ap-6142	167	9	)	)	PUNCT
ap-6142	167	10	dx	dx	PROPN
ap-6142	168	1	=	=	SYM
ap-6142	168	2	〈	〈	PROPN
ap-6142	168	3	∂tw	∂tw	PROPN
ap-6142	168	4	,	,	PUNCT
ap-6142	168	5	w	w	PROPN
ap-6142	168	6	−	−	PROPN
ap-6142	168	7	v〉,∫	v〉,∫	NOUN
ap-6142	168	8	ω	ω	NUM
ap-6142	168	9	f	f	X
ap-6142	168	10	·	·	PUNCT
ap-6142	168	11	(	(	PUNCT
ap-6142	168	12	w	w	NOUN
ap-6142	168	13	−	−	PROPN
ap-6142	168	14	v	v	NOUN
ap-6142	168	15	)	)	PUNCT
ap-6142	168	16	dx	dx	PROPN
ap-6142	169	1	=	=	SYM
ap-6142	169	2	〈	〈	PROPN
ap-6142	169	3	f	f	PROPN
ap-6142	169	4	,	,	PUNCT
ap-6142	169	5	w	w	PROPN
ap-6142	169	6	−	−	PROPN
ap-6142	169	7	v	v	ADP
ap-6142	169	8	〉	〉	NOUN
ap-6142	169	9	,	,	PUNCT
ap-6142	169	10	(	(	PUNCT
ap-6142	169	11	15	15	NUM
ap-6142	169	12	)	)	PUNCT
ap-6142	169	13	and	and	CCONJ
ap-6142	169	14	(	(	PUNCT
ap-6142	169	15	14	14	NUM
ap-6142	169	16	)	)	PUNCT
ap-6142	169	17	yield∫	yield∫	NOUN
ap-6142	169	18	t	t	PROPN
ap-6142	169	19	0	0	NUM
ap-6142	170	1	〈	〈	PROPN
ap-6142	170	2	∂tw	∂tw	PROPN
ap-6142	170	3	,	,	PUNCT
ap-6142	170	4	w	w	PROPN
ap-6142	170	5	−	−	PROPN
ap-6142	170	6	v	v	NUM
ap-6142	170	7	〉	〉	NOUN
ap-6142	170	8	dt+	dt+	NOUN
ap-6142	170	9	∫	∫	PROPN
ap-6142	170	10	t	t	PROPN
ap-6142	170	11	0	0	NUM
ap-6142	171	1	∫	∫	PROPN
ap-6142	171	2	ω	ω	NUM
ap-6142	171	3	v	v	X
ap-6142	171	4	·	·	PUNCT
ap-6142	171	5	∇v	∇v	NOUN
ap-6142	171	6	·	·	PUNCT
ap-6142	172	1	(	(	PUNCT
ap-6142	172	2	w	w	NOUN
ap-6142	172	3	−	−	PROPN
ap-6142	172	4	v	v	NOUN
ap-6142	172	5	)	)	PUNCT
ap-6142	172	6	dx	dx	PROPN
ap-6142	173	1	dt	dt	PROPN
ap-6142	174	1	+	+	CCONJ
ap-6142	174	2	∫	∫	PROPN
ap-6142	174	3	t	t	PROPN
ap-6142	174	4	0	0	NUM
ap-6142	174	5	∫	∫	PROPN
ap-6142	175	1	ω	ω	PROPN
ap-6142	175	2	ν∇v	ν∇v	NOUN
ap-6142	175	3	:	:	PUNCT
ap-6142	175	4	∇(w	∇(w	ADJ
ap-6142	175	5	−	−	PROPN
ap-6142	175	6	v	v	NOUN
ap-6142	175	7	)	)	PUNCT
ap-6142	175	8	dx	dx	PROPN
ap-6142	176	1	dt	dt	PROPN
ap-6142	176	2	≥	≥	PROPN
ap-6142	177	1	∫	∫	PROPN
ap-6142	177	2	t	t	PROPN
ap-6142	177	3	0	0	PUNCT
ap-6142	178	1	〈	〈	PROPN
ap-6142	178	2	f	f	PROPN
ap-6142	178	3	,	,	PUNCT
ap-6142	178	4	w	w	PROPN
ap-6142	178	5	−	−	PROPN
ap-6142	178	6	v	v	NOUN
ap-6142	178	7	〉	〉	NUM
ap-6142	178	8	dt+	dt+	NOUN
ap-6142	178	9	∫	∫	PROPN
ap-6142	178	10	t	t	PROPN
ap-6142	178	11	0	0	NUM
ap-6142	178	12	∫	∫	PROPN
ap-6142	178	13	γ2	γ2	PROPN
ap-6142	178	14	g	g	PROPN
ap-6142	178	15	·	·	PUNCT
ap-6142	178	16	(	(	PUNCT
ap-6142	178	17	w	w	NOUN
ap-6142	178	18	−	−	PROPN
ap-6142	178	19	v	v	NOUN
ap-6142	178	20	)	)	PUNCT
ap-6142	178	21	ds	ds	NOUN
ap-6142	178	22	dt	dt	NOUN
ap-6142	178	23	−	−	PROPN
ap-6142	178	24	1	1	NUM
ap-6142	178	25	2	2	NUM
ap-6142	178	26	‖w(0)−	‖w(0)−	NUM
ap-6142	178	27	v0‖22	v0‖22	NOUN
ap-6142	178	28	.	.	PUNCT
ap-6142	179	1	(	(	PUNCT
ap-6142	179	2	16	16	NUM
ap-6142	179	3	)	)	PUNCT
ap-6142	179	4	since	since	SCONJ
ap-6142	179	5	(	(	PUNCT
ap-6142	179	6	16	16	NUM
ap-6142	179	7	)	)	PUNCT
ap-6142	179	8	is	be	AUX
ap-6142	179	9	an	an	DET
ap-6142	179	10	inequality	inequality	NOUN
ap-6142	179	11	,	,	PUNCT
ap-6142	179	12	we	we	PRON
ap-6142	179	13	have	have	VERB
ap-6142	179	14	the	the	DET
ap-6142	179	15	possibility	possibility	NOUN
ap-6142	179	16	to	to	PART
ap-6142	179	17	choose	choose	VERB
ap-6142	179	18	another	another	DET
ap-6142	179	19	condition	condition	NOUN
ap-6142	179	20	and	and	CCONJ
ap-6142	179	21	to	to	PART
ap-6142	179	22	impose	impose	VERB
ap-6142	179	23	it	it	PRON
ap-6142	179	24	on	on	ADP
ap-6142	179	25	the	the	DET
ap-6142	179	26	solution	solution	NOUN
ap-6142	179	27	v	v	ADP
ap-6142	179	28	:	:	PUNCT
ap-6142	179	29	we	we	PRON
ap-6142	179	30	require	require	VERB
ap-6142	179	31	that	that	SCONJ
ap-6142	179	32	the	the	DET
ap-6142	179	33	inclusion	inclusion	NOUN
ap-6142	179	34	v(t	v(t	AUX
ap-6142	179	35	)	)	PUNCT
ap-6142	179	36	∈	∈	PROPN
ap-6142	179	37	kc	kc	PROPN
ap-6142	179	38	t	t	PROPN
ap-6142	179	39	holds	hold	VERB
ap-6142	179	40	for	for	ADP
ap-6142	179	41	a.a	a.a	PROPN
ap-6142	179	42	.	.	PROPN
ap-6142	179	43	t	t	PROPN
ap-6142	179	44	∈	∈	PROPN
ap-6142	179	45	(	(	PUNCT
ap-6142	179	46	0	0	NUM
ap-6142	179	47	,	,	PUNCT
ap-6142	179	48	t	t	NOUN
ap-6142	179	49	)	)	PUNCT
ap-6142	179	50	.	.	PUNCT
ap-6142	180	1	3.3	3.3	NUM
ap-6142	180	2	.	.	PUNCT
ap-6142	181	1	definition	definition	NOUN
ap-6142	181	2	of	of	ADP
ap-6142	181	3	the	the	DET
ap-6142	181	4	initial	initial	ADJ
ap-6142	181	5	–	–	PUNCT
ap-6142	181	6	boundary	boundary	ADJ
ap-6142	181	7	value	value	NOUN
ap-6142	181	8	problem	problem	NOUN
ap-6142	181	9	(	(	PUNCT
ap-6142	181	10	p	p	X
ap-6142	181	11	)	)	PUNCT
ap-6142	181	12	let	let	VERB
ap-6142	181	13	v∗ext	v∗ext	PROPN
ap-6142	181	14	be	be	AUX
ap-6142	181	15	the	the	DET
ap-6142	181	16	extension	extension	NOUN
ap-6142	181	17	of	of	ADP
ap-6142	181	18	function	function	NOUN
ap-6142	181	19	v∗	v∗	ADJ
ap-6142	181	20	with	with	ADP
ap-6142	181	21	the	the	DET
ap-6142	181	22	properties	property	NOUN
ap-6142	181	23	(	(	PUNCT
ap-6142	181	24	i	i	NOUN
ap-6142	181	25	)	)	PUNCT
ap-6142	181	26	and	and	CCONJ
ap-6142	181	27	(	(	PUNCT
ap-6142	181	28	ii	ii	NOUN
ap-6142	181	29	)	)	PUNCT
ap-6142	181	30	from	from	ADP
ap-6142	181	31	paragraph	paragraph	NOUN
ap-6142	181	32	3.2	3.2	NUM
ap-6142	181	33	.	.	PUNCT
ap-6142	182	1	let	let	VERB
ap-6142	182	2	v0	v0	VERB
ap-6142	182	3	∈	∈	PROPN
ap-6142	182	4	l2(ω	l2(ω	PROPN
ap-6142	182	5	)	)	PUNCT
ap-6142	182	6	,	,	PUNCT
ap-6142	182	7	div	div	X
ap-6142	182	8	v0	v0	NOUN
ap-6142	182	9	=	=	NOUN
ap-6142	182	10	0	0	NUM
ap-6142	182	11	in	in	ADP
ap-6142	182	12	ω	ω	PROPN
ap-6142	182	13	in	in	ADP
ap-6142	182	14	the	the	DET
ap-6142	182	15	sense	sense	NOUN
ap-6142	182	16	of	of	ADP
ap-6142	182	17	distributions	distribution	NOUN
ap-6142	182	18	,	,	PUNCT
ap-6142	182	19	v0	v0	NOUN
ap-6142	182	20	·	·	PUNCT
ap-6142	182	21	n	n	NOUN
ap-6142	182	22	=	=	SYM
ap-6142	182	23	0	0	NUM
ap-6142	182	24	on	on	ADP
ap-6142	182	25	γ0	γ0	NOUN
ap-6142	182	26	and	and	CCONJ
ap-6142	182	27	v0	v0	NOUN
ap-6142	182	28	·	·	PUNCT
ap-6142	182	29	n	n	CCONJ
ap-6142	182	30	=	=	PUNCT
ap-6142	182	31	v∗(0	v∗(0	NOUN
ap-6142	182	32	)	)	PUNCT
ap-6142	182	33	·	·	PUNCT
ap-6142	183	1	n	n	CCONJ
ap-6142	183	2	on	on	ADP
ap-6142	183	3	γ1	γ1	PROPN
ap-6142	183	4	in	in	ADP
ap-6142	183	5	the	the	DET
ap-6142	183	6	sense	sense	NOUN
ap-6142	183	7	of	of	ADP
ap-6142	183	8	traces	trace	NOUN
ap-6142	183	9	.	.	PUNCT
ap-6142	184	1	let	let	VERB
ap-6142	184	2	f	f	PROPN
ap-6142	184	3	∈	∈	PROPN
ap-6142	184	4	l2(0	l2(0	PROPN
ap-6142	184	5	,	,	PUNCT
ap-6142	184	6	t	t	NOUN
ap-6142	184	7	;	;	PUNCT
ap-6142	184	8	w−1,2(ω	w−1,2(ω	ADJ
ap-6142	184	9	)	)	PUNCT
ap-6142	184	10	)	)	PUNCT
ap-6142	185	1	and	and	CCONJ
ap-6142	185	2	g	g	PROPN
ap-6142	185	3	∈	∈	PROPN
ap-6142	185	4	l2(0	l2(0	NOUN
ap-6142	185	5	,	,	PUNCT
ap-6142	185	6	t	t	NOUN
ap-6142	185	7	;	;	PUNCT
ap-6142	185	8	l4/3(γ2	l4/3(γ2	PROPN
ap-6142	185	9	)	)	PUNCT
ap-6142	185	10	)	)	PUNCT
ap-6142	185	11	.	.	PUNCT
ap-6142	186	1	one	one	NUM
ap-6142	186	2	looks	look	VERB
ap-6142	186	3	for	for	ADP
ap-6142	186	4	v	v	NOUN
ap-6142	186	5	∈	∈	PROPN
ap-6142	186	6	l∞(0	l∞(0	PRON
ap-6142	186	7	,	,	PUNCT
ap-6142	186	8	t	t	PROPN
ap-6142	186	9	;	;	PUNCT
ap-6142	186	10	l2(ω))∩l2(0	l2(ω))∩l2(0	X
ap-6142	186	11	,	,	PUNCT
ap-6142	186	12	t	t	PROPN
ap-6142	186	13	;	;	PUNCT
ap-6142	186	14	w	w	PROPN
ap-6142	186	15	1,2(ω	1,2(ω	NUM
ap-6142	186	16	)	)	PUNCT
ap-6142	186	17	)	)	PUNCT
ap-6142	186	18	such	such	ADJ
ap-6142	186	19	that	that	SCONJ
ap-6142	186	20	v(t	v(t	NOUN
ap-6142	186	21	)	)	PUNCT
ap-6142	186	22	∈	∈	PROPN
ap-6142	186	23	kc	kc	PROPN
ap-6142	186	24	t	t	PROPN
ap-6142	186	25	for	for	ADP
ap-6142	186	26	a.a	a.a	PROPN
ap-6142	186	27	.	.	PROPN
ap-6142	186	28	t	t	PROPN
ap-6142	186	29	∈	∈	PROPN
ap-6142	186	30	(	(	PUNCT
ap-6142	186	31	0	0	NUM
ap-6142	186	32	,	,	PUNCT
ap-6142	186	33	t	t	NOUN
ap-6142	186	34	)	)	PUNCT
ap-6142	186	35	and	and	CCONJ
ap-6142	186	36	v	v	X
ap-6142	186	37	satisfies	satisfie	NOUN
ap-6142	186	38	inequality	inequality	NOUN
ap-6142	186	39	(	(	PUNCT
ap-6142	186	40	16	16	NUM
ap-6142	186	41	)	)	PUNCT
ap-6142	186	42	for	for	ADP
ap-6142	186	43	all	all	DET
ap-6142	186	44	w	w	PROPN
ap-6142	186	45	∈	∈	PROPN
ap-6142	186	46	k	k	PROPN
ap-6142	186	47	c(0	c(0	PROPN
ap-6142	186	48	,	,	PUNCT
ap-6142	186	49	t	t	NOUN
ap-6142	186	50	)	)	PUNCT
ap-6142	186	51	.	.	PUNCT
ap-6142	187	1	it	it	PRON
ap-6142	187	2	is	be	AUX
ap-6142	187	3	well	well	ADV
ap-6142	187	4	known	know	VERB
ap-6142	187	5	that	that	SCONJ
ap-6142	187	6	for	for	ADP
ap-6142	187	7	v0	v0	PROPN
ap-6142	187	8	∈	∈	PROPN
ap-6142	187	9	l2(ω	l2(ω	PROPN
ap-6142	187	10	)	)	PUNCT
ap-6142	187	11	,	,	PUNCT
ap-6142	187	12	such	such	ADJ
ap-6142	187	13	that	that	SCONJ
ap-6142	187	14	div	div	PROPN
ap-6142	187	15	v0	v0	NOUN
ap-6142	187	16	∈	∈	PROPN
ap-6142	187	17	l2(ω	l2(ω	PROPN
ap-6142	187	18	)	)	PUNCT
ap-6142	187	19	(	(	PUNCT
ap-6142	187	20	which	which	PRON
ap-6142	187	21	it	it	PRON
ap-6142	187	22	definitely	definitely	ADV
ap-6142	187	23	satisfies	satisfy	VERB
ap-6142	187	24	if	if	SCONJ
ap-6142	187	25	v0	v0	NOUN
ap-6142	187	26	is	be	AUX
ap-6142	187	27	92	92	NUM
ap-6142	187	28	vol	vol	NOUN
ap-6142	187	29	.	.	PUNCT
ap-6142	188	1	61	61	NUM
ap-6142	188	2	special	special	ADJ
ap-6142	188	3	issue/2021	issue/2021	NOUN
ap-6142	188	4	modeling	modeling	NOUN
ap-6142	188	5	of	of	ADP
ap-6142	188	6	flows	flow	NOUN
ap-6142	188	7	through	through	ADP
ap-6142	188	8	a	a	DET
ap-6142	188	9	channel	channel	NOUN
ap-6142	188	10	divergence	divergence	NOUN
ap-6142	188	11	–	–	PUNCT
ap-6142	188	12	free	free	ADJ
ap-6142	188	13	in	in	ADP
ap-6142	188	14	the	the	DET
ap-6142	188	15	sense	sense	NOUN
ap-6142	188	16	of	of	ADP
ap-6142	188	17	distributions	distribution	NOUN
ap-6142	188	18	)	)	PUNCT
ap-6142	188	19	,	,	PUNCT
ap-6142	188	20	the	the	DET
ap-6142	188	21	scalar	scalar	ADJ
ap-6142	188	22	product	product	NOUN
ap-6142	188	23	v	v	NOUN
ap-6142	188	24	·	·	PUNCT
ap-6142	188	25	n	n	PRON
ap-6142	188	26	makes	make	VERB
ap-6142	188	27	sense	sense	NOUN
ap-6142	188	28	on	on	ADP
ap-6142	188	29	∂ω	∂ω	PROPN
ap-6142	188	30	,	,	PUNCT
ap-6142	188	31	as	as	ADP
ap-6142	188	32	an	an	DET
ap-6142	188	33	element	element	NOUN
ap-6142	188	34	of	of	ADP
ap-6142	188	35	w−1/2,2(∂ω	w−1/2,2(∂ω	PROPN
ap-6142	188	36	)	)	PUNCT
ap-6142	188	37	.	.	PUNCT
ap-6142	189	1	(	(	PUNCT
ap-6142	189	2	this	this	PRON
ap-6142	189	3	follows	follow	VERB
ap-6142	189	4	e.g.	e.g.	ADV
ap-6142	189	5	from	from	ADP
ap-6142	189	6	[	[	X
ap-6142	189	7	21	21	NUM
ap-6142	189	8	,	,	PUNCT
ap-6142	189	9	theorem	theorem	VERB
ap-6142	189	10	iii.2.2	iii.2.2	PROPN
ap-6142	189	11	]	]	PUNCT
ap-6142	189	12	.	.	PUNCT
ap-6142	189	13	)	)	PUNCT
ap-6142	190	1	thus	thus	ADV
ap-6142	190	2	,	,	PUNCT
ap-6142	190	3	the	the	DET
ap-6142	190	4	conditions	condition	NOUN
ap-6142	190	5	v0	v0	X
ap-6142	190	6	·	·	PUNCT
ap-6142	190	7	n	n	NOUN
ap-6142	190	8	=	=	SYM
ap-6142	190	9	0	0	NUM
ap-6142	190	10	on	on	ADP
ap-6142	190	11	γ0	γ0	NOUN
ap-6142	190	12	and	and	CCONJ
ap-6142	190	13	v0	v0	NOUN
ap-6142	190	14	·	·	PUNCT
ap-6142	190	15	n	n	CCONJ
ap-6142	190	16	=	=	PUNCT
ap-6142	190	17	v∗(0	v∗(0	NOUN
ap-6142	190	18	)	)	PUNCT
ap-6142	190	19	·	·	PUNCT
ap-6142	191	1	n	n	PRON
ap-6142	191	2	are	be	AUX
ap-6142	191	3	assumed	assume	VERB
ap-6142	191	4	to	to	PART
ap-6142	191	5	hold	hold	VERB
ap-6142	191	6	on	on	ADP
ap-6142	191	7	γ0	γ0	NOUN
ap-6142	191	8	and	and	CCONJ
ap-6142	191	9	γ1	γ1	NOUN
ap-6142	191	10	as	as	ADP
ap-6142	191	11	equalities	equality	NOUN
ap-6142	191	12	in	in	ADP
ap-6142	191	13	w−1/2,2(γ0	w−1/2,2(γ0	NOUN
ap-6142	191	14	)	)	PUNCT
ap-6142	191	15	and	and	CCONJ
ap-6142	191	16	w−1/2,2(γ1	w−1/2,2(γ1	NOUN
ap-6142	191	17	)	)	PUNCT
ap-6142	191	18	,	,	PUNCT
ap-6142	191	19	respectively	respectively	ADV
ap-6142	191	20	.	.	PUNCT
ap-6142	192	1	the	the	DET
ap-6142	192	2	next	next	ADJ
ap-6142	192	3	theorem	theorem	NOUN
ap-6142	192	4	provides	provide	VERB
ap-6142	192	5	the	the	DET
ap-6142	192	6	information	information	NOUN
ap-6142	192	7	on	on	ADP
ap-6142	192	8	the	the	DET
ap-6142	192	9	existence	existence	NOUN
ap-6142	192	10	of	of	ADP
ap-6142	192	11	a	a	DET
ap-6142	192	12	solution	solution	NOUN
ap-6142	192	13	of	of	ADP
ap-6142	192	14	a	a	DET
ap-6142	192	15	problem	problem	NOUN
ap-6142	192	16	(	(	PUNCT
ap-6142	192	17	p	p	NOUN
ap-6142	192	18	)	)	PUNCT
ap-6142	192	19	on	on	ADP
ap-6142	192	20	an	an	DET
ap-6142	192	21	arbitrarily	arbitrarily	ADV
ap-6142	192	22	long	long	ADJ
ap-6142	192	23	time	time	NOUN
ap-6142	192	24	interval	interval	NOUN
ap-6142	192	25	(	(	PUNCT
ap-6142	192	26	0	0	NUM
ap-6142	192	27	,	,	PUNCT
ap-6142	192	28	t	t	NOUN
ap-6142	192	29	)	)	PUNCT
ap-6142	192	30	.	.	PUNCT
ap-6142	193	1	theorem	theorem	NOUN
ap-6142	193	2	1	1	NUM
ap-6142	193	3	.	.	PUNCT
ap-6142	194	1	let	let	VERB
ap-6142	194	2	v0	v0	NOUN
ap-6142	194	3	,	,	PUNCT
ap-6142	194	4	v∗ext	v∗ext	PROPN
ap-6142	194	5	,	,	PUNCT
ap-6142	194	6	f	f	PROPN
ap-6142	194	7	and	and	CCONJ
ap-6142	194	8	g	g	PROPN
ap-6142	194	9	be	be	VERB
ap-6142	194	10	the	the	DET
ap-6142	194	11	functions	function	NOUN
ap-6142	194	12	with	with	ADP
ap-6142	194	13	the	the	DET
ap-6142	194	14	aforementioned	aforementioned	ADJ
ap-6142	194	15	properties	property	NOUN
ap-6142	194	16	.	.	PUNCT
ap-6142	195	1	then	then	ADV
ap-6142	195	2	problem	problem	NOUN
ap-6142	195	3	(	(	PUNCT
ap-6142	195	4	p	p	X
ap-6142	195	5	)	)	PUNCT
ap-6142	195	6	is	be	AUX
ap-6142	195	7	solvable	solvable	ADJ
ap-6142	195	8	.	.	PUNCT
ap-6142	196	1	the	the	DET
ap-6142	196	2	solution	solution	NOUN
ap-6142	196	3	can	can	AUX
ap-6142	196	4	be	be	AUX
ap-6142	196	5	expressed	express	VERB
ap-6142	196	6	in	in	ADP
ap-6142	196	7	the	the	DET
ap-6142	196	8	form	form	NOUN
ap-6142	196	9	v	v	ADP
ap-6142	196	10	=	=	SYM
ap-6142	196	11	v∗ext	v∗ext	PROPN
ap-6142	196	12	+	+	CCONJ
ap-6142	196	13	u	u	NOUN
ap-6142	196	14	,	,	PUNCT
ap-6142	196	15	where	where	SCONJ
ap-6142	196	16	u	u	PROPN
ap-6142	196	17	∈	∈	PROPN
ap-6142	196	18	l∞(0	l∞(0	PRON
ap-6142	196	19	,	,	PUNCT
ap-6142	196	20	t	t	NOUN
ap-6142	196	21	;	;	PUNCT
ap-6142	196	22	l2(ω	l2(ω	NOUN
ap-6142	196	23	)	)	PUNCT
ap-6142	196	24	)	)	PUNCT
ap-6142	196	25	∩	∩	ADJ
ap-6142	196	26	l2(0	l2(0	NOUN
ap-6142	196	27	,	,	PUNCT
ap-6142	196	28	t	t	PROPN
ap-6142	196	29	;	;	PUNCT
ap-6142	196	30	v	v	X
ap-6142	196	31	)	)	PUNCT
ap-6142	196	32	satisfies	satisfy	VERB
ap-6142	196	33	the	the	DET
ap-6142	196	34	inequality	inequality	NOUN
ap-6142	196	35	‖u(t)‖22	‖u(t)‖22	PROPN
ap-6142	196	36	+	+	CCONJ
ap-6142	196	37	ν	ν	PROPN
ap-6142	196	38	∫	∫	PROPN
ap-6142	196	39	t	t	PROPN
ap-6142	196	40	0	0	NUM
ap-6142	196	41	‖∇u(s)‖22	‖∇u(s)‖22	NOUN
ap-6142	196	42	ds	ds	PROPN
ap-6142	196	43	≤	≤	NUM
ap-6142	196	44	‖u(0)‖22	‖u(0)‖22	NOUN
ap-6142	197	1	−	−	NOUN
ap-6142	197	2	∫	∫	NOUN
ap-6142	197	3	t∗	t∗	PROPN
ap-6142	197	4	0	0	NUM
ap-6142	197	5	∫	∫	PROPN
ap-6142	197	6	γ1	γ1	PROPN
ap-6142	197	7	(	(	PUNCT
ap-6142	197	8	v∗	v∗	PROPN
ap-6142	197	9	·	·	PUNCT
ap-6142	197	10	n	n	CCONJ
ap-6142	197	11	)	)	PUNCT
ap-6142	197	12	|v∗|2	|v∗|2	NUM
ap-6142	197	13	ds	ds	ADJ
ap-6142	197	14	dt	dt	NOUN
ap-6142	197	15	+	+	CCONJ
ap-6142	197	16	c1	c1	PROPN
ap-6142	197	17	∫	∫	PROPN
ap-6142	197	18	t	t	PROPN
ap-6142	197	19	0	0	NUM
ap-6142	197	20	‖u(s)‖22	‖u(s)‖22	NOUN
ap-6142	197	21	ds+	ds+	PROPN
ap-6142	197	22	∫	∫	PROPN
ap-6142	197	23	t	t	PROPN
ap-6142	197	24	0	0	NUM
ap-6142	198	1	[	[	PUNCT
ap-6142	198	2	c2	c2	PROPN
ap-6142	198	3	‖f(s)‖2−1,2	‖f(s)‖2−1,2	PROPN
ap-6142	198	4	+	+	CCONJ
ap-6142	198	5	c3	c3	PROPN
ap-6142	198	6	‖v∗ext(s)‖21,2	‖v∗ext(s)‖21,2	PROPN
ap-6142	198	7	+	+	CCONJ
ap-6142	198	8	c4	c4	NOUN
ap-6142	198	9	‖∂tv∗ext(s)‖2−1,2	‖∂tv∗ext(s)‖2−1,2	PROPN
ap-6142	198	10	+	+	CCONJ
ap-6142	198	11	c5	c5	PROPN
ap-6142	198	12	‖g(s)‖24/3	‖g(s)‖24/3	PROPN
ap-6142	198	13	;	;	PUNCT
ap-6142	198	14	γ2	γ2	ADJ
ap-6142	198	15	]	]	PUNCT
ap-6142	198	16	ds	ds	INTJ
ap-6142	198	17	(	(	PUNCT
ap-6142	198	18	17	17	NUM
ap-6142	198	19	)	)	PUNCT
ap-6142	198	20	for	for	ADP
ap-6142	198	21	all	all	DET
ap-6142	198	22	t	t	PROPN
ap-6142	198	23	in(0	in(0	PROPN
ap-6142	198	24	,	,	PUNCT
ap-6142	198	25	t	t	PROPN
ap-6142	198	26	)	)	PUNCT
ap-6142	198	27	,	,	PUNCT
ap-6142	198	28	where	where	SCONJ
ap-6142	198	29	all	all	DET
ap-6142	198	30	the	the	DET
ap-6142	198	31	constants	constant	NOUN
ap-6142	198	32	c1	c1	PROPN
ap-6142	198	33	–	–	PUNCT
ap-6142	198	34	c5	c5	PROPN
ap-6142	198	35	are	be	AUX
ap-6142	198	36	independent	independent	ADJ
ap-6142	198	37	of	of	ADP
ap-6142	198	38	v0	v0	NOUN
ap-6142	198	39	,	,	PUNCT
ap-6142	198	40	v∗	v∗	PROPN
ap-6142	198	41	,	,	PUNCT
ap-6142	198	42	v∗ext	v∗ext	PROPN
ap-6142	198	43	,	,	PUNCT
ap-6142	198	44	f	f	PROPN
ap-6142	198	45	,	,	PUNCT
ap-6142	198	46	g	g	PROPN
ap-6142	198	47	and	and	CCONJ
ap-6142	198	48	u.	u.	PROPN
ap-6142	198	49	note	note	VERB
ap-6142	198	50	that	that	SCONJ
ap-6142	198	51	there	there	PRON
ap-6142	198	52	is	be	VERB
ap-6142	198	53	a	a	DET
ap-6142	198	54	minus	minus	NOUN
ap-6142	198	55	sign	sign	NOUN
ap-6142	198	56	in	in	ADP
ap-6142	198	57	front	front	NOUN
ap-6142	198	58	of	of	ADP
ap-6142	198	59	the	the	DET
ap-6142	198	60	first	first	ADJ
ap-6142	198	61	integral	integral	NOUN
ap-6142	198	62	on	on	ADP
ap-6142	198	63	the	the	DET
ap-6142	198	64	right	right	ADJ
ap-6142	198	65	hand	hand	NOUN
ap-6142	198	66	side	side	NOUN
ap-6142	198	67	,	,	PUNCT
ap-6142	198	68	because	because	SCONJ
ap-6142	198	69	n	n	NUM
ap-6142	198	70	is	be	AUX
ap-6142	198	71	the	the	DET
ap-6142	198	72	outer	outer	ADJ
ap-6142	198	73	normal	normal	ADJ
ap-6142	198	74	vector	vector	NOUN
ap-6142	198	75	and	and	CCONJ
ap-6142	198	76	therefore	therefore	ADV
ap-6142	198	77	−	−	PROPN
ap-6142	198	78	1	1	NUM
ap-6142	198	79	2	2	NUM
ap-6142	198	80	∫	∫	NOUN
ap-6142	198	81	t∗	t∗	NOUN
ap-6142	198	82	0	0	NUM
ap-6142	198	83	∫	∫	PROPN
ap-6142	198	84	γ1	γ1	PROPN
ap-6142	198	85	(	(	PUNCT
ap-6142	198	86	v∗	v∗	PROPN
ap-6142	198	87	·	·	SYM
ap-6142	198	88	n	n	CCONJ
ap-6142	198	89	)	)	PUNCT
ap-6142	198	90	|v∗|2	|v∗|2	NUM
ap-6142	198	91	ds	ds	ADJ
ap-6142	198	92	dt	dt	NOUN
ap-6142	198	93	represents	represent	VERB
ap-6142	198	94	the	the	DET
ap-6142	198	95	inflow	inflow	NOUN
ap-6142	198	96	of	of	ADP
ap-6142	198	97	the	the	DET
ap-6142	198	98	kinetic	kinetic	ADJ
ap-6142	198	99	energy	energy	NOUN
ap-6142	198	100	to	to	ADP
ap-6142	198	101	ω	ω	PROPN
ap-6142	198	102	through	through	ADP
ap-6142	198	103	γ1	γ1	PROPN
ap-6142	198	104	in	in	ADP
ap-6142	198	105	the	the	DET
ap-6142	198	106	time	time	NOUN
ap-6142	198	107	interval	interval	NOUN
ap-6142	198	108	(	(	PUNCT
ap-6142	198	109	0	0	NUM
ap-6142	198	110	,	,	PUNCT
ap-6142	198	111	t∗	t∗	PROPN
ap-6142	198	112	)	)	PUNCT
ap-6142	198	113	.	.	PUNCT
ap-6142	199	1	an	an	DET
ap-6142	199	2	analogous	analogous	ADJ
ap-6142	199	3	theorem	theorem	NOUN
ap-6142	199	4	,	,	PUNCT
ap-6142	199	5	with	with	ADP
ap-6142	199	6	a	a	DET
ap-6142	199	7	different	different	ADJ
ap-6142	199	8	convex	convex	NOUN
ap-6142	199	9	set	set	VERB
ap-6142	199	10	kc	kc	PROPN
ap-6142	199	11	t	t	PROPN
ap-6142	199	12	,	,	PUNCT
ap-6142	199	13	has	have	AUX
ap-6142	199	14	been	be	AUX
ap-6142	199	15	proven	prove	VERB
ap-6142	199	16	in	in	ADP
ap-6142	199	17	[	[	X
ap-6142	199	18	15	15	NUM
ap-6142	199	19	]	]	SYM
ap-6142	199	20	.	.	PUNCT
ap-6142	200	1	3.4	3.4	NUM
ap-6142	200	2	.	.	PUNCT
ap-6142	201	1	the	the	DET
ap-6142	201	2	principle	principle	NOUN
ap-6142	201	3	of	of	ADP
ap-6142	201	4	the	the	DET
ap-6142	201	5	proof	proof	NOUN
ap-6142	201	6	and	and	CCONJ
ap-6142	201	7	a	a	DET
ap-6142	201	8	priori	priori	ADJ
ap-6142	201	9	estimates	estimate	VERB
ap-6142	201	10	the	the	DET
ap-6142	201	11	complete	complete	ADJ
ap-6142	201	12	way	way	NOUN
ap-6142	201	13	theorem	theorem	VERB
ap-6142	201	14	1	1	NUM
ap-6142	201	15	can	can	AUX
ap-6142	201	16	be	be	AUX
ap-6142	201	17	proven	prove	VERB
ap-6142	201	18	consists	consist	NOUN
ap-6142	201	19	of	of	ADP
ap-6142	201	20	these	these	DET
ap-6142	201	21	main	main	ADJ
ap-6142	201	22	steps	step	NOUN
ap-6142	201	23	:	:	PUNCT
ap-6142	201	24	1	1	NUM
ap-6142	201	25	)	)	PUNCT
ap-6142	201	26	construction	construction	NOUN
ap-6142	201	27	of	of	ADP
ap-6142	201	28	appropriate	appropriate	ADJ
ap-6142	201	29	approximations	approximation	NOUN
ap-6142	201	30	vn	vn	X
ap-6142	201	31	(	(	PUNCT
ap-6142	201	32	for	for	ADP
ap-6142	201	33	n	n	PRON
ap-6142	201	34	∈	∈	PROPN
ap-6142	201	35	n	n	CCONJ
ap-6142	201	36	)	)	PUNCT
ap-6142	201	37	of	of	ADP
ap-6142	201	38	solution	solution	NOUN
ap-6142	201	39	v	v	NOUN
ap-6142	201	40	,	,	PUNCT
ap-6142	201	41	2	2	NUM
ap-6142	201	42	)	)	PUNCT
ap-6142	201	43	derivation	derivation	NOUN
ap-6142	201	44	of	of	ADP
ap-6142	201	45	a	a	DET
ap-6142	201	46	series	series	NOUN
ap-6142	201	47	of	of	ADP
ap-6142	201	48	estimates	estimate	NOUN
ap-6142	201	49	of	of	ADP
ap-6142	201	50	the	the	DET
ap-6142	201	51	approximations	approximation	NOUN
ap-6142	201	52	,	,	PUNCT
ap-6142	201	53	3	3	X
ap-6142	201	54	)	)	PUNCT
ap-6142	201	55	derivation	derivation	NOUN
ap-6142	201	56	of	of	ADP
ap-6142	201	57	various	various	ADJ
ap-6142	201	58	types	type	NOUN
ap-6142	201	59	of	of	ADP
ap-6142	201	60	convergence	convergence	NOUN
ap-6142	201	61	of	of	ADP
ap-6142	201	62	a	a	DET
ap-6142	201	63	subsequence	subsequence	NOUN
ap-6142	201	64	of	of	ADP
ap-6142	201	65	{	{	PUNCT
ap-6142	201	66	vn	vn	NOUN
ap-6142	201	67	}	}	PUNCT
ap-6142	201	68	in	in	ADP
ap-6142	201	69	various	various	ADJ
ap-6142	201	70	spaces	space	NOUN
ap-6142	201	71	,	,	PUNCT
ap-6142	201	72	4	4	X
ap-6142	201	73	)	)	PUNCT
ap-6142	201	74	verification	verification	NOUN
ap-6142	201	75	that	that	PRON
ap-6142	201	76	the	the	DET
ap-6142	201	77	limit	limit	NOUN
ap-6142	201	78	is	be	AUX
ap-6142	201	79	the	the	DET
ap-6142	201	80	solution	solution	NOUN
ap-6142	201	81	v.	v.	ADP
ap-6142	201	82	among	among	ADP
ap-6142	201	83	others	other	NOUN
ap-6142	201	84	,	,	PUNCT
ap-6142	201	85	one	one	PRON
ap-6142	201	86	also	also	ADV
ap-6142	201	87	needs	need	VERB
ap-6142	201	88	the	the	DET
ap-6142	201	89	strong	strong	ADJ
ap-6142	201	90	convergence	convergence	NOUN
ap-6142	201	91	in	in	ADP
ap-6142	201	92	l2(0	l2(0	NOUN
ap-6142	201	93	,	,	PUNCT
ap-6142	201	94	t	t	PROPN
ap-6142	201	95	;	;	PUNCT
ap-6142	201	96	w	w	PROPN
ap-6142	201	97	1,2(ω	1,2(ω	NUM
ap-6142	201	98	)	)	PUNCT
ap-6142	201	99	)	)	PUNCT
ap-6142	201	100	,	,	PUNCT
ap-6142	201	101	which	which	PRON
ap-6142	201	102	follows	follow	VERB
ap-6142	201	103	from	from	ADP
ap-6142	201	104	an	an	DET
ap-6142	201	105	estimate	estimate	NOUN
ap-6142	201	106	of	of	ADP
ap-6142	201	107	a	a	DET
ap-6142	201	108	fractional	fractional	ADJ
ap-6142	201	109	derivative	derivative	NOUN
ap-6142	201	110	with	with	ADP
ap-6142	201	111	respect	respect	NOUN
ap-6142	201	112	to	to	ADP
ap-6142	201	113	t	t	PROPN
ap-6142	201	114	of	of	ADP
ap-6142	201	115	vn	vn	PROPN
ap-6142	201	116	and	and	CCONJ
ap-6142	201	117	from	from	ADP
ap-6142	201	118	the	the	DET
ap-6142	201	119	lions	lion	NOUN
ap-6142	201	120	–	–	PUNCT
ap-6142	201	121	aubin	aubin	PROPN
ap-6142	201	122	lemma	lemma	PROPN
ap-6142	201	123	,	,	PUNCT
ap-6142	201	124	see	see	VERB
ap-6142	202	1	e.g.	e.g.	ADV
ap-6142	202	2	[	[	X
ap-6142	202	3	22	22	NUM
ap-6142	202	4	]	]	PUNCT
ap-6142	202	5	.	.	PUNCT
ap-6142	203	1	since	since	SCONJ
ap-6142	203	2	the	the	DET
ap-6142	203	3	complete	complete	ADJ
ap-6142	203	4	estimates	estimate	NOUN
ap-6142	203	5	of	of	ADP
ap-6142	203	6	the	the	DET
ap-6142	203	7	approximations	approximation	NOUN
ap-6142	203	8	are	be	AUX
ap-6142	203	9	laborious	laborious	ADJ
ap-6142	203	10	,	,	PUNCT
ap-6142	203	11	technically	technically	ADV
ap-6142	203	12	complicated	complicated	ADJ
ap-6142	203	13	and	and	CCONJ
ap-6142	203	14	necessarily	necessarily	ADV
ap-6142	203	15	influenced	influence	VERB
ap-6142	203	16	by	by	ADP
ap-6142	203	17	the	the	DET
ap-6142	203	18	technique	technique	NOUN
ap-6142	203	19	,	,	PUNCT
ap-6142	203	20	used	use	VERB
ap-6142	203	21	just	just	ADV
ap-6142	203	22	for	for	ADP
ap-6142	203	23	the	the	DET
ap-6142	203	24	construction	construction	NOUN
ap-6142	203	25	of	of	ADP
ap-6142	203	26	the	the	DET
ap-6142	203	27	approximations	approximation	NOUN
ap-6142	203	28	,	,	PUNCT
ap-6142	203	29	we	we	PRON
ap-6142	203	30	show	show	VERB
ap-6142	203	31	below	below	ADV
ap-6142	203	32	on	on	ADP
ap-6142	203	33	an	an	DET
ap-6142	203	34	a	a	DET
ap-6142	203	35	priori	priori	ADJ
ap-6142	203	36	level	level	NOUN
ap-6142	203	37	how	how	SCONJ
ap-6142	203	38	one	one	NOUN
ap-6142	203	39	can	can	AUX
ap-6142	203	40	directly	directly	ADV
ap-6142	203	41	obtain	obtain	VERB
ap-6142	203	42	from	from	ADP
ap-6142	203	43	the	the	DET
ap-6142	203	44	variational	variational	ADJ
ap-6142	203	45	inequality	inequality	NOUN
ap-6142	203	46	the	the	DET
ap-6142	203	47	estimates	estimate	NOUN
ap-6142	203	48	of	of	ADP
ap-6142	203	49	u	u	PROPN
ap-6142	203	50	in	in	ADP
ap-6142	203	51	l∞(0	l∞(0	PRON
ap-6142	203	52	,	,	PUNCT
ap-6142	203	53	t	t	PROPN
ap-6142	203	54	;	;	PUNCT
ap-6142	203	55	l2(ω	l2(ω	NOUN
ap-6142	203	56	)	)	PUNCT
ap-6142	203	57	)	)	PUNCT
ap-6142	203	58	and	and	CCONJ
ap-6142	203	59	in	in	ADP
ap-6142	203	60	l2(0	l2(0	NOUN
ap-6142	203	61	,	,	PUNCT
ap-6142	203	62	t	t	PROPN
ap-6142	203	63	;	;	PUNCT
ap-6142	203	64	w	w	PROPN
ap-6142	203	65	1,2(ω	1,2(ω	NUM
ap-6142	203	66	)	)	PUNCT
ap-6142	203	67	)	)	PUNCT
ap-6142	203	68	.	.	PUNCT
ap-6142	204	1	the	the	DET
ap-6142	204	2	advantage	advantage	NOUN
ap-6142	204	3	of	of	ADP
ap-6142	204	4	a	a	DET
ap-6142	204	5	priori	priori	ADJ
ap-6142	204	6	estimates	estimate	NOUN
ap-6142	204	7	is	be	AUX
ap-6142	204	8	that	that	SCONJ
ap-6142	204	9	they	they	PRON
ap-6142	204	10	enable	enable	VERB
ap-6142	204	11	one	one	NUM
ap-6142	204	12	to	to	PART
ap-6142	204	13	abstract	abstract	VERB
ap-6142	204	14	from	from	ADP
ap-6142	204	15	the	the	DET
ap-6142	204	16	whole	whole	ADJ
ap-6142	204	17	machinery	machinery	NOUN
ap-6142	204	18	,	,	PUNCT
ap-6142	204	19	which	which	PRON
ap-6142	204	20	is	be	AUX
ap-6142	204	21	necessary	necessary	ADJ
ap-6142	204	22	in	in	ADP
ap-6142	204	23	the	the	DET
ap-6142	204	24	proof	proof	NOUN
ap-6142	204	25	of	of	ADP
ap-6142	204	26	existence	existence	NOUN
ap-6142	204	27	of	of	ADP
ap-6142	204	28	the	the	DET
ap-6142	204	29	approximations	approximation	NOUN
ap-6142	204	30	.	.	PUNCT
ap-6142	205	1	on	on	ADP
ap-6142	205	2	the	the	DET
ap-6142	205	3	other	other	ADJ
ap-6142	205	4	hand	hand	NOUN
ap-6142	205	5	,	,	PUNCT
ap-6142	205	6	we	we	PRON
ap-6142	205	7	assume	assume	VERB
ap-6142	205	8	,	,	PUNCT
ap-6142	205	9	just	just	ADV
ap-6142	205	10	inside	inside	ADP
ap-6142	205	11	the	the	DET
ap-6142	205	12	procedure	procedure	NOUN
ap-6142	205	13	,	,	PUNCT
ap-6142	205	14	that	that	SCONJ
ap-6142	205	15	u	u	NOUN
ap-6142	205	16	is	be	AUX
ap-6142	205	17	smooth	smooth	ADJ
ap-6142	205	18	.	.	PUNCT
ap-6142	206	1	(	(	PUNCT
ap-6142	206	2	this	this	DET
ap-6142	206	3	formal	formal	ADJ
ap-6142	206	4	assumption	assumption	NOUN
ap-6142	206	5	is	be	AUX
ap-6142	206	6	naturally	naturally	ADV
ap-6142	206	7	satisfied	satisfied	ADJ
ap-6142	206	8	on	on	ADP
ap-6142	206	9	the	the	DET
ap-6142	206	10	level	level	NOUN
ap-6142	206	11	of	of	ADP
ap-6142	206	12	approximations	approximation	NOUN
ap-6142	206	13	.	.	PUNCT
ap-6142	206	14	)	)	PUNCT
ap-6142	207	1	thus	thus	ADV
ap-6142	207	2	,	,	PUNCT
ap-6142	207	3	let	let	VERB
ap-6142	207	4	t∗	t∗	NOUN
ap-6142	207	5	∈	∈	PROPN
ap-6142	207	6	(	(	PUNCT
ap-6142	207	7	0	0	NUM
ap-6142	207	8	,	,	PUNCT
ap-6142	207	9	t	t	PROPN
ap-6142	207	10	)	)	PUNCT
ap-6142	207	11	,	,	PUNCT
ap-6142	207	12	α	α	PROPN
ap-6142	207	13	∈	∈	PROPN
ap-6142	207	14	(	(	PUNCT
ap-6142	207	15	0	0	NUM
ap-6142	207	16	,	,	PUNCT
ap-6142	207	17	1	1	NUM
ap-6142	207	18	)	)	PUNCT
ap-6142	207	19	and	and	CCONJ
ap-6142	207	20	δ	δ	PROPN
ap-6142	207	21	>	>	X
ap-6142	207	22	0	0	PUNCT
ap-6142	207	23	be	be	VERB
ap-6142	207	24	so	so	ADV
ap-6142	207	25	small	small	ADJ
ap-6142	207	26	that	that	PRON
ap-6142	207	27	t∗+δ	t∗+δ	VERB
ap-6142	207	28	<	<	X
ap-6142	207	29	t	t	PROPN
ap-6142	207	30	.	.	PUNCT
ap-6142	208	1	define	define	VERB
ap-6142	208	2	function	function	PROPN
ap-6142	208	3	η	η	PROPN
ap-6142	208	4	of	of	ADP
ap-6142	208	5	one	one	NUM
ap-6142	208	6	variable	variable	ADJ
ap-6142	208	7	t	t	NOUN
ap-6142	208	8	by	by	ADP
ap-6142	208	9	the	the	DET
ap-6142	208	10	formulas	formula	NOUN
ap-6142	208	11	η(t	η(t	NOUN
ap-6142	208	12	)	)	PUNCT
ap-6142	209	1	=	=	PUNCT
ap-6142	210	1			PRON
ap-6142	210	2	α	α	VERB
ap-6142	210	3	for	for	ADP
ap-6142	210	4	0	0	NUM
ap-6142	210	5	<	<	X
ap-6142	210	6	t	t	PROPN
ap-6142	210	7	≤	≤	NUM
ap-6142	210	8	t∗	t∗	NOUN
ap-6142	210	9	,	,	PUNCT
ap-6142	210	10	α+	α+	PUNCT
ap-6142	210	11	(	(	PUNCT
ap-6142	210	12	1−	1−	NUM
ap-6142	210	13	α	α	NOUN
ap-6142	210	14	)	)	PUNCT
ap-6142	210	15	δ	δ	PROPN
ap-6142	210	16	(	(	PUNCT
ap-6142	210	17	t−	t−	PROPN
ap-6142	210	18	t∗	t∗	PROPN
ap-6142	210	19	)	)	PUNCT
ap-6142	210	20	for	for	ADP
ap-6142	210	21	t∗	t∗	NOUN
ap-6142	210	22	<	<	X
ap-6142	210	23	t	t	X
ap-6142	210	24	<	<	X
ap-6142	210	25	t∗	t∗	PROPN
ap-6142	210	26	+	+	CCONJ
ap-6142	210	27	δ	δ	PROPN
ap-6142	210	28	,	,	PUNCT
ap-6142	210	29	1	1	NUM
ap-6142	210	30	for	for	ADP
ap-6142	210	31	t∗	t∗	NOUN
ap-6142	210	32	+	+	CCONJ
ap-6142	210	33	δ	δ	PROPN
ap-6142	210	34	≤	≤	PROPN
ap-6142	210	35	t	t	PROPN
ap-6142	210	36	<	<	X
ap-6142	210	37	t.	t.	PROPN
ap-6142	210	38	(	(	PUNCT
ap-6142	210	39	function	function	PROPN
ap-6142	210	40	η	η	PROPN
ap-6142	210	41	is	be	AUX
ap-6142	210	42	continuous	continuous	ADJ
ap-6142	210	43	on	on	ADP
ap-6142	210	44	(	(	PUNCT
ap-6142	210	45	0	0	NUM
ap-6142	210	46	,	,	PUNCT
ap-6142	210	47	t	t	NOUN
ap-6142	210	48	)	)	PUNCT
ap-6142	210	49	,	,	PUNCT
ap-6142	210	50	constant	constant	ADJ
ap-6142	210	51	on	on	ADP
ap-6142	210	52	(	(	PUNCT
ap-6142	210	53	0	0	NUM
ap-6142	210	54	,	,	PUNCT
ap-6142	210	55	t∗	t∗	PROPN
ap-6142	210	56	]	]	PUNCT
ap-6142	210	57	and	and	CCONJ
ap-6142	210	58	on	on	ADP
ap-6142	210	59	[	[	X
ap-6142	210	60	t∗	t∗	NOUN
ap-6142	210	61	+	+	CCONJ
ap-6142	210	62	δ	δ	PROPN
ap-6142	210	63	,	,	PUNCT
ap-6142	210	64	t	t	PROPN
ap-6142	210	65	)	)	PUNCT
ap-6142	210	66	and	and	CCONJ
ap-6142	210	67	linear	linear	VERB
ap-6142	210	68	on	on	ADP
ap-6142	210	69	[	[	X
ap-6142	210	70	t∗	t∗	NOUN
ap-6142	210	71	,	,	PUNCT
ap-6142	210	72	t∗	t∗	NOUN
ap-6142	210	73	+	+	CCONJ
ap-6142	210	74	δ	δ	PROPN
ap-6142	210	75	]	]	X
ap-6142	210	76	.	.	PUNCT
ap-6142	210	77	)	)	PUNCT
ap-6142	211	1	solution	solution	NOUN
ap-6142	211	2	v	v	NOUN
ap-6142	211	3	can	can	AUX
ap-6142	211	4	be	be	AUX
ap-6142	211	5	expressed	express	VERB
ap-6142	211	6	in	in	ADP
ap-6142	211	7	the	the	DET
ap-6142	211	8	form	form	NOUN
ap-6142	211	9	v	v	ADP
ap-6142	211	10	=	=	SYM
ap-6142	211	11	v∗ext	v∗ext	PROPN
ap-6142	211	12	+	+	CCONJ
ap-6142	211	13	u	u	NOUN
ap-6142	211	14	,	,	PUNCT
ap-6142	211	15	where	where	SCONJ
ap-6142	211	16	u	u	PROPN
ap-6142	211	17	∈	∈	PROPN
ap-6142	211	18	v	v	NOUN
ap-6142	211	19	.	.	PUNCT
ap-6142	212	1	put	put	VERB
ap-6142	212	2	w	w	ADP
ap-6142	212	3	:	:	PUNCT
ap-6142	212	4	=	=	SYM
ap-6142	212	5	v∗ext	v∗ext	PROPN
ap-6142	212	6	+	+	CCONJ
ap-6142	212	7	ηu	ηu	X
ap-6142	212	8	=	=	SYM
ap-6142	212	9	(	(	PUNCT
ap-6142	212	10	1−	1−	NUM
ap-6142	212	11	η)v∗ext	η)v∗ext	NOUN
ap-6142	212	12	+	+	CCONJ
ap-6142	212	13	ηv	ηv	VERB
ap-6142	212	14	.	.	PUNCT
ap-6142	213	1	(	(	PUNCT
ap-6142	213	2	as	as	SCONJ
ap-6142	213	3	set	set	VERB
ap-6142	213	4	k	k	PROPN
ap-6142	213	5	c(0	c(0	PROPN
ap-6142	213	6	,	,	PUNCT
ap-6142	213	7	t	t	PROPN
ap-6142	213	8	)	)	PUNCT
ap-6142	213	9	is	be	AUX
ap-6142	213	10	convex	convex	ADJ
ap-6142	213	11	and	and	CCONJ
ap-6142	213	12	0	0	NUM
ap-6142	213	13	<	<	X
ap-6142	213	14	η	η	PROPN
ap-6142	213	15	≤	≤	PROPN
ap-6142	213	16	1	1	NUM
ap-6142	213	17	,	,	PUNCT
ap-6142	213	18	w	w	NOUN
ap-6142	213	19	belongs	belong	VERB
ap-6142	213	20	to	to	ADP
ap-6142	213	21	k	k	PROPN
ap-6142	213	22	c(0	c(0	PROPN
ap-6142	213	23	,	,	PUNCT
ap-6142	213	24	t	t	NOUN
ap-6142	213	25	)	)	PUNCT
ap-6142	213	26	.	.	PUNCT
ap-6142	213	27	)	)	PUNCT
ap-6142	214	1	then	then	ADV
ap-6142	214	2	w	w	ADP
ap-6142	214	3	−	−	PROPN
ap-6142	214	4	v	v	NOUN
ap-6142	214	5	=	=	SYM
ap-6142	214	6	(	(	PUNCT
ap-6142	214	7	η	η	PROPN
ap-6142	214	8	−	−	PROPN
ap-6142	214	9	1)u	1)u	NUM
ap-6142	214	10	(	(	PUNCT
ap-6142	214	11	which	which	PRON
ap-6142	214	12	equals	equal	VERB
ap-6142	214	13	0	0	NUM
ap-6142	214	14	on	on	ADP
ap-6142	214	15	the	the	DET
ap-6142	214	16	interval	interval	NOUN
ap-6142	214	17	[	[	X
ap-6142	214	18	t∗	t∗	NOUN
ap-6142	214	19	+	+	CCONJ
ap-6142	214	20	δ	δ	PROPN
ap-6142	214	21	,	,	PUNCT
ap-6142	214	22	t	t	NOUN
ap-6142	214	23	)	)	PUNCT
ap-6142	214	24	)	)	PUNCT
ap-6142	214	25	.	.	PUNCT
ap-6142	215	1	substituting	substitute	VERB
ap-6142	215	2	this	this	PRON
ap-6142	215	3	to	to	ADP
ap-6142	215	4	the	the	DET
ap-6142	215	5	first	first	ADJ
ap-6142	215	6	term	term	NOUN
ap-6142	215	7	in	in	ADP
ap-6142	215	8	(	(	PUNCT
ap-6142	215	9	16	16	NUM
ap-6142	215	10	)	)	PUNCT
ap-6142	215	11	,	,	PUNCT
ap-6142	215	12	we	we	PRON
ap-6142	215	13	obtain∫	obtain∫	VERB
ap-6142	215	14	t	t	PROPN
ap-6142	215	15	0	0	NUM
ap-6142	215	16	〈	〈	PROPN
ap-6142	215	17	∂tw	∂tw	PROPN
ap-6142	215	18	,	,	PUNCT
ap-6142	215	19	w	w	PROPN
ap-6142	215	20	−	−	PROPN
ap-6142	215	21	v	v	NUM
ap-6142	215	22	〉	〉	NOUN
ap-6142	216	1	dt	dt	NOUN
ap-6142	216	2	=	=	SYM
ap-6142	216	3	∫	∫	PROPN
ap-6142	216	4	t∗	t∗	NOUN
ap-6142	216	5	0	0	NUM
ap-6142	216	6	〈	〈	PROPN
ap-6142	216	7	∂t(v∗ext	∂t(v∗ext	PROPN
ap-6142	216	8	+	+	CCONJ
ap-6142	216	9	αu	αu	NOUN
ap-6142	216	10	)	)	PUNCT
ap-6142	216	11	,	,	PUNCT
ap-6142	216	12	(	(	PUNCT
ap-6142	216	13	α−	α−	ADP
ap-6142	216	14	1)u	1)u	NUM
ap-6142	216	15	〉	〉	NOUN
ap-6142	216	16	dt	dt	NOUN
ap-6142	216	17	+	+	CCONJ
ap-6142	216	18	∫	∫	PROPN
ap-6142	216	19	t∗+δ	t∗+δ	ADJ
ap-6142	216	20	t∗	t∗	NOUN
ap-6142	216	21	〈	〈	PROPN
ap-6142	216	22	∂t(v∗ext	∂t(v∗ext	PROPN
ap-6142	216	23	+	+	CCONJ
ap-6142	216	24	ηu	ηu	NOUN
ap-6142	216	25	)	)	PUNCT
ap-6142	216	26	,	,	PUNCT
ap-6142	216	27	(	(	PUNCT
ap-6142	216	28	η	η	PROPN
ap-6142	216	29	−	−	PROPN
ap-6142	216	30	1)u	1)u	NUM
ap-6142	216	31	〉	〉	NOUN
ap-6142	216	32	dt	dt	NOUN
ap-6142	216	33	=	=	PUNCT
ap-6142	216	34	(	(	PUNCT
ap-6142	216	35	α−	α−	ADP
ap-6142	216	36	1	1	NUM
ap-6142	216	37	)	)	PUNCT
ap-6142	216	38	∫	∫	PROPN
ap-6142	216	39	t∗	t∗	NOUN
ap-6142	216	40	0	0	NUM
ap-6142	216	41	〈	〈	PROPN
ap-6142	216	42	∂tv	∂tv	PROPN
ap-6142	216	43	∗	∗	NOUN
ap-6142	216	44	ext	ext	NOUN
ap-6142	216	45	,	,	PUNCT
ap-6142	216	46	u	u	NOUN
ap-6142	216	47	〉	〉	NOUN
ap-6142	216	48	dt	dt	NOUN
ap-6142	216	49	+	+	CCONJ
ap-6142	216	50	α(α−	α(α−	PROPN
ap-6142	216	51	1	1	NUM
ap-6142	216	52	)	)	PUNCT
ap-6142	216	53	∫	∫	PROPN
ap-6142	216	54	t∗	t∗	PROPN
ap-6142	216	55	0	0	NUM
ap-6142	216	56	〈	〈	PROPN
ap-6142	216	57	∂tu	∂tu	ADJ
ap-6142	216	58	,	,	PUNCT
ap-6142	216	59	u	u	NOUN
ap-6142	216	60	〉	〉	NOUN
ap-6142	216	61	dt	dt	NOUN
ap-6142	216	62	+	+	CCONJ
ap-6142	216	63	∫	∫	PROPN
ap-6142	216	64	t∗+δ	t∗+δ	ADJ
ap-6142	216	65	t∗	t∗	PROPN
ap-6142	216	66	〈	〈	PROPN
ap-6142	216	67	∂tv	∂tv	PROPN
ap-6142	216	68	∗	∗	NOUN
ap-6142	216	69	ext	ext	NOUN
ap-6142	216	70	,	,	PUNCT
ap-6142	216	71	(	(	PUNCT
ap-6142	216	72	η	η	PROPN
ap-6142	216	73	−	−	PROPN
ap-6142	216	74	1)u	1)u	NUM
ap-6142	216	75	〉	〉	NOUN
ap-6142	216	76	dt	dt	NOUN
ap-6142	216	77	+	+	CCONJ
ap-6142	216	78	∫	∫	PROPN
ap-6142	216	79	t∗+δ	t∗+δ	ADJ
ap-6142	216	80	t∗	t∗	PROPN
ap-6142	216	81	〈	〈	PROPN
ap-6142	216	82	∂t(ηu	∂t(ηu	PROPN
ap-6142	216	83	)	)	PUNCT
ap-6142	216	84	,	,	PUNCT
ap-6142	216	85	ηu	ηu	X
ap-6142	216	86	〉	〉	NOUN
ap-6142	216	87	dt−	dt−	NUM
ap-6142	216	88	∫	∫	NOUN
ap-6142	216	89	t∗+δ	t∗+δ	PROPN
ap-6142	216	90	t∗	t∗	PROPN
ap-6142	216	91	〈	〈	PROPN
ap-6142	216	92	η̇u	η̇u	PROPN
ap-6142	216	93	,	,	PUNCT
ap-6142	216	94	u	u	NOUN
ap-6142	216	95	〉	〉	NOUN
ap-6142	216	96	dt	dt	NOUN
ap-6142	216	97	−	−	PROPN
ap-6142	216	98	∫	∫	PROPN
ap-6142	216	99	t∗+δ	t∗+δ	PROPN
ap-6142	216	100	t∗	t∗	PROPN
ap-6142	216	101	〈	〈	PROPN
ap-6142	216	102	η	η	PROPN
ap-6142	216	103	∂tu	∂tu	PROPN
ap-6142	216	104	,	,	PUNCT
ap-6142	216	105	u	u	NOUN
ap-6142	216	106	〉	〉	NOUN
ap-6142	216	107	dt	dt	NOUN
ap-6142	216	108	=	=	SYM
ap-6142	216	109	∫	∫	PROPN
ap-6142	217	1	t∗+δ	t∗+δ	NOUN
ap-6142	217	2	0	0	NUM
ap-6142	217	3	(	(	PUNCT
ap-6142	217	4	η	η	PROPN
ap-6142	217	5	−	−	PROPN
ap-6142	217	6	1	1	NUM
ap-6142	217	7	)	)	PUNCT
ap-6142	217	8	〈	〈	PROPN
ap-6142	217	9	∂tv	∂tv	PROPN
ap-6142	217	10	∗	∗	NOUN
ap-6142	217	11	ext	ext	NOUN
ap-6142	217	12	,	,	PUNCT
ap-6142	217	13	u	u	NOUN
ap-6142	217	14	〉	〉	NOUN
ap-6142	217	15	dt	dt	NOUN
ap-6142	217	16	+	+	CCONJ
ap-6142	217	17	α(α−	α(α−	PROPN
ap-6142	217	18	1	1	NUM
ap-6142	217	19	)	)	PUNCT
ap-6142	217	20	2	2	NUM
ap-6142	217	21	(	(	PUNCT
ap-6142	217	22	‖u(t∗)‖22	‖u(t∗)‖22	PROPN
ap-6142	217	23	−	−	NOUN
ap-6142	217	24	‖u(0)‖22	‖u(0)‖22	NOUN
ap-6142	217	25	)	)	PUNCT
ap-6142	218	1	+	+	CCONJ
ap-6142	218	2	1	1	NUM
ap-6142	218	3	2	2	NUM
ap-6142	218	4	(	(	PUNCT
ap-6142	218	5	‖η(t∗	‖η(t∗	PUNCT
ap-6142	218	6	+	+	PUNCT
ap-6142	218	7	δ)u(t∗	δ)u(t∗	NOUN
ap-6142	218	8	+	+	CCONJ
ap-6142	218	9	δ)‖22	δ)‖22	ADJ
ap-6142	218	10	−	−	NOUN
ap-6142	218	11	‖η(t∗)u(t∗)‖22	‖η(t∗)u(t∗)‖22	NOUN
ap-6142	218	12	)	)	PUNCT
ap-6142	219	1	−	−	PROPN
ap-6142	220	1	1−	1−	NUM
ap-6142	220	2	α	α	NUM
ap-6142	220	3	δ	δ	PROPN
ap-6142	220	4	∫	∫	PROPN
ap-6142	220	5	t∗+δ	t∗+δ	PROPN
ap-6142	220	6	t∗	t∗	PROPN
ap-6142	220	7	‖u‖22	‖u‖22	NOUN
ap-6142	220	8	dt	dt	NOUN
ap-6142	220	9	−	−	NOUN
ap-6142	220	10	1	1	NUM
ap-6142	220	11	2	2	NUM
ap-6142	220	12	∫	∫	NOUN
ap-6142	220	13	t∗+δ	t∗+δ	PROPN
ap-6142	220	14	t∗	t∗	PROPN
ap-6142	220	15	η	η	PROPN
ap-6142	220	16	d	d	NOUN
ap-6142	220	17	dt	dt	X
ap-6142	220	18	‖u‖	‖u‖	PROPN
ap-6142	220	19	2	2	NUM
ap-6142	220	20	2	2	NUM
ap-6142	220	21	dt	dt	NOUN
ap-6142	220	22	=	=	SYM
ap-6142	220	23	∫	∫	PROPN
ap-6142	221	1	t∗+δ	t∗+δ	NOUN
ap-6142	221	2	0	0	NUM
ap-6142	221	3	(	(	PUNCT
ap-6142	221	4	η	η	PROPN
ap-6142	221	5	−	−	PROPN
ap-6142	221	6	1	1	NUM
ap-6142	221	7	)	)	PUNCT
ap-6142	221	8	〈	〈	PROPN
ap-6142	221	9	∂tv	∂tv	PROPN
ap-6142	221	10	∗	∗	NOUN
ap-6142	221	11	ext	ext	NOUN
ap-6142	221	12	,	,	PUNCT
ap-6142	221	13	u	u	NOUN
ap-6142	221	14	〉	〉	NOUN
ap-6142	221	15	dt	dt	NOUN
ap-6142	221	16	+	+	CCONJ
ap-6142	221	17	α(α−	α(α−	PROPN
ap-6142	221	18	1	1	NUM
ap-6142	221	19	)	)	PUNCT
ap-6142	221	20	2	2	NUM
ap-6142	221	21	(	(	PUNCT
ap-6142	221	22	‖u(t∗)‖22	‖u(t∗)‖22	PROPN
ap-6142	221	23	−	−	NOUN
ap-6142	221	24	‖u(0)‖22	‖u(0)‖22	NOUN
ap-6142	221	25	)	)	PUNCT
ap-6142	222	1	+	+	CCONJ
ap-6142	222	2	1	1	NUM
ap-6142	222	3	2	2	NUM
ap-6142	222	4	(	(	PUNCT
ap-6142	222	5	‖η(t∗	‖η(t∗	PUNCT
ap-6142	222	6	+	+	PUNCT
ap-6142	222	7	δ)u(t∗	δ)u(t∗	NOUN
ap-6142	222	8	+	+	CCONJ
ap-6142	222	9	δ)‖22	δ)‖22	ADJ
ap-6142	222	10	−	−	NOUN
ap-6142	222	11	‖η(t∗)u(t∗)‖22	‖η(t∗)u(t∗)‖22	NOUN
ap-6142	222	12	)	)	PUNCT
ap-6142	223	1	93	93	NUM
ap-6142	223	2	stanislav	stanislav	X
ap-6142	223	3	kračmar	kračmar	PROPN
ap-6142	223	4	,	,	PUNCT
ap-6142	223	5	jiří	jiří	NOUN
ap-6142	223	6	neustupa	neustupa	PROPN
ap-6142	223	7	acta	acta	PROPN
ap-6142	223	8	polytechnica	polytechnica	PROPN
ap-6142	223	9	−	−	PROPN
ap-6142	223	10	1−	1−	NUM
ap-6142	224	1	α	α	NUM
ap-6142	224	2	δ	δ	PROPN
ap-6142	224	3	∫	∫	PROPN
ap-6142	224	4	t∗+δ	t∗+δ	PROPN
ap-6142	224	5	t∗	t∗	PROPN
ap-6142	224	6	‖u‖22	‖u‖22	NOUN
ap-6142	225	1	dt	dt	NOUN
ap-6142	225	2	−	−	PROPN
ap-6142	225	3	1	1	NUM
ap-6142	225	4	2	2	NUM
ap-6142	225	5	(	(	PUNCT
ap-6142	225	6	η(t∗	η(t∗	NOUN
ap-6142	225	7	+	+	CCONJ
ap-6142	225	8	δ	δ	PROPN
ap-6142	225	9	)	)	PUNCT
ap-6142	225	10	‖u(t∗	‖u(t∗	NOUN
ap-6142	226	1	+	+	NUM
ap-6142	226	2	δ)‖22	δ)‖22	ADJ
ap-6142	226	3	−	−	NOUN
ap-6142	226	4	η(t∗	η(t∗	NOUN
ap-6142	226	5	)	)	PUNCT
ap-6142	226	6	‖u(t∗)‖22	‖u(t∗)‖22	PROPN
ap-6142	226	7	)	)	PUNCT
ap-6142	227	1	+	+	CCONJ
ap-6142	227	2	1	1	NUM
ap-6142	227	3	2	2	NUM
ap-6142	227	4	∫	∫	NOUN
ap-6142	227	5	t∗+δ	t∗+δ	NOUN
ap-6142	227	6	t∗	t∗	PROPN
ap-6142	227	7	η̇	η̇	PROPN
ap-6142	227	8	‖u‖22	‖u‖22	ADP
ap-6142	227	9	dt	dt	PROPN
ap-6142	227	10	=	=	SYM
ap-6142	227	11	∫	∫	PROPN
ap-6142	228	1	t∗+δ	t∗+δ	NOUN
ap-6142	228	2	0	0	NUM
ap-6142	228	3	(	(	PUNCT
ap-6142	228	4	η	η	PROPN
ap-6142	228	5	−	−	PROPN
ap-6142	228	6	1	1	NUM
ap-6142	228	7	)	)	PUNCT
ap-6142	228	8	〈	〈	PROPN
ap-6142	228	9	∂tv	∂tv	PROPN
ap-6142	228	10	∗	∗	NOUN
ap-6142	228	11	ext	ext	NOUN
ap-6142	228	12	,	,	PUNCT
ap-6142	228	13	u	u	NOUN
ap-6142	228	14	〉	〉	NOUN
ap-6142	228	15	dt	dt	NOUN
ap-6142	228	16	+	+	CCONJ
ap-6142	228	17	α(α−	α(α−	PROPN
ap-6142	228	18	1	1	NUM
ap-6142	228	19	)	)	PUNCT
ap-6142	228	20	2	2	NUM
ap-6142	228	21	(	(	PUNCT
ap-6142	228	22	‖u(t∗)‖22	‖u(t∗)‖22	PROPN
ap-6142	228	23	−	−	NOUN
ap-6142	228	24	‖u(0)‖22	‖u(0)‖22	NOUN
ap-6142	228	25	)	)	PUNCT
ap-6142	229	1	+	+	CCONJ
ap-6142	229	2	1	1	NUM
ap-6142	229	3	2	2	NUM
ap-6142	229	4	(	(	PUNCT
ap-6142	229	5	‖η(t∗	‖η(t∗	PUNCT
ap-6142	229	6	+	+	PUNCT
ap-6142	229	7	δ)u(t∗	δ)u(t∗	NOUN
ap-6142	229	8	+	+	CCONJ
ap-6142	229	9	δ)‖22	δ)‖22	ADJ
ap-6142	229	10	−	−	NOUN
ap-6142	229	11	‖η(t∗)u(t∗)‖22	‖η(t∗)u(t∗)‖22	NOUN
ap-6142	229	12	)	)	PUNCT
ap-6142	230	1	−	−	PROPN
ap-6142	231	1	1−	1−	NUM
ap-6142	231	2	α	α	NUM
ap-6142	231	3	δ	δ	PROPN
ap-6142	231	4	∫	∫	PROPN
ap-6142	231	5	t∗+δ	t∗+δ	PROPN
ap-6142	231	6	t∗	t∗	PROPN
ap-6142	231	7	‖u‖22	‖u‖22	NOUN
ap-6142	231	8	dt	dt	NOUN
ap-6142	231	9	−	−	PROPN
ap-6142	231	10	1	1	NUM
ap-6142	231	11	2	2	NUM
ap-6142	231	12	(	(	PUNCT
ap-6142	231	13	η(t∗	η(t∗	NOUN
ap-6142	231	14	+	+	CCONJ
ap-6142	231	15	δ	δ	PROPN
ap-6142	231	16	)	)	PUNCT
ap-6142	231	17	‖u(t∗	‖u(t∗	NOUN
ap-6142	232	1	+	+	NUM
ap-6142	232	2	δ)‖22	δ)‖22	ADJ
ap-6142	232	3	−	−	NOUN
ap-6142	232	4	η(t∗	η(t∗	NOUN
ap-6142	232	5	)	)	PUNCT
ap-6142	232	6	‖u(t∗)‖22	‖u(t∗)‖22	PROPN
ap-6142	232	7	)	)	PUNCT
ap-6142	233	1	+	+	CCONJ
ap-6142	233	2	1−	1−	NUM
ap-6142	233	3	α	α	NUM
ap-6142	233	4	2δ	2δ	NUM
ap-6142	233	5	∫	∫	PROPN
ap-6142	233	6	t∗+δ	t∗+δ	PROPN
ap-6142	233	7	t∗	t∗	PROPN
ap-6142	233	8	‖u‖22	‖u‖22	ADV
ap-6142	233	9	dt	dt	X
ap-6142	233	10	.	.	PUNCT
ap-6142	234	1	considering	consider	VERB
ap-6142	234	2	δ	δ	PROPN
ap-6142	234	3	→	→	X
ap-6142	234	4	0	0	NUM
ap-6142	234	5	+	+	ADJ
ap-6142	234	6	,	,	PUNCT
ap-6142	234	7	we	we	PRON
ap-6142	234	8	get∫	get∫	VERB
ap-6142	234	9	t	t	PROPN
ap-6142	234	10	0	0	NUM
ap-6142	234	11	〈	〈	PROPN
ap-6142	234	12	∂tw	∂tw	PROPN
ap-6142	234	13	,	,	PUNCT
ap-6142	234	14	w	w	PROPN
ap-6142	234	15	−	−	PROPN
ap-6142	234	16	v	v	NUM
ap-6142	234	17	〉	〉	NOUN
ap-6142	234	18	dt	dt	NOUN
ap-6142	234	19	=	=	PUNCT
ap-6142	234	20	(	(	PUNCT
ap-6142	234	21	α−	α−	ADP
ap-6142	234	22	1	1	NUM
ap-6142	234	23	)	)	PUNCT
ap-6142	234	24	∫	∫	PROPN
ap-6142	234	25	t∗	t∗	NOUN
ap-6142	234	26	0	0	NUM
ap-6142	235	1	〈	〈	PROPN
ap-6142	235	2	∂tv∗ext	∂tv∗ext	PROPN
ap-6142	235	3	,	,	PUNCT
ap-6142	235	4	u	u	NOUN
ap-6142	235	5	〉	〉	NOUN
ap-6142	235	6	dt	dt	NOUN
ap-6142	235	7	+	+	CCONJ
ap-6142	235	8	α2	α2	ADJ
ap-6142	235	9	−	−	NOUN
ap-6142	235	10	1	1	NUM
ap-6142	235	11	2	2	NUM
ap-6142	235	12	‖u(t∗)‖22	‖u(t∗)‖22	PROPN
ap-6142	235	13	−	−	NOUN
ap-6142	235	14	α(α−	α(α−	PROPN
ap-6142	235	15	1	1	NUM
ap-6142	235	16	)	)	SYM
ap-6142	235	17	2	2	NUM
ap-6142	235	18	‖u(0‖22	‖u(0‖22	NOUN
ap-6142	235	19	.	.	PUNCT
ap-6142	236	1	substituting	substitute	VERB
ap-6142	236	2	this	this	PRON
ap-6142	236	3	to	to	ADP
ap-6142	236	4	(	(	PUNCT
ap-6142	236	5	16	16	NUM
ap-6142	236	6	)	)	PUNCT
ap-6142	236	7	,	,	PUNCT
ap-6142	236	8	using	use	VERB
ap-6142	236	9	v	v	ADP
ap-6142	236	10	=	=	SYM
ap-6142	236	11	v∗ext	v∗ext	PROPN
ap-6142	236	12	+	+	CCONJ
ap-6142	236	13	u	u	NOUN
ap-6142	236	14	and	and	CCONJ
ap-6142	236	15	w	w	PROPN
ap-6142	236	16	=	=	SYM
ap-6142	236	17	v∗ext	v∗ext	PROPN
ap-6142	237	1	+	+	NUM
ap-6142	237	2	ηu	ηu	NOUN
ap-6142	237	3	in	in	ADP
ap-6142	237	4	all	all	DET
ap-6142	237	5	other	other	ADJ
ap-6142	237	6	terms	term	NOUN
ap-6142	237	7	in	in	ADP
ap-6142	237	8	(	(	PUNCT
ap-6142	237	9	16	16	NUM
ap-6142	237	10	)	)	PUNCT
ap-6142	237	11	,	,	PUNCT
ap-6142	237	12	considering	consider	VERB
ap-6142	237	13	δ	δ	X
ap-6142	237	14	→	→	SYM
ap-6142	237	15	0	0	NUM
ap-6142	237	16	+	+	PROPN
ap-6142	237	17	,	,	PUNCT
ap-6142	237	18	dividing	divide	VERB
ap-6142	237	19	the	the	DET
ap-6142	237	20	whole	whole	ADJ
ap-6142	237	21	inequality	inequality	NOUN
ap-6142	237	22	by	by	ADP
ap-6142	237	23	α−1	α−1	PROPN
ap-6142	237	24	(	(	PUNCT
ap-6142	237	25	which	which	PRON
ap-6142	237	26	is	be	AUX
ap-6142	237	27	negative	negative	ADJ
ap-6142	237	28	)	)	PUNCT
ap-6142	237	29	,	,	PUNCT
ap-6142	237	30	and	and	CCONJ
ap-6142	237	31	considering	consider	VERB
ap-6142	237	32	finally	finally	ADV
ap-6142	237	33	α	α	X
ap-6142	237	34	→	→	SYM
ap-6142	237	35	0	0	NUM
ap-6142	237	36	+	+	NUM
ap-6142	237	37	,	,	PUNCT
ap-6142	237	38	we	we	PRON
ap-6142	237	39	obtain∫	obtain∫	VERB
ap-6142	237	40	t∗	t∗	NOUN
ap-6142	237	41	0	0	PUNCT
ap-6142	238	1	〈	〈	PROPN
ap-6142	238	2	∂tv∗ext	∂tv∗ext	PROPN
ap-6142	238	3	,	,	PUNCT
ap-6142	238	4	u	u	NOUN
ap-6142	238	5	〉	〉	NUM
ap-6142	238	6	dt+	dt+	NOUN
ap-6142	238	7	1	1	NUM
ap-6142	238	8	2	2	NUM
ap-6142	238	9	‖u(t∗)‖22	‖u(t∗)‖22	PROPN
ap-6142	238	10	+	+	CCONJ
ap-6142	238	11	∫	∫	PROPN
ap-6142	238	12	t∗	t∗	PROPN
ap-6142	238	13	0	0	NUM
ap-6142	239	1	∫	∫	PROPN
ap-6142	239	2	ω	ω	PROPN
ap-6142	239	3	(	(	PUNCT
ap-6142	239	4	v∗ext	v∗ext	PROPN
ap-6142	239	5	+	+	CCONJ
ap-6142	239	6	u	u	NOUN
ap-6142	239	7	)	)	PUNCT
ap-6142	239	8	·	·	PUNCT
ap-6142	240	1	∇(v∗ext	∇(v∗ext	PROPN
ap-6142	240	2	+	+	CCONJ
ap-6142	240	3	u	u	NOUN
ap-6142	240	4	)	)	PUNCT
ap-6142	240	5	·	·	PUNCT
ap-6142	240	6	u	u	NOUN
ap-6142	240	7	dx	dx	PROPN
ap-6142	241	1	dt	dt	PROPN
ap-6142	241	2	+	+	CCONJ
ap-6142	241	3	∫	∫	PROPN
ap-6142	241	4	t∗	t∗	PROPN
ap-6142	241	5	0	0	NUM
ap-6142	241	6	∫	∫	PROPN
ap-6142	241	7	ω	ω	NUM
ap-6142	241	8	ν∇(v∗ext	ν∇(v∗ext	NOUN
ap-6142	241	9	+	+	CCONJ
ap-6142	241	10	u	u	NOUN
ap-6142	241	11	)	)	PUNCT
ap-6142	241	12	:	:	PUNCT
ap-6142	242	1	∇u	∇u	PROPN
ap-6142	242	2	dx	dx	PROPN
ap-6142	242	3	≤	≤	NUM
ap-6142	242	4	∫	∫	PROPN
ap-6142	242	5	t∗	t∗	PROPN
ap-6142	242	6	0	0	PUNCT
ap-6142	243	1	〈	〈	PROPN
ap-6142	243	2	f	f	X
ap-6142	243	3	,	,	PUNCT
ap-6142	243	4	u	u	NOUN
ap-6142	243	5	〉	〉	NUM
ap-6142	243	6	dt+	dt+	NOUN
ap-6142	243	7	∫	∫	NOUN
ap-6142	243	8	t∗	t∗	NOUN
ap-6142	243	9	0	0	NUM
ap-6142	243	10	∫	∫	PROPN
ap-6142	243	11	γ2	γ2	PROPN
ap-6142	243	12	g	g	PROPN
ap-6142	243	13	·	·	PUNCT
ap-6142	243	14	u	u	NOUN
ap-6142	243	15	ds	ds	ADJ
ap-6142	243	16	dt+	dt+	NOUN
ap-6142	243	17	1	1	NUM
ap-6142	243	18	2	2	NUM
ap-6142	243	19	‖u(0)‖22	‖u(0)‖22	NOUN
ap-6142	243	20	,	,	PUNCT
ap-6142	243	21	1	1	NUM
ap-6142	243	22	2	2	NUM
ap-6142	243	23	‖u(t∗)‖22	‖u(t∗)‖22	PROPN
ap-6142	243	24	+	+	NUM
ap-6142	243	25	∫	∫	PROPN
ap-6142	243	26	t∗	t∗	NOUN
ap-6142	243	27	0	0	PUNCT
ap-6142	243	28	ν	ν	PRON
ap-6142	243	29	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	243	30	dt	dt	X
ap-6142	244	1	+	+	CCONJ
ap-6142	244	2	∫	∫	PROPN
ap-6142	244	3	t∗	t∗	PROPN
ap-6142	244	4	0	0	NUM
ap-6142	244	5	∫	∫	PROPN
ap-6142	244	6	ω	ω	PROPN
ap-6142	244	7	(	(	PUNCT
ap-6142	244	8	v∗ext	v∗ext	PROPN
ap-6142	244	9	+	+	CCONJ
ap-6142	244	10	u	u	NOUN
ap-6142	244	11	)	)	PUNCT
ap-6142	244	12	·	·	PUNCT
ap-6142	245	1	∇(v∗ext	∇(v∗ext	PROPN
ap-6142	245	2	+	+	CCONJ
ap-6142	245	3	u	u	NOUN
ap-6142	245	4	)	)	PUNCT
ap-6142	245	5	·	·	PUNCT
ap-6142	246	1	(	(	PUNCT
ap-6142	246	2	v∗ext	v∗ext	NOUN
ap-6142	246	3	+	+	CCONJ
ap-6142	246	4	u	u	NOUN
ap-6142	246	5	)	)	PUNCT
ap-6142	246	6	dx	dx	PROPN
ap-6142	246	7	dt	dt	PROPN
ap-6142	247	1	+	+	CCONJ
ap-6142	247	2	∫	∫	PROPN
ap-6142	247	3	t∗	t∗	NOUN
ap-6142	247	4	0	0	NUM
ap-6142	248	1	〈	〈	PROPN
ap-6142	248	2	∂tv∗ext	∂tv∗ext	PROPN
ap-6142	248	3	,	,	PUNCT
ap-6142	248	4	u	u	NOUN
ap-6142	248	5	〉	〉	NOUN
ap-6142	248	6	dt	dt	NOUN
ap-6142	249	1	≤	≤	NUM
ap-6142	249	2	∫	∫	PROPN
ap-6142	249	3	t∗	t∗	PROPN
ap-6142	249	4	0	0	NUM
ap-6142	249	5	∫	∫	PROPN
ap-6142	249	6	ω	ω	PROPN
ap-6142	249	7	(	(	PUNCT
ap-6142	249	8	v∗ext	v∗ext	PROPN
ap-6142	249	9	+	+	CCONJ
ap-6142	249	10	u	u	NOUN
ap-6142	249	11	)	)	PUNCT
ap-6142	249	12	·	·	PUNCT
ap-6142	250	1	∇(v∗ext	∇(v∗ext	PROPN
ap-6142	250	2	+	+	CCONJ
ap-6142	250	3	u	u	NOUN
ap-6142	250	4	)	)	PUNCT
ap-6142	250	5	·	·	PUNCT
ap-6142	251	1	v∗ext	v∗ext	NOUN
ap-6142	251	2	dx	dx	PROPN
ap-6142	251	3	dt	dt	PROPN
ap-6142	252	1	+	+	CCONJ
ap-6142	252	2	∫	∫	PROPN
ap-6142	252	3	t∗	t∗	PROPN
ap-6142	252	4	0	0	NUM
ap-6142	252	5	∫	∫	PROPN
ap-6142	252	6	ω	ω	NUM
ap-6142	252	7	ν∇v∗ext	ν∇v∗ext	NOUN
ap-6142	252	8	:	:	PUNCT
ap-6142	252	9	∇u	∇u	PROPN
ap-6142	252	10	dx	dx	PROPN
ap-6142	252	11	dt+	dt+	NOUN
ap-6142	252	12	∫	∫	PROPN
ap-6142	252	13	t∗	t∗	NOUN
ap-6142	252	14	0	0	PUNCT
ap-6142	253	1	〈	〈	PROPN
ap-6142	253	2	f	f	X
ap-6142	253	3	,	,	PUNCT
ap-6142	253	4	u	u	NOUN
ap-6142	253	5	〉	〉	NOUN
ap-6142	253	6	dt	dt	NOUN
ap-6142	253	7	+	+	NUM
ap-6142	253	8	∫	∫	PROPN
ap-6142	253	9	t∗	t∗	PROPN
ap-6142	253	10	0	0	NUM
ap-6142	253	11	∫	∫	PROPN
ap-6142	253	12	γ2	γ2	PROPN
ap-6142	253	13	g	g	PROPN
ap-6142	253	14	·	·	PUNCT
ap-6142	253	15	u	u	NOUN
ap-6142	253	16	ds	ds	ADJ
ap-6142	253	17	dt+	dt+	NOUN
ap-6142	253	18	1	1	NUM
ap-6142	253	19	2	2	NUM
ap-6142	253	20	‖u(0)‖22	‖u(0)‖22	NOUN
ap-6142	253	21	,	,	PUNCT
ap-6142	253	22	1	1	NUM
ap-6142	253	23	2	2	NUM
ap-6142	253	24	‖u(t∗)‖22	‖u(t∗)‖22	PROPN
ap-6142	253	25	+	+	NUM
ap-6142	253	26	∫	∫	PROPN
ap-6142	253	27	t∗	t∗	NOUN
ap-6142	253	28	0	0	PUNCT
ap-6142	253	29	ν	ν	PRON
ap-6142	253	30	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	253	31	dt	dt	NOUN
ap-6142	254	1	+	+	CCONJ
ap-6142	254	2	1	1	NUM
ap-6142	254	3	2	2	NUM
ap-6142	254	4	∫	∫	NOUN
ap-6142	254	5	t∗	t∗	NOUN
ap-6142	254	6	0	0	NUM
ap-6142	254	7	∫	∫	PROPN
ap-6142	254	8	γ1	γ1	PROPN
ap-6142	254	9	(	(	PUNCT
ap-6142	254	10	v∗	v∗	PROPN
ap-6142	254	11	·	·	PUNCT
ap-6142	254	12	n	n	CCONJ
ap-6142	254	13	)	)	PUNCT
ap-6142	254	14	|v∗|2	|v∗|2	NUM
ap-6142	254	15	ds	ds	ADJ
ap-6142	254	16	dt	dt	NOUN
ap-6142	254	17	+	+	NOUN
ap-6142	254	18	1	1	NUM
ap-6142	254	19	2	2	NUM
ap-6142	254	20	∫	∫	NOUN
ap-6142	254	21	t∗	t∗	NOUN
ap-6142	254	22	0	0	NUM
ap-6142	254	23	∫	∫	PROPN
ap-6142	254	24	γ2	γ2	PROPN
ap-6142	255	1	[	[	X
ap-6142	255	2	(	(	PUNCT
ap-6142	255	3	v∗ext	v∗ext	PROPN
ap-6142	255	4	+	+	CCONJ
ap-6142	255	5	u	u	NOUN
ap-6142	255	6	)	)	PUNCT
ap-6142	255	7	·	·	PUNCT
ap-6142	255	8	n	n	CCONJ
ap-6142	256	1	]	]	X
ap-6142	256	2	|v∗ext	|v∗ext	NOUN
ap-6142	256	3	+	+	CCONJ
ap-6142	256	4	u|2	u|2	PROPN
ap-6142	256	5	ds	ds	ADJ
ap-6142	256	6	dt	dt	NOUN
ap-6142	256	7	+	+	CCONJ
ap-6142	256	8	∫	∫	PROPN
ap-6142	256	9	t∗	t∗	NOUN
ap-6142	256	10	0	0	NUM
ap-6142	256	11	〈	〈	PROPN
ap-6142	256	12	∂tv∗ext	∂tv∗ext	PROPN
ap-6142	256	13	,	,	PUNCT
ap-6142	256	14	u	u	NOUN
ap-6142	256	15	〉	〉	NOUN
ap-6142	256	16	dt	dt	NOUN
ap-6142	257	1	≤	≤	NUM
ap-6142	257	2	∫	∫	PROPN
ap-6142	257	3	t∗	t∗	PROPN
ap-6142	257	4	0	0	NUM
ap-6142	257	5	∫	∫	PROPN
ap-6142	257	6	ω	ω	PROPN
ap-6142	257	7	(	(	PUNCT
ap-6142	257	8	v∗ext	v∗ext	PROPN
ap-6142	257	9	·	·	PUNCT
ap-6142	257	10	∇v∗ext	∇v∗ext	PROPN
ap-6142	257	11	·	·	PUNCT
ap-6142	257	12	v∗ext	v∗ext	PROPN
ap-6142	257	13	+	+	CCONJ
ap-6142	257	14	v∗ext	v∗ext	PROPN
ap-6142	257	15	·	·	PUNCT
ap-6142	258	1	∇u	∇u	PROPN
ap-6142	258	2	·	·	PUNCT
ap-6142	258	3	v∗ext	v∗ext	PROPN
ap-6142	258	4	+	+	CCONJ
ap-6142	258	5	u	u	X
ap-6142	258	6	·	·	PUNCT
ap-6142	258	7	∇v∗ext	∇v∗ext	PROPN
ap-6142	258	8	·	·	PUNCT
ap-6142	258	9	v∗ext	v∗ext	PROPN
ap-6142	258	10	+	+	CCONJ
ap-6142	258	11	u	u	PROPN
ap-6142	258	12	·	·	PUNCT
ap-6142	258	13	∇u	∇u	PROPN
ap-6142	258	14	·	·	PUNCT
ap-6142	258	15	v∗ext	v∗ext	NOUN
ap-6142	258	16	)	)	PUNCT
ap-6142	258	17	dx	dx	PROPN
ap-6142	259	1	dt	dt	PROPN
ap-6142	260	1	+	+	CCONJ
ap-6142	260	2	∫	∫	PROPN
ap-6142	260	3	t∗	t∗	PROPN
ap-6142	260	4	0	0	NUM
ap-6142	260	5	∫	∫	PROPN
ap-6142	260	6	ω	ω	NUM
ap-6142	260	7	ν∇v∗ext	ν∇v∗ext	NOUN
ap-6142	260	8	:	:	PUNCT
ap-6142	260	9	∇u	∇u	PROPN
ap-6142	260	10	dx	dx	PROPN
ap-6142	260	11	dt+	dt+	NOUN
ap-6142	260	12	∫	∫	PROPN
ap-6142	260	13	t∗	t∗	NOUN
ap-6142	260	14	0	0	PUNCT
ap-6142	261	1	〈	〈	PROPN
ap-6142	261	2	f	f	X
ap-6142	261	3	,	,	PUNCT
ap-6142	261	4	u	u	NOUN
ap-6142	261	5	〉	〉	NOUN
ap-6142	261	6	dt	dt	NOUN
ap-6142	261	7	+	+	NUM
ap-6142	261	8	∫	∫	PROPN
ap-6142	261	9	t∗	t∗	PROPN
ap-6142	261	10	0	0	NUM
ap-6142	261	11	∫	∫	PROPN
ap-6142	261	12	γ2	γ2	PROPN
ap-6142	261	13	g	g	PROPN
ap-6142	261	14	·	·	PUNCT
ap-6142	261	15	u	u	NOUN
ap-6142	261	16	ds	ds	ADJ
ap-6142	261	17	dt+	dt+	NOUN
ap-6142	261	18	1	1	NUM
ap-6142	261	19	2	2	NUM
ap-6142	261	20	‖u(0)‖22	‖u(0)‖22	NOUN
ap-6142	261	21	.	.	PUNCT
ap-6142	262	1	since	since	SCONJ
ap-6142	262	2	∣∣∣∣∫	∣∣∣∣∫	DET
ap-6142	262	3	t∗	t∗	PROPN
ap-6142	262	4	0	0	NUM
ap-6142	262	5	∫	∫	PROPN
ap-6142	262	6	ω	ω	NUM
ap-6142	262	7	u	u	PROPN
ap-6142	262	8	·	·	PUNCT
ap-6142	262	9	∇u	∇u	PROPN
ap-6142	262	10	·	·	PUNCT
ap-6142	262	11	v∗ext	v∗ext	NOUN
ap-6142	262	12	dx	dx	PROPN
ap-6142	263	1	dt	dt	PROPN
ap-6142	263	2	∣∣∣∣	∣∣∣∣	PROPN
ap-6142	263	3	≤	≤	NUM
ap-6142	263	4	∫	∫	PROPN
ap-6142	263	5	t∗	t∗	NOUN
ap-6142	263	6	0	0	NUM
ap-6142	263	7	‖u‖3	‖u‖3	NOUN
ap-6142	263	8	‖∇u‖2	‖∇u‖2	PROPN
ap-6142	263	9	‖v∗ext‖6	‖v∗ext‖6	PROPN
ap-6142	263	10	dt	dt	NOUN
ap-6142	263	11	≤	≤	PROPN
ap-6142	263	12	c	c	NOUN
ap-6142	263	13	∫	∫	PROPN
ap-6142	263	14	t∗	t∗	NOUN
ap-6142	263	15	0	0	NUM
ap-6142	263	16	‖u‖3	‖u‖3	NOUN
ap-6142	263	17	‖∇u‖2	‖∇u‖2	ADJ
ap-6142	263	18	‖v∗ext‖1,2	‖v∗ext‖1,2	ADJ
ap-6142	263	19	dt	dt	X
ap-6142	263	20	≤	≤	NUM
ap-6142	263	21	c	c	NOUN
ap-6142	263	22	∫	∫	PROPN
ap-6142	263	23	t∗	t∗	NOUN
ap-6142	263	24	0	0	NUM
ap-6142	263	25	‖u‖3	‖u‖3	NOUN
ap-6142	263	26	‖∇u‖2	‖∇u‖2	NOUN
ap-6142	263	27	dt	dt	PROPN
ap-6142	263	28	≤	≤	PROPN
ap-6142	263	29	c	c	NOUN
ap-6142	263	30	∫	∫	PROPN
ap-6142	263	31	t∗	t∗	PROPN
ap-6142	263	32	0	0	NUM
ap-6142	263	33	‖u‖1/22	‖u‖1/22	SYM
ap-6142	263	34	‖u‖1/26	‖u‖1/26	SYM
ap-6142	263	35	‖∇u‖2	‖∇u‖2	PROPN
ap-6142	263	36	dt	dt	NOUN
ap-6142	263	37	≤	≤	PROPN
ap-6142	263	38	c	c	NOUN
ap-6142	263	39	∫	∫	PROPN
ap-6142	263	40	t∗	t∗	PROPN
ap-6142	263	41	0	0	NUM
ap-6142	263	42	‖u‖1/22	‖u‖1/22	PUNCT
ap-6142	264	1	‖∇u‖3/22	‖∇u‖3/22	PROPN
ap-6142	264	2	dt	dt	X
ap-6142	264	3	≤	≤	NUM
ap-6142	264	4	∫	∫	PROPN
ap-6142	264	5	t∗	t∗	NOUN
ap-6142	264	6	0	0	NUM
ap-6142	264	7	(	(	PUNCT
ap-6142	264	8	ξ	ξ	X
ap-6142	264	9	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	264	10	+	+	CCONJ
ap-6142	264	11	c(ξ	c(ξ	NOUN
ap-6142	264	12	)	)	PUNCT
ap-6142	264	13	‖u‖2	‖u‖2	PROPN
ap-6142	264	14	)	)	PUNCT
ap-6142	265	1	dt	dt	NOUN
ap-6142	265	2	,	,	PUNCT
ap-6142	265	3	where	where	SCONJ
ap-6142	265	4	c	c	PROPN
ap-6142	265	5	is	be	AUX
ap-6142	265	6	a	a	DET
ap-6142	265	7	generic	generic	ADJ
ap-6142	265	8	constant	constant	ADJ
ap-6142	265	9	,	,	PUNCT
ap-6142	265	10	we	we	PRON
ap-6142	265	11	get	get	VERB
ap-6142	265	12	1	1	NUM
ap-6142	265	13	2	2	NUM
ap-6142	265	14	‖u(t∗)‖22	‖u(t∗)‖22	PROPN
ap-6142	266	1	+	+	CCONJ
ap-6142	266	2	(	(	PUNCT
ap-6142	266	3	ν	ν	X
ap-6142	266	4	−	−	PROPN
ap-6142	266	5	ξ	ξ	PROPN
ap-6142	266	6	)	)	PUNCT
ap-6142	266	7	∫	∫	PROPN
ap-6142	266	8	t∗	t∗	NOUN
ap-6142	266	9	0	0	NUM
ap-6142	266	10	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	267	1	dt	dt	NOUN
ap-6142	268	1	+	+	NOUN
ap-6142	268	2	1	1	NUM
ap-6142	268	3	2	2	NUM
ap-6142	268	4	∫	∫	NOUN
ap-6142	268	5	t∗	t∗	NOUN
ap-6142	268	6	0	0	NUM
ap-6142	268	7	∫	∫	PROPN
ap-6142	268	8	γ1	γ1	PROPN
ap-6142	268	9	(	(	PUNCT
ap-6142	268	10	v∗	v∗	PROPN
ap-6142	268	11	·	·	PUNCT
ap-6142	268	12	n	n	CCONJ
ap-6142	268	13	)	)	PUNCT
ap-6142	268	14	|v∗|2	|v∗|2	NUM
ap-6142	268	15	ds	ds	ADJ
ap-6142	268	16	dt+	dt+	NOUN
ap-6142	268	17	∫	∫	PROPN
ap-6142	268	18	t	t	PROPN
ap-6142	268	19	0	0	NUM
ap-6142	269	1	〈	〈	PROPN
ap-6142	269	2	∂tv∗ext	∂tv∗ext	PROPN
ap-6142	269	3	,	,	PUNCT
ap-6142	269	4	u	u	NOUN
ap-6142	269	5	〉	〉	NOUN
ap-6142	269	6	dt	dt	NOUN
ap-6142	269	7	≤	≤	NUM
ap-6142	269	8	1	1	NUM
ap-6142	269	9	2	2	NUM
ap-6142	269	10	∫	∫	NOUN
ap-6142	269	11	t∗	t∗	NOUN
ap-6142	269	12	0	0	NUM
ap-6142	269	13	∫	∫	PROPN
ap-6142	269	14	γ2	γ2	PROPN
ap-6142	270	1	[	[	X
ap-6142	270	2	(	(	PUNCT
ap-6142	270	3	v∗ext	v∗ext	PROPN
ap-6142	270	4	+	+	CCONJ
ap-6142	270	5	u	u	NOUN
ap-6142	270	6	)	)	PUNCT
ap-6142	270	7	·	·	PUNCT
ap-6142	270	8	n]−	n]−	ADP
ap-6142	270	9	|v∗ext	|v∗ext	NOUN
ap-6142	270	10	+	+	CCONJ
ap-6142	270	11	u|2	u|2	PROPN
ap-6142	270	12	ds	ds	ADJ
ap-6142	270	13	dt	dt	NOUN
ap-6142	270	14	+	+	CCONJ
ap-6142	270	15	∫	∫	PROPN
ap-6142	270	16	t∗	t∗	PROPN
ap-6142	270	17	0	0	NUM
ap-6142	270	18	∫	∫	PROPN
ap-6142	270	19	ω	ω	PROPN
ap-6142	270	20	(	(	PUNCT
ap-6142	270	21	v∗ext	v∗ext	PROPN
ap-6142	270	22	·	·	PUNCT
ap-6142	271	1	∇v∗ext	∇v∗ext	PROPN
ap-6142	271	2	·	·	PUNCT
ap-6142	271	3	v∗ext	v∗ext	PROPN
ap-6142	271	4	+	+	CCONJ
ap-6142	271	5	v∗ext	v∗ext	PROPN
ap-6142	271	6	·	·	PUNCT
ap-6142	271	7	∇u	∇u	PROPN
ap-6142	271	8	·	·	PUNCT
ap-6142	271	9	v∗ext	v∗ext	PROPN
ap-6142	271	10	+	+	CCONJ
ap-6142	271	11	u	u	X
ap-6142	271	12	·	·	PUNCT
ap-6142	271	13	∇v∗ext	∇v∗ext	PROPN
ap-6142	271	14	·	·	PUNCT
ap-6142	271	15	v∗ext	v∗ext	PROPN
ap-6142	271	16	)	)	PUNCT
ap-6142	271	17	dx	dx	PROPN
ap-6142	272	1	dt	dt	PROPN
ap-6142	272	2	+	+	NUM
ap-6142	272	3	c(ξ	c(ξ	NOUN
ap-6142	272	4	)	)	PUNCT
ap-6142	272	5	∫	∫	PROPN
ap-6142	272	6	t∗	t∗	NOUN
ap-6142	272	7	0	0	NUM
ap-6142	272	8	‖u‖2	‖u‖2	ADJ
ap-6142	272	9	dt+	dt+	NOUN
ap-6142	272	10	∫	∫	PROPN
ap-6142	272	11	t∗	t∗	NOUN
ap-6142	272	12	0	0	NUM
ap-6142	273	1	∫	∫	PROPN
ap-6142	273	2	ω	ω	NUM
ap-6142	273	3	ν∇v∗ext	ν∇v∗ext	NOUN
ap-6142	273	4	:	:	PUNCT
ap-6142	273	5	∇u	∇u	PROPN
ap-6142	273	6	dx	dx	PROPN
ap-6142	274	1	dt	dt	NOUN
ap-6142	274	2	+	+	CCONJ
ap-6142	274	3	∫	∫	PROPN
ap-6142	274	4	t∗	t∗	NOUN
ap-6142	274	5	0	0	PUNCT
ap-6142	275	1	〈	〈	PROPN
ap-6142	275	2	f	f	X
ap-6142	275	3	,	,	PUNCT
ap-6142	275	4	u	u	NOUN
ap-6142	275	5	〉	〉	NOUN
ap-6142	275	6	dt	dt	NOUN
ap-6142	276	1	+	+	CCONJ
ap-6142	276	2	∫	∫	PROPN
ap-6142	276	3	t	t	PROPN
ap-6142	276	4	0	0	NUM
ap-6142	276	5	∫	∫	PROPN
ap-6142	276	6	γ2	γ2	PROPN
ap-6142	276	7	g	g	PROPN
ap-6142	276	8	·	·	PUNCT
ap-6142	276	9	u	u	NOUN
ap-6142	276	10	ds	ds	ADJ
ap-6142	276	11	dt+	dt+	NOUN
ap-6142	276	12	1	1	NUM
ap-6142	276	13	2	2	NUM
ap-6142	276	14	‖u(0)‖22	‖u(0)‖22	NOUN
ap-6142	276	15	.	.	PUNCT
ap-6142	277	1	(	(	PUNCT
ap-6142	277	2	18	18	NUM
ap-6142	277	3	)	)	PUNCT
ap-6142	277	4	(	(	PUNCT
ap-6142	277	5	note	note	VERB
ap-6142	277	6	that	that	SCONJ
ap-6142	277	7	ξ	ξ	PROPN
ap-6142	277	8	>	>	SYM
ap-6142	277	9	0	0	NUM
ap-6142	277	10	can	can	AUX
ap-6142	277	11	be	be	AUX
ap-6142	277	12	chosen	choose	VERB
ap-6142	277	13	arbitrarily	arbitrarily	ADV
ap-6142	277	14	small	small	ADJ
ap-6142	277	15	.	.	PUNCT
ap-6142	277	16	)	)	PUNCT
ap-6142	278	1	the	the	DET
ap-6142	278	2	first	first	ADJ
ap-6142	278	3	integral	integral	NOUN
ap-6142	278	4	on	on	ADP
ap-6142	278	5	the	the	DET
ap-6142	278	6	right	right	ADJ
ap-6142	278	7	hand	hand	NOUN
ap-6142	278	8	side	side	NOUN
ap-6142	278	9	satisfies	satisfy	VERB
ap-6142	278	10	the	the	DET
ap-6142	278	11	94	94	NUM
ap-6142	278	12	vol	vol	NOUN
ap-6142	278	13	.	.	PUNCT
ap-6142	279	1	61	61	NUM
ap-6142	279	2	special	special	ADJ
ap-6142	279	3	issue/2021	issue/2021	NOUN
ap-6142	279	4	modeling	modeling	NOUN
ap-6142	279	5	of	of	ADP
ap-6142	279	6	flows	flow	NOUN
ap-6142	279	7	through	through	ADP
ap-6142	279	8	a	a	DET
ap-6142	279	9	channel	channel	NOUN
ap-6142	279	10	inequality∫	inequality∫	ADV
ap-6142	279	11	γ2	γ2	NOUN
ap-6142	279	12	[	[	X
ap-6142	279	13	(	(	PUNCT
ap-6142	279	14	v∗ext	v∗ext	PROPN
ap-6142	279	15	+	+	CCONJ
ap-6142	279	16	u	u	NOUN
ap-6142	279	17	)	)	PUNCT
ap-6142	279	18	·	·	PUNCT
ap-6142	279	19	n]−	n]−	ADP
ap-6142	279	20	|v∗ext	|v∗ext	NOUN
ap-6142	279	21	+	+	CCONJ
ap-6142	279	22	u|2	u|2	PROPN
ap-6142	279	23	ds	ds	ADJ
ap-6142	279	24	≤	≤	NOUN
ap-6142	279	25	(	(	PUNCT
ap-6142	279	26	∫	∫	PROPN
ap-6142	279	27	γ2	γ2	PROPN
ap-6142	279	28	[	[	X
ap-6142	279	29	(	(	PUNCT
ap-6142	279	30	v∗ext	v∗ext	PROPN
ap-6142	279	31	+	+	CCONJ
ap-6142	279	32	u	u	NOUN
ap-6142	279	33	)	)	PUNCT
ap-6142	279	34	·	·	PUNCT
ap-6142	280	1	n]3−	n]3−	PROPN
ap-6142	280	2	ds	ds	ADJ
ap-6142	280	3	)	)	PUNCT
ap-6142	280	4	1	1	NUM
ap-6142	280	5	3	3	NUM
ap-6142	280	6	·	·	PUNCT
ap-6142	280	7	(	(	PUNCT
ap-6142	280	8	∫	∫	PROPN
ap-6142	280	9	γ2	γ2	PROPN
ap-6142	280	10	|v∗ext	|v∗ext	NOUN
ap-6142	281	1	+	+	CCONJ
ap-6142	281	2	u|3	u|3	ADJ
ap-6142	281	3	ds	ds	ADJ
ap-6142	281	4	)	)	PUNCT
ap-6142	281	5	2	2	NUM
ap-6142	281	6	3	3	NUM
ap-6142	281	7	.	.	PUNCT
ap-6142	282	1	(	(	PUNCT
ap-6142	282	2	19	19	NUM
ap-6142	282	3	)	)	PUNCT
ap-6142	282	4	since	since	SCONJ
ap-6142	282	5	v∗ext	v∗ext	PROPN
ap-6142	282	6	+	+	CCONJ
ap-6142	282	7	u	u	PROPN
ap-6142	282	8	∈kc	∈kc	PROPN
ap-6142	282	9	t	t	NOUN
ap-6142	282	10	,	,	PUNCT
ap-6142	282	11	there	there	PRON
ap-6142	282	12	exists	exist	VERB
ap-6142	282	13	a	a	DET
ap-6142	282	14	sequence	sequence	NOUN
ap-6142	282	15	{	{	PUNCT
ap-6142	282	16	uk	uk	PROPN
ap-6142	282	17	}	}	PUNCT
ap-6142	282	18	in	in	ADP
ap-6142	282	19	kc	kc	PROPN
ap-6142	282	20	t	t	PROPN
ap-6142	282	21	,	,	PUNCT
ap-6142	282	22	such	such	ADJ
ap-6142	282	23	that	that	SCONJ
ap-6142	282	24	uk	uk	PROPN
ap-6142	282	25	→	→	SYM
ap-6142	282	26	u	u	PROPN
ap-6142	282	27	(	(	PUNCT
ap-6142	282	28	for	for	ADP
ap-6142	282	29	k	k	PROPN
ap-6142	282	30	→	→	SYM
ap-6142	282	31	∞	∞	PROPN
ap-6142	282	32	)	)	PUNCT
ap-6142	282	33	in	in	ADP
ap-6142	282	34	the	the	DET
ap-6142	282	35	norm	norm	NOUN
ap-6142	282	36	of	of	ADP
ap-6142	282	37	w	w	PROPN
ap-6142	282	38	1,2(ω	1,2(ω	NUM
ap-6142	282	39	)	)	PUNCT
ap-6142	282	40	.	.	PUNCT
ap-6142	283	1	then	then	ADV
ap-6142	283	2	we	we	PRON
ap-6142	283	3	also	also	ADV
ap-6142	283	4	have(∫	have(∫	VERB
ap-6142	283	5	γ2	γ2	PROPN
ap-6142	284	1	[	[	X
ap-6142	284	2	(	(	PUNCT
ap-6142	284	3	v∗ext	v∗ext	PROPN
ap-6142	284	4	+	+	CCONJ
ap-6142	284	5	u	u	NOUN
ap-6142	284	6	)	)	PUNCT
ap-6142	284	7	·	·	PUNCT
ap-6142	284	8	n]3−	n]3−	PROPN
ap-6142	284	9	ds	ds	ADJ
ap-6142	284	10	)	)	PUNCT
ap-6142	284	11	1	1	NUM
ap-6142	284	12	3	3	NUM
ap-6142	284	13	=	=	SYM
ap-6142	284	14	lim	lim	PROPN
ap-6142	284	15	k→∞	k→∞	PROPN
ap-6142	284	16	(	(	PUNCT
ap-6142	284	17	∫	∫	PROPN
ap-6142	284	18	γ2	γ2	PROPN
ap-6142	285	1	[	[	X
ap-6142	285	2	(	(	PUNCT
ap-6142	285	3	v∗ext	v∗ext	PROPN
ap-6142	285	4	+	+	CCONJ
ap-6142	285	5	uk	uk	PROPN
ap-6142	285	6	)	)	PUNCT
ap-6142	285	7	·	·	PUNCT
ap-6142	286	1	n]3−	n]3−	PROPN
ap-6142	286	2	ds	ds	ADJ
ap-6142	286	3	)	)	PUNCT
ap-6142	286	4	1	1	NUM
ap-6142	286	5	3	3	NUM
ap-6142	286	6	.	.	PUNCT
ap-6142	287	1	to	to	ADP
ap-6142	287	2	each	each	DET
ap-6142	287	3	function	function	NOUN
ap-6142	287	4	uk	uk	PROPN
ap-6142	287	5	,	,	PUNCT
ap-6142	287	6	there	there	PRON
ap-6142	287	7	exist	exist	VERB
ap-6142	287	8	finite	finite	ADJ
ap-6142	287	9	families	family	NOUN
ap-6142	287	10	{	{	PUNCT
ap-6142	287	11	θki}nk	θki}nk	PROPN
ap-6142	287	12	i=1	i=1	PROPN
ap-6142	287	13	and	and	CCONJ
ap-6142	287	14	{	{	PUNCT
ap-6142	287	15	uki}nk	uki}nk	ADV
ap-6142	287	16	i=1	i=1	ADV
ap-6142	287	17	in	in	ADP
ap-6142	287	18	[	[	X
ap-6142	287	19	0	0	NUM
ap-6142	287	20	,	,	PUNCT
ap-6142	287	21	1	1	NUM
ap-6142	287	22	]	]	PUNCT
ap-6142	287	23	and	and	CCONJ
ap-6142	287	24	kt	kt	PROPN
ap-6142	287	25	,	,	PUNCT
ap-6142	287	26	respectively	respectively	ADV
ap-6142	287	27	,	,	PUNCT
ap-6142	287	28	such	such	ADJ
ap-6142	287	29	that	that	SCONJ
ap-6142	287	30	nk∑	nk∑	PRON
ap-6142	287	31	i=1	i=1	PRON
ap-6142	287	32	θki	θki	VERB
ap-6142	287	33	=	=	SYM
ap-6142	287	34	1	1	NUM
ap-6142	287	35	and	and	CCONJ
ap-6142	287	36	uk	uk	PROPN
ap-6142	287	37	=	=	NOUN
ap-6142	287	38	nk∑	nk∑	PROPN
ap-6142	287	39	i=1	i=1	PROPN
ap-6142	287	40	θkiuki	θkiuki	NOUN
ap-6142	287	41	.	.	PUNCT
ap-6142	288	1	then	then	ADV
ap-6142	288	2	,	,	PUNCT
ap-6142	288	3	applying	apply	VERB
ap-6142	288	4	minkowski	minkowski	PROPN
ap-6142	288	5	’s	’s	PART
ap-6142	288	6	inequality	inequality	NOUN
ap-6142	288	7	,	,	PUNCT
ap-6142	288	8	we	we	PRON
ap-6142	288	9	get(∫	get(∫	VERB
ap-6142	288	10	γ2	γ2	PROPN
ap-6142	288	11	[	[	X
ap-6142	288	12	(	(	PUNCT
ap-6142	288	13	v∗ext	v∗ext	PROPN
ap-6142	288	14	+	+	CCONJ
ap-6142	288	15	uk	uk	PROPN
ap-6142	288	16	)	)	PUNCT
ap-6142	288	17	·	·	PUNCT
ap-6142	289	1	n]3−	n]3−	PROPN
ap-6142	289	2	ds	ds	ADJ
ap-6142	289	3	)	)	PUNCT
ap-6142	289	4	1	1	NUM
ap-6142	289	5	3	3	NUM
ap-6142	289	6	=	=	SYM
ap-6142	289	7	(	(	PUNCT
ap-6142	289	8	∫	∫	PROPN
ap-6142	289	9	γ2	γ2	PROPN
ap-6142	290	1	[	[	X
ap-6142	290	2	nk∑	nk∑	PROPN
ap-6142	290	3	i=1	i=1	PROPN
ap-6142	290	4	θki(v∗ext	θki(v∗ext	PROPN
ap-6142	291	1	+	+	CCONJ
ap-6142	291	2	uki	uki	PROPN
ap-6142	291	3	)	)	PUNCT
ap-6142	291	4	·	·	PUNCT
ap-6142	292	1	n	n	CCONJ
ap-6142	292	2	]	]	SYM
ap-6142	292	3	3	3	NUM
ap-6142	292	4	−	−	NOUN
ap-6142	292	5	ds	ds	ADJ
ap-6142	292	6	)	)	PUNCT
ap-6142	292	7	1	1	NUM
ap-6142	292	8	3	3	NUM
ap-6142	292	9	≤	≤	NOUN
ap-6142	292	10	(	(	PUNCT
ap-6142	292	11	∫	∫	PROPN
ap-6142	292	12	γ2	γ2	PROPN
ap-6142	292	13	nk∑	nk∑	PROPN
ap-6142	292	14	i=1	i=1	PUNCT
ap-6142	293	1	[	[	X
ap-6142	293	2	θki(v∗ext	θki(v∗ext	X
ap-6142	293	3	+	+	CCONJ
ap-6142	293	4	uki	uki	PROPN
ap-6142	293	5	)	)	PUNCT
ap-6142	293	6	·	·	PUNCT
ap-6142	294	1	n]3−	n]3−	PROPN
ap-6142	294	2	ds	ds	ADJ
ap-6142	294	3	)	)	PUNCT
ap-6142	294	4	1	1	NUM
ap-6142	294	5	3	3	NUM
ap-6142	294	6	≤	≤	NUM
ap-6142	294	7	nk∑	nk∑	PRON
ap-6142	294	8	i=1	i=1	PROPN
ap-6142	295	1	(	(	PUNCT
ap-6142	296	1	∫	∫	PROPN
ap-6142	296	2	γ2	γ2	PROPN
ap-6142	296	3	[	[	X
ap-6142	296	4	θki(v∗ext	θki(v∗ext	PROPN
ap-6142	296	5	+	+	CCONJ
ap-6142	296	6	uki	uki	PROPN
ap-6142	296	7	)	)	PUNCT
ap-6142	296	8	·	·	PUNCT
ap-6142	297	1	n]3−	n]3−	PROPN
ap-6142	297	2	ds	ds	ADJ
ap-6142	297	3	)	)	PUNCT
ap-6142	297	4	1	1	NUM
ap-6142	297	5	3	3	NUM
ap-6142	297	6	=	=	SYM
ap-6142	297	7	nk∑	nk∑	PRON
ap-6142	297	8	i=1	i=1	PRON
ap-6142	297	9	θki	θki	X
ap-6142	297	10	(	(	PUNCT
ap-6142	297	11	∫	∫	PROPN
ap-6142	297	12	γ2	γ2	PROPN
ap-6142	297	13	[	[	X
ap-6142	297	14	(	(	PUNCT
ap-6142	297	15	v∗ext	v∗ext	PROPN
ap-6142	297	16	+	+	CCONJ
ap-6142	297	17	uki	uki	PROPN
ap-6142	297	18	)	)	PUNCT
ap-6142	297	19	·	·	PUNCT
ap-6142	297	20	n]3−	n]3−	PROPN
ap-6142	297	21	ds	ds	ADJ
ap-6142	297	22	)	)	PUNCT
ap-6142	297	23	1	1	NUM
ap-6142	297	24	3	3	NUM
ap-6142	297	25	≤	≤	NUM
ap-6142	297	26	nk∑	nk∑	PROPN
ap-6142	297	27	i=1	i=1	PROPN
ap-6142	297	28	θkiζ	θkiζ	PROPN
ap-6142	297	29	=	=	SYM
ap-6142	297	30	ζ	ζ	X
ap-6142	297	31	.	.	PUNCT
ap-6142	298	1	hence	hence	ADV
ap-6142	298	2	(	(	PUNCT
ap-6142	298	3	∫	∫	PROPN
ap-6142	298	4	γ2	γ2	PROPN
ap-6142	298	5	[	[	X
ap-6142	298	6	(	(	PUNCT
ap-6142	298	7	v∗ext	v∗ext	PROPN
ap-6142	298	8	+	+	CCONJ
ap-6142	298	9	u	u	NOUN
ap-6142	298	10	)	)	PUNCT
ap-6142	298	11	·	·	PUNCT
ap-6142	298	12	n]3−	n]3−	PROPN
ap-6142	298	13	ds	ds	ADJ
ap-6142	298	14	)	)	PUNCT
ap-6142	298	15	1	1	NUM
ap-6142	298	16	3	3	NUM
ap-6142	298	17	≤	≤	NUM
ap-6142	298	18	ζ	ζ	NOUN
ap-6142	298	19	,	,	PUNCT
ap-6142	298	20	(	(	PUNCT
ap-6142	298	21	20	20	NUM
ap-6142	298	22	)	)	PUNCT
ap-6142	298	23	too	too	ADV
ap-6142	298	24	.	.	PUNCT
ap-6142	299	1	note	note	VERB
ap-6142	299	2	that	that	SCONJ
ap-6142	299	3	this	this	PRON
ap-6142	299	4	is	be	AUX
ap-6142	299	5	a	a	DET
ap-6142	299	6	crucial	crucial	ADJ
ap-6142	299	7	part	part	NOUN
ap-6142	299	8	,	,	PUNCT
ap-6142	299	9	where	where	SCONJ
ap-6142	299	10	we	we	PRON
ap-6142	299	11	use	use	VERB
ap-6142	299	12	the	the	DET
ap-6142	299	13	fact	fact	NOUN
ap-6142	299	14	that	that	SCONJ
ap-6142	299	15	v∗ext	v∗ext	PROPN
ap-6142	299	16	+	+	NOUN
ap-6142	299	17	u	u	PROPN
ap-6142	299	18	lies	lie	VERB
ap-6142	299	19	in	in	ADP
ap-6142	299	20	kc	kc	PROPN
ap-6142	299	21	t	t	PROPN
ap-6142	299	22	.	.	PUNCT
ap-6142	300	1	the	the	DET
ap-6142	300	2	estimates	estimate	NOUN
ap-6142	300	3	,	,	PUNCT
ap-6142	300	4	following	follow	VERB
ap-6142	300	5	from	from	ADP
ap-6142	300	6	this	this	DET
ap-6142	300	7	information	information	NOUN
ap-6142	300	8	,	,	PUNCT
ap-6142	300	9	are	be	AUX
ap-6142	300	10	not	not	PART
ap-6142	300	11	available	available	ADJ
ap-6142	300	12	if	if	SCONJ
ap-6142	300	13	one	one	NUM
ap-6142	300	14	deals	deal	NOUN
ap-6142	300	15	with	with	ADP
ap-6142	300	16	the	the	DET
ap-6142	300	17	navier	navier	NOUN
ap-6142	300	18	–	–	PUNCT
ap-6142	300	19	stokes	stoke	VERB
ap-6142	300	20	equation	equation	NOUN
ap-6142	300	21	instead	instead	ADV
ap-6142	300	22	of	of	ADP
ap-6142	300	23	the	the	DET
ap-6142	300	24	navier	navier	NOUN
ap-6142	300	25	–	–	PUNCT
ap-6142	300	26	stokes	stoke	VERB
ap-6142	300	27	variational	variational	ADJ
ap-6142	300	28	inequality	inequality	NOUN
ap-6142	300	29	(	(	PUNCT
ap-6142	300	30	16	16	NUM
ap-6142	300	31	)	)	PUNCT
ap-6142	300	32	.	.	PUNCT
ap-6142	301	1	as	as	SCONJ
ap-6142	301	2	there	there	PRON
ap-6142	301	3	exists	exist	VERB
ap-6142	301	4	a	a	DET
ap-6142	301	5	continuous	continuous	ADJ
ap-6142	301	6	operator	operator	NOUN
ap-6142	301	7	of	of	ADP
ap-6142	301	8	traces	trace	NOUN
ap-6142	301	9	from	from	ADP
ap-6142	301	10	the	the	DET
ap-6142	301	11	sobolev	sobolev	NOUN
ap-6142	301	12	–	–	PUNCT
ap-6142	301	13	slobodetski	slobodetski	NOUN
ap-6142	301	14	spacew	spacew	NOUN
ap-6142	301	15	5/6,2(ω	5/6,2(ω	NOUN
ap-6142	301	16	)	)	PUNCT
ap-6142	301	17	to	to	ADP
ap-6142	301	18	l3(γ2	l3(γ2	NOUN
ap-6142	301	19	)	)	PUNCT
ap-6142	301	20	,	,	PUNCT
ap-6142	301	21	which	which	PRON
ap-6142	301	22	can	can	AUX
ap-6142	301	23	be	be	AUX
ap-6142	301	24	deduced	deduce	VERB
ap-6142	301	25	e.g.	e.g.	ADV
ap-6142	301	26	by	by	ADP
ap-6142	301	27	means	mean	NOUN
ap-6142	301	28	of	of	ADP
ap-6142	301	29	[	[	X
ap-6142	301	30	23	23	NUM
ap-6142	301	31	]	]	PUNCT
ap-6142	301	32	,	,	PUNCT
ap-6142	301	33	we	we	PRON
ap-6142	301	34	have(∫	have(∫	VERB
ap-6142	301	35	γ2	γ2	PROPN
ap-6142	302	1	[	[	X
ap-6142	302	2	(	(	PUNCT
ap-6142	302	3	v∗ext	v∗ext	PROPN
ap-6142	302	4	+	+	CCONJ
ap-6142	302	5	u	u	NOUN
ap-6142	302	6	)	)	PUNCT
ap-6142	302	7	·	·	PUNCT
ap-6142	302	8	n]3−	n]3−	PROPN
ap-6142	302	9	ds	ds	ADJ
ap-6142	302	10	)	)	PUNCT
ap-6142	302	11	1	1	NUM
ap-6142	302	12	3	3	NUM
ap-6142	302	13	(	(	PUNCT
ap-6142	302	14	∫	∫	PROPN
ap-6142	302	15	γ2	γ2	PROPN
ap-6142	302	16	|v∗ext	|v∗ext	NOUN
ap-6142	303	1	+	+	CCONJ
ap-6142	303	2	u|3	u|3	ADJ
ap-6142	303	3	ds	ds	ADJ
ap-6142	303	4	)	)	PUNCT
ap-6142	303	5	2	2	NUM
ap-6142	303	6	3	3	NUM
ap-6142	303	7	≤	≤	NOUN
ap-6142	303	8	ζ	ζ	NOUN
ap-6142	303	9	‖v∗ext	‖v∗ext	NOUN
ap-6142	303	10	+	+	CCONJ
ap-6142	303	11	u‖23	u‖23	NOUN
ap-6142	303	12	;	;	PUNCT
ap-6142	303	13	γ2	γ2	PROPN
ap-6142	303	14	≤	≤	PROPN
ap-6142	303	15	c	c	AUX
ap-6142	303	16	‖v∗ext	‖v∗ext	ADJ
ap-6142	303	17	+	+	CCONJ
ap-6142	303	18	u‖25/6,2	u‖25/6,2	ADJ
ap-6142	303	19	≤	≤	NOUN
ap-6142	303	20	c	c	NOUN
ap-6142	303	21	ζ	ζ	NOUN
ap-6142	303	22	‖v∗ext	‖v∗ext	NOUN
ap-6142	303	23	+	+	CCONJ
ap-6142	303	24	u‖	u‖	ADJ
ap-6142	303	25	1	1	NUM
ap-6142	303	26	3	3	NUM
ap-6142	303	27	2	2	NUM
ap-6142	303	28	‖v∗ext	‖v∗ext	NOUN
ap-6142	303	29	+	+	CCONJ
ap-6142	303	30	u‖	u‖	ADJ
ap-6142	303	31	5	5	NUM
ap-6142	303	32	3	3	NUM
ap-6142	303	33	1,2	1,2	NUM
ap-6142	303	34	≤	≤	NUM
ap-6142	303	35	c	c	NOUN
ap-6142	303	36	ζ	ζ	NOUN
ap-6142	303	37	‖v∗ext	‖v∗ext	NOUN
ap-6142	303	38	+	+	CCONJ
ap-6142	303	39	u‖	u‖	ADJ
ap-6142	303	40	1	1	NUM
ap-6142	303	41	3	3	NUM
ap-6142	303	42	2	2	NUM
ap-6142	303	43	(	(	PUNCT
ap-6142	303	44	‖v∗ext‖	‖v∗ext‖	PUNCT
ap-6142	303	45	5	5	NUM
ap-6142	303	46	3	3	NUM
ap-6142	303	47	1,2	1,2	NUM
ap-6142	303	48	+	+	CCONJ
ap-6142	303	49	‖∇u‖	‖∇u‖	NOUN
ap-6142	303	50	5	5	NUM
ap-6142	303	51	3	3	NUM
ap-6142	303	52	2	2	NUM
ap-6142	303	53	)	)	PUNCT
ap-6142	303	54	≤	≤	NOUN
ap-6142	303	55	ξ	ξ	DET
ap-6142	303	56	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	303	57	+	+	CCONJ
ap-6142	303	58	c(ξ	c(ξ	NOUN
ap-6142	303	59	)	)	PUNCT
ap-6142	303	60	ζ6	ζ6	VERB
ap-6142	303	61	‖v∗ext	‖v∗ext	ADJ
ap-6142	303	62	+	+	CCONJ
ap-6142	303	63	u‖22	u‖22	ADJ
ap-6142	303	64	+	+	CCONJ
ap-6142	303	65	‖v∗ext‖21,2	‖v∗ext‖21,2	PROPN
ap-6142	303	66	.	.	PUNCT
ap-6142	303	67	recall	recall	VERB
ap-6142	303	68	that	that	SCONJ
ap-6142	303	69	ζ	ζ	PROPN
ap-6142	303	70	∈	∈	PROPN
ap-6142	303	71	l∞(0	l∞(0	NOUN
ap-6142	303	72	,	,	PUNCT
ap-6142	303	73	t	t	NOUN
ap-6142	303	74	)	)	PUNCT
ap-6142	303	75	.	.	PUNCT
ap-6142	304	1	substituting	substitute	VERB
ap-6142	304	2	to	to	ADP
ap-6142	304	3	(	(	PUNCT
ap-6142	304	4	18	18	NUM
ap-6142	304	5	)	)	PUNCT
ap-6142	304	6	,	,	PUNCT
ap-6142	304	7	and	and	CCONJ
ap-6142	304	8	using	use	VERB
ap-6142	304	9	also	also	ADV
ap-6142	304	10	the	the	DET
ap-6142	304	11	estimates∫	estimates∫	NOUN
ap-6142	304	12	t∗	t∗	NOUN
ap-6142	304	13	0	0	NUM
ap-6142	304	14	∫	∫	PROPN
ap-6142	305	1	ω	ω	NUM
ap-6142	305	2	ν∇v∗ext	ν∇v∗ext	NOUN
ap-6142	305	3	:	:	PUNCT
ap-6142	306	1	∇u	∇u	PROPN
ap-6142	306	2	dx	dx	PROPN
ap-6142	306	3	dt	dt	X
ap-6142	306	4	≤	≤	NUM
ap-6142	306	5	∫	∫	PROPN
ap-6142	306	6	t∗	t∗	PROPN
ap-6142	306	7	0	0	PUNCT
ap-6142	306	8	ξ	ξ	DET
ap-6142	306	9	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	306	10	dt+	dt+	NOUN
ap-6142	306	11	c(ξ	c(ξ	NOUN
ap-6142	306	12	)	)	PUNCT
ap-6142	306	13	ν2	ν2	ADJ
ap-6142	306	14	∫	∫	PROPN
ap-6142	306	15	t∗	t∗	PROPN
ap-6142	306	16	0	0	NUM
ap-6142	306	17	‖∇v∗ext‖22	‖∇v∗ext‖22	NUM
ap-6142	306	18	dt	dt	X
ap-6142	306	19	=	=	SYM
ap-6142	306	20	∫	∫	PROPN
ap-6142	306	21	t∗	t∗	NOUN
ap-6142	306	22	0	0	PUNCT
ap-6142	306	23	ξ	ξ	DET
ap-6142	306	24	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	306	25	dt+	dt+	NOUN
ap-6142	306	26	c(ξ	c(ξ	NOUN
ap-6142	306	27	,	,	PUNCT
ap-6142	306	28	v∗ext),∣∣∣∣∫	v∗ext),∣∣∣∣∫	NOUN
ap-6142	306	29	t∗	t∗	NOUN
ap-6142	306	30	0	0	NUM
ap-6142	307	1	〈	〈	PROPN
ap-6142	307	2	∂tv∗ext	∂tv∗ext	PROPN
ap-6142	307	3	,	,	PUNCT
ap-6142	307	4	u	u	NOUN
ap-6142	307	5	〉	〉	NOUN
ap-6142	307	6	dt	dt	NOUN
ap-6142	307	7	∣∣∣∣	∣∣∣∣	PROPN
ap-6142	307	8	≤	≤	NUM
ap-6142	307	9	∫	∫	PROPN
ap-6142	307	10	t∗	t∗	PROPN
ap-6142	307	11	0	0	NUM
ap-6142	307	12	‖∂tv∗ext‖−1,2	‖∂tv∗ext‖−1,2	NUM
ap-6142	307	13	‖u‖1,2	‖u‖1,2	ADJ
ap-6142	307	14	dt	dt	X
ap-6142	307	15	≤	≤	NUM
ap-6142	307	16	c	c	NOUN
ap-6142	307	17	∫	∫	PROPN
ap-6142	307	18	t∗	t∗	NOUN
ap-6142	307	19	0	0	NUM
ap-6142	307	20	‖∂tv∗ext‖−1,2	‖∂tv∗ext‖−1,2	NUM
ap-6142	307	21	‖∇u‖2	‖∇u‖2	ADJ
ap-6142	307	22	dt	dt	ADJ
ap-6142	307	23	≤	≤	NUM
ap-6142	307	24	∫	∫	PROPN
ap-6142	307	25	t∗	t∗	NOUN
ap-6142	307	26	0	0	PUNCT
ap-6142	307	27	ξ	ξ	DET
ap-6142	307	28	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	307	29	dt+	dt+	NOUN
ap-6142	307	30	c(ξ	c(ξ	NOUN
ap-6142	307	31	)	)	PUNCT
ap-6142	307	32	∫	∫	PROPN
ap-6142	307	33	t∗	t∗	NOUN
ap-6142	307	34	0	0	NUM
ap-6142	308	1	‖∂tv∗ext‖2−1,2	‖∂tv∗ext‖2−1,2	ADJ
ap-6142	308	2	dt	dt	X
ap-6142	308	3	=	=	SYM
ap-6142	308	4	∫	∫	PROPN
ap-6142	308	5	t∗	t∗	NOUN
ap-6142	308	6	0	0	PUNCT
ap-6142	308	7	ξ	ξ	DET
ap-6142	308	8	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	308	9	dt+	dt+	NOUN
ap-6142	308	10	c(ξ	c(ξ	NOUN
ap-6142	308	11	,	,	PUNCT
ap-6142	308	12	v∗ext),∫	v∗ext),∫	ADJ
ap-6142	308	13	t∗	t∗	NOUN
ap-6142	308	14	0	0	NUM
ap-6142	308	15	∫	∫	PROPN
ap-6142	308	16	ω	ω	NUM
ap-6142	308	17	v∗ext	v∗ext	PROPN
ap-6142	308	18	·	·	PUNCT
ap-6142	309	1	∇u	∇u	PROPN
ap-6142	309	2	·	·	PUNCT
ap-6142	309	3	v∗ext	v∗ext	NOUN
ap-6142	309	4	dx	dx	PROPN
ap-6142	309	5	dt	dt	PROPN
ap-6142	310	1	≤	≤	NUM
ap-6142	310	2	∫	∫	PROPN
ap-6142	310	3	t∗	t∗	PROPN
ap-6142	310	4	0	0	NUM
ap-6142	310	5	‖∇u‖2	‖∇u‖2	PROPN
ap-6142	310	6	‖v∗ext‖24	‖v∗ext‖24	PROPN
ap-6142	310	7	dt	dt	NOUN
ap-6142	310	8	≤	≤	NUM
ap-6142	310	9	∫	∫	PROPN
ap-6142	310	10	t∗	t∗	PROPN
ap-6142	310	11	0	0	PUNCT
ap-6142	310	12	ξ	ξ	DET
ap-6142	310	13	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	310	14	dt+	dt+	NOUN
ap-6142	310	15	c(ξ	c(ξ	NOUN
ap-6142	310	16	)	)	PUNCT
ap-6142	310	17	∫	∫	PROPN
ap-6142	310	18	t∗	t∗	NOUN
ap-6142	310	19	0	0	NUM
ap-6142	310	20	‖v∗ext‖44	‖v∗ext‖44	NOUN
ap-6142	310	21	dt	dt	X
ap-6142	310	22	=	=	SYM
ap-6142	310	23	∫	∫	PROPN
ap-6142	310	24	t∗	t∗	NOUN
ap-6142	310	25	0	0	PUNCT
ap-6142	311	1	ξ	ξ	DET
ap-6142	311	2	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	311	3	dt+	dt+	NOUN
ap-6142	311	4	c(ξ	c(ξ	NOUN
ap-6142	311	5	,	,	PUNCT
ap-6142	311	6	v∗ext),∫	v∗ext),∫	ADJ
ap-6142	311	7	t∗	t∗	NOUN
ap-6142	311	8	0	0	NUM
ap-6142	311	9	∫	∫	PROPN
ap-6142	311	10	ω	ω	PROPN
ap-6142	311	11	(	(	PUNCT
ap-6142	311	12	v∗ext	v∗ext	PROPN
ap-6142	311	13	·	·	PUNCT
ap-6142	312	1	∇v∗ext	∇v∗ext	PROPN
ap-6142	312	2	·	·	PUNCT
ap-6142	312	3	v∗ext	v∗ext	PROPN
ap-6142	312	4	+	+	CCONJ
ap-6142	312	5	u	u	X
ap-6142	312	6	·	·	PUNCT
ap-6142	312	7	∇v∗ext	∇v∗ext	PROPN
ap-6142	312	8	·	·	PUNCT
ap-6142	312	9	v∗ext	v∗ext	PROPN
ap-6142	312	10	)	)	PUNCT
ap-6142	312	11	dx	dx	PROPN
ap-6142	312	12	dt	dt	X
ap-6142	312	13	≤	≤	PUNCT
ap-6142	312	14	c(v∗ext	c(v∗ext	NOUN
ap-6142	312	15	)	)	PUNCT
ap-6142	312	16	+	+	NUM
ap-6142	312	17	∫	∫	PROPN
ap-6142	312	18	t∗	t∗	NOUN
ap-6142	312	19	0	0	NUM
ap-6142	312	20	∫	∫	PROPN
ap-6142	312	21	ω	ω	PROPN
ap-6142	312	22	‖u‖4	‖u‖4	PROPN
ap-6142	312	23	‖∇v∗ext‖2	‖∇v∗ext‖2	PUNCT
ap-6142	312	24	‖v∗ext‖4	‖v∗ext‖4	NUM
ap-6142	313	1	dt	dt	PROPN
ap-6142	314	1	≤	≤	NUM
ap-6142	314	2	∫	∫	PROPN
ap-6142	314	3	t∗	t∗	NOUN
ap-6142	314	4	0	0	PUNCT
ap-6142	314	5	ξ	ξ	PRON
ap-6142	314	6	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	314	7	dt+	dt+	NOUN
ap-6142	314	8	c(ξ	c(ξ	NOUN
ap-6142	314	9	,	,	PUNCT
ap-6142	314	10	v∗ext),∫	v∗ext),∫	ADJ
ap-6142	314	11	t∗	t∗	NOUN
ap-6142	314	12	0	0	PUNCT
ap-6142	315	1	〈	〈	PROPN
ap-6142	315	2	f	f	X
ap-6142	315	3	,	,	PUNCT
ap-6142	315	4	u	u	NOUN
ap-6142	315	5	〉	〉	NOUN
ap-6142	315	6	dt	dt	NOUN
ap-6142	315	7	≤	≤	NUM
ap-6142	315	8	∫	∫	PROPN
ap-6142	315	9	t∗	t∗	PROPN
ap-6142	315	10	0	0	NUM
ap-6142	315	11	‖f‖−1,2	‖f‖−1,2	NOUN
ap-6142	315	12	‖u‖1,2	‖u‖1,2	ADJ
ap-6142	315	13	dt	dt	X
ap-6142	315	14	≤	≤	NUM
ap-6142	315	15	∫	∫	PROPN
ap-6142	315	16	t∗	t∗	PROPN
ap-6142	315	17	0	0	PUNCT
ap-6142	316	1	ξ	ξ	DET
ap-6142	316	2	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	316	3	dt+	dt+	NOUN
ap-6142	316	4	c(ξ	c(ξ	NOUN
ap-6142	316	5	,	,	PUNCT
ap-6142	316	6	f),∫	f),∫	PROPN
ap-6142	316	7	t∗	t∗	NOUN
ap-6142	316	8	0	0	NUM
ap-6142	316	9	∫	∫	PROPN
ap-6142	316	10	γ2	γ2	PROPN
ap-6142	316	11	g	g	PROPN
ap-6142	316	12	·	·	PUNCT
ap-6142	316	13	u	u	NOUN
ap-6142	316	14	ds	ds	NOUN
ap-6142	316	15	dt	dt	X
ap-6142	316	16	≤	≤	NUM
ap-6142	316	17	∫	∫	PROPN
ap-6142	316	18	t∗	t∗	NOUN
ap-6142	316	19	0	0	PUNCT
ap-6142	317	1	‖g‖4/3	‖g‖4/3	ADJ
ap-6142	317	2	;	;	PUNCT
ap-6142	317	3	γ2	γ2	PROPN
ap-6142	317	4	‖u‖4	‖u‖4	PROPN
ap-6142	317	5	;	;	PUNCT
ap-6142	317	6	γ2	γ2	PROPN
ap-6142	317	7	dt	dt	PROPN
ap-6142	317	8	≤	≤	NUM
ap-6142	317	9	∫	∫	PROPN
ap-6142	317	10	t∗	t∗	NOUN
ap-6142	317	11	0	0	PUNCT
ap-6142	318	1	‖g‖4/3	‖g‖4/3	ADJ
ap-6142	318	2	;	;	PUNCT
ap-6142	318	3	γ2	γ2	PROPN
ap-6142	318	4	‖u‖1,2	‖u‖1,2	NUM
ap-6142	318	5	dt	dt	X
ap-6142	318	6	≤	≤	PROPN
ap-6142	318	7	c	c	NOUN
ap-6142	318	8	∫	∫	PROPN
ap-6142	318	9	t∗	t∗	NOUN
ap-6142	318	10	0	0	PUNCT
ap-6142	318	11	‖g‖4/3	‖g‖4/3	ADJ
ap-6142	318	12	;	;	PUNCT
ap-6142	318	13	γ2	γ2	PROPN
ap-6142	318	14	‖∇u‖2	‖∇u‖2	PROPN
ap-6142	318	15	dt	dt	PROPN
ap-6142	318	16	≤	≤	NUM
ap-6142	318	17	∫	∫	PROPN
ap-6142	318	18	t∗	t∗	PROPN
ap-6142	318	19	0	0	PUNCT
ap-6142	318	20	ξ	ξ	DET
ap-6142	318	21	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	318	22	+	+	CCONJ
ap-6142	318	23	c(ξ	c(ξ	NOUN
ap-6142	318	24	,	,	PUNCT
ap-6142	318	25	g	g	NOUN
ap-6142	318	26	)	)	PUNCT
ap-6142	318	27	,	,	PUNCT
ap-6142	318	28	95	95	NUM
ap-6142	318	29	stanislav	stanislav	X
ap-6142	318	30	kračmar	kračmar	PROPN
ap-6142	318	31	,	,	PUNCT
ap-6142	318	32	jiří	jiří	NOUN
ap-6142	318	33	neustupa	neustupa	PROPN
ap-6142	318	34	acta	acta	PROPN
ap-6142	318	35	polytechnica	polytechnica	PROPN
ap-6142	318	36	where	where	SCONJ
ap-6142	318	37	c	c	PROPN
ap-6142	318	38	is	be	AUX
ap-6142	318	39	independent	independent	ADJ
ap-6142	318	40	of	of	ADP
ap-6142	318	41	t∗	t∗	PROPN
ap-6142	318	42	,	,	PUNCT
ap-6142	318	43	we	we	PRON
ap-6142	318	44	obtain	obtain	VERB
ap-6142	318	45	1	1	NUM
ap-6142	318	46	2	2	NUM
ap-6142	318	47	‖u(t∗)‖22	‖u(t∗)‖22	PROPN
ap-6142	318	48	+	+	CCONJ
ap-6142	318	49	(	(	PUNCT
ap-6142	318	50	ν	ν	X
ap-6142	318	51	−	−	PROPN
ap-6142	318	52	9ξ	9ξ	NUM
ap-6142	318	53	)	)	PUNCT
ap-6142	318	54	∫	∫	PROPN
ap-6142	319	1	t∗	t∗	NOUN
ap-6142	319	2	0	0	NUM
ap-6142	319	3	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	319	4	dt	dt	NOUN
ap-6142	320	1	+	+	NOUN
ap-6142	320	2	1	1	NUM
ap-6142	320	3	2	2	NUM
ap-6142	320	4	∫	∫	NOUN
ap-6142	320	5	t∗	t∗	NOUN
ap-6142	320	6	0	0	NUM
ap-6142	320	7	∫	∫	PROPN
ap-6142	320	8	γ1	γ1	PROPN
ap-6142	320	9	(	(	PUNCT
ap-6142	320	10	v∗	v∗	PROPN
ap-6142	320	11	·	·	PUNCT
ap-6142	320	12	n	n	CCONJ
ap-6142	320	13	)	)	PUNCT
ap-6142	320	14	|v∗|2	|v∗|2	NUM
ap-6142	320	15	ds	ds	ADJ
ap-6142	320	16	dt	dt	NOUN
ap-6142	320	17	≤	≤	NUM
ap-6142	320	18	c(ξ	c(ξ	NOUN
ap-6142	320	19	)	)	PUNCT
ap-6142	320	20	∫	∫	PROPN
ap-6142	320	21	t∗	t∗	NOUN
ap-6142	320	22	0	0	NUM
ap-6142	320	23	‖u‖2	‖u‖2	ADJ
ap-6142	320	24	dt+	dt+	NOUN
ap-6142	320	25	c(ξ	c(ξ	NOUN
ap-6142	320	26	,	,	PUNCT
ap-6142	320	27	v∗ext	v∗ext	PROPN
ap-6142	320	28	,	,	PUNCT
ap-6142	320	29	f	f	PROPN
ap-6142	320	30	,	,	PUNCT
ap-6142	320	31	g)+	g)+	ADJ
ap-6142	320	32	+	+	CCONJ
ap-6142	320	33	c(ξ	c(ξ	NOUN
ap-6142	320	34	)	)	PUNCT
ap-6142	320	35	∫	∫	PROPN
ap-6142	320	36	t∗	t∗	NOUN
ap-6142	320	37	0	0	NUM
ap-6142	320	38	ζ6(t	ζ6(t	NOUN
ap-6142	320	39	)	)	PUNCT
ap-6142	320	40	(	(	PUNCT
ap-6142	320	41	‖v∗ext	‖v∗ext	ADJ
ap-6142	320	42	+	+	CCONJ
ap-6142	320	43	u‖22	u‖22	ADJ
ap-6142	320	44	+	+	CCONJ
ap-6142	320	45	‖v∗ext‖21,2	‖v∗ext‖21,2	ADJ
ap-6142	320	46	)	)	PUNCT
ap-6142	320	47	dt	dt	X
ap-6142	321	1	+	+	NOUN
ap-6142	321	2	1	1	NUM
ap-6142	321	3	2	2	NUM
ap-6142	321	4	‖u(0)‖22	‖u(0)‖22	NOUN
ap-6142	321	5	.	.	PUNCT
ap-6142	322	1	(	(	PUNCT
ap-6142	322	2	21	21	NUM
ap-6142	322	3	)	)	PUNCT
ap-6142	322	4	choose	choose	VERB
ap-6142	322	5	ξ	ξ	NOUN
ap-6142	322	6	so	so	ADV
ap-6142	322	7	small	small	ADJ
ap-6142	322	8	that	that	SCONJ
ap-6142	322	9	ξ	ξ	X
ap-6142	322	10	<	<	X
ap-6142	322	11	1	1	NUM
ap-6142	322	12	18ν	18ν	NOUN
ap-6142	322	13	.	.	PUNCT
ap-6142	323	1	evaluating	evaluate	VERB
ap-6142	323	2	precisely	precisely	ADV
ap-6142	323	3	the	the	DET
ap-6142	323	4	right	right	ADJ
ap-6142	323	5	hand	hand	NOUN
ap-6142	323	6	side	side	NOUN
ap-6142	323	7	(	(	PUNCT
ap-6142	323	8	which	which	PRON
ap-6142	323	9	concerns	concern	VERB
ap-6142	323	10	especially	especially	ADV
ap-6142	323	11	c(ξ	c(ξ	NOUN
ap-6142	323	12	,	,	PUNCT
ap-6142	323	13	v∗ext	v∗ext	PROPN
ap-6142	323	14	,	,	PUNCT
ap-6142	323	15	f	f	PROPN
ap-6142	323	16	,	,	PUNCT
ap-6142	323	17	g	g	NOUN
ap-6142	323	18	)	)	PUNCT
ap-6142	323	19	)	)	PUNCT
ap-6142	323	20	,	,	PUNCT
ap-6142	323	21	we	we	PRON
ap-6142	323	22	can	can	AUX
ap-6142	323	23	rewrite	rewrite	VERB
ap-6142	323	24	the	the	DET
ap-6142	323	25	inequality	inequality	NOUN
ap-6142	323	26	in	in	ADP
ap-6142	323	27	the	the	DET
ap-6142	323	28	form	form	NOUN
ap-6142	323	29	(	(	PUNCT
ap-6142	323	30	17	17	NUM
ap-6142	323	31	)	)	PUNCT
ap-6142	323	32	.	.	PUNCT
ap-6142	324	1	omitting	omit	VERB
ap-6142	324	2	at	at	ADP
ap-6142	324	3	first	first	ADV
ap-6142	324	4	the	the	DET
ap-6142	324	5	second	second	ADJ
ap-6142	324	6	term	term	NOUN
ap-6142	324	7	on	on	ADP
ap-6142	324	8	the	the	DET
ap-6142	324	9	left	left	ADJ
ap-6142	324	10	hand	hand	NOUN
ap-6142	324	11	side	side	NOUN
ap-6142	324	12	(	(	PUNCT
ap-6142	324	13	i.e.	i.e.	X
ap-6142	324	14	the	the	DET
ap-6142	324	15	integral	integral	ADJ
ap-6142	324	16	of	of	ADP
ap-6142	324	17	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	324	18	)	)	PUNCT
ap-6142	324	19	and	and	CCONJ
ap-6142	324	20	applying	apply	VERB
ap-6142	324	21	the	the	DET
ap-6142	324	22	generalized	generalized	ADJ
ap-6142	324	23	gronwall	gronwall	ADJ
ap-6142	324	24	inequality	inequality	NOUN
ap-6142	324	25	,	,	PUNCT
ap-6142	324	26	we	we	PRON
ap-6142	324	27	obtain	obtain	VERB
ap-6142	324	28	the	the	DET
ap-6142	324	29	estimate	estimate	NOUN
ap-6142	324	30	of	of	ADP
ap-6142	324	31	u	u	NOUN
ap-6142	324	32	in	in	ADP
ap-6142	324	33	l∞(0	l∞(0	PRON
ap-6142	324	34	,	,	PUNCT
ap-6142	324	35	t	t	PROPN
ap-6142	324	36	;	;	PUNCT
ap-6142	324	37	l2(ω	l2(ω	X
ap-6142	324	38	)	)	PUNCT
ap-6142	324	39	)	)	PUNCT
ap-6142	324	40	in	in	ADP
ap-6142	324	41	terms	term	NOUN
ap-6142	324	42	of	of	ADP
ap-6142	324	43	the	the	DET
ap-6142	324	44	norms	norm	NOUN
ap-6142	324	45	of	of	ADP
ap-6142	324	46	ζ(t	ζ(t	PROPN
ap-6142	324	47	)	)	PUNCT
ap-6142	324	48	,	,	PUNCT
ap-6142	324	49	v∗ext	v∗ext	PROPN
ap-6142	324	50	,	,	PUNCT
ap-6142	324	51	f	f	PROPN
ap-6142	324	52	and	and	CCONJ
ap-6142	324	53	g	g	PROPN
ap-6142	324	54	in	in	ADP
ap-6142	324	55	appropriate	appropriate	ADJ
ap-6142	324	56	spaces	space	NOUN
ap-6142	324	57	,	,	PUNCT
ap-6142	324	58	which	which	PRON
ap-6142	324	59	are	be	AUX
ap-6142	324	60	all	all	PRON
ap-6142	324	61	finite	finite	ADJ
ap-6142	324	62	.	.	PUNCT
ap-6142	325	1	then	then	ADV
ap-6142	325	2	,	,	PUNCT
ap-6142	325	3	omitting	omit	VERB
ap-6142	325	4	the	the	DET
ap-6142	325	5	first	first	ADJ
ap-6142	325	6	term	term	NOUN
ap-6142	325	7	on	on	ADP
ap-6142	325	8	the	the	DET
ap-6142	325	9	left	left	ADJ
ap-6142	325	10	hand	hand	NOUN
ap-6142	325	11	side	side	NOUN
ap-6142	325	12	in	in	ADP
ap-6142	325	13	(	(	PUNCT
ap-6142	325	14	21	21	NUM
ap-6142	325	15	)	)	PUNCT
ap-6142	325	16	and	and	CCONJ
ap-6142	325	17	considering	consider	VERB
ap-6142	325	18	t∗	t∗	NOUN
ap-6142	325	19	→	→	SYM
ap-6142	325	20	t−	t−	PROPN
ap-6142	325	21	,	,	PUNCT
ap-6142	325	22	we	we	PRON
ap-6142	325	23	obtain	obtain	VERB
ap-6142	325	24	the	the	DET
ap-6142	325	25	estimate	estimate	NOUN
ap-6142	325	26	of	of	ADP
ap-6142	325	27	the	the	DET
ap-6142	325	28	norm	norm	NOUN
ap-6142	325	29	of	of	ADP
ap-6142	325	30	u	u	PROPN
ap-6142	325	31	in	in	ADP
ap-6142	325	32	l2(0	l2(0	NOUN
ap-6142	325	33	,	,	PUNCT
ap-6142	325	34	t	t	PROPN
ap-6142	325	35	;	;	PUNCT
ap-6142	325	36	w	w	PROPN
ap-6142	325	37	1,2(ω	1,2(ω	NUM
ap-6142	325	38	)	)	PUNCT
ap-6142	325	39	)	)	PUNCT
ap-6142	325	40	.	.	PUNCT
ap-6142	326	1	3.5	3.5	NUM
ap-6142	326	2	.	.	PUNCT
ap-6142	326	3	remark	remark	NOUN
ap-6142	326	4	by	by	ADP
ap-6142	326	5	analogy	analogy	NOUN
ap-6142	326	6	with	with	ADP
ap-6142	326	7	[	[	X
ap-6142	326	8	15	15	NUM
ap-6142	326	9	]	]	X
ap-6142	326	10	,	,	PUNCT
ap-6142	326	11	one	one	PRON
ap-6142	326	12	can	can	AUX
ap-6142	326	13	show	show	VERB
ap-6142	326	14	that	that	SCONJ
ap-6142	326	15	if	if	SCONJ
ap-6142	326	16	v	v	NOUN
ap-6142	326	17	is	be	AUX
ap-6142	326	18	a	a	DET
ap-6142	326	19	solution	solution	NOUN
ap-6142	326	20	of	of	ADP
ap-6142	326	21	a	a	DET
ap-6142	326	22	problem	problem	NOUN
ap-6142	326	23	(	(	PUNCT
ap-6142	326	24	p	p	NOUN
ap-6142	326	25	)	)	PUNCT
ap-6142	326	26	then	then	ADV
ap-6142	326	27	there	there	PRON
ap-6142	326	28	exists	exist	VERB
ap-6142	326	29	an	an	DET
ap-6142	326	30	associated	associated	ADJ
ap-6142	326	31	pressure	pressure	NOUN
ap-6142	326	32	p	p	NOUN
ap-6142	326	33	as	as	ADP
ap-6142	326	34	a	a	DET
ap-6142	326	35	distribution	distribution	NOUN
ap-6142	326	36	in	in	ADP
ap-6142	326	37	ω	ω	NUM
ap-6142	326	38	×	×	NOUN
ap-6142	326	39	(	(	PUNCT
ap-6142	326	40	0	0	NUM
ap-6142	326	41	,	,	PUNCT
ap-6142	326	42	t	t	NOUN
ap-6142	326	43	)	)	PUNCT
ap-6142	326	44	.	.	PUNCT
ap-6142	327	1	the	the	DET
ap-6142	327	2	pair	pair	NOUN
ap-6142	327	3	(	(	PUNCT
ap-6142	327	4	v	v	NOUN
ap-6142	327	5	,	,	PUNCT
ap-6142	327	6	p	p	NOUN
ap-6142	327	7	)	)	PUNCT
ap-6142	327	8	satisfies	satisfy	VERB
ap-6142	327	9	the	the	DET
ap-6142	327	10	equations	equation	NOUN
ap-6142	327	11	(	(	PUNCT
ap-6142	327	12	1	1	NUM
ap-6142	327	13	)	)	PUNCT
ap-6142	327	14	,	,	PUNCT
ap-6142	327	15	(	(	PUNCT
ap-6142	327	16	2	2	X
ap-6142	327	17	)	)	PUNCT
ap-6142	327	18	in	in	ADP
ap-6142	327	19	the	the	DET
ap-6142	327	20	sense	sense	NOUN
ap-6142	327	21	of	of	ADP
ap-6142	327	22	distributions	distribution	NOUN
ap-6142	327	23	in	in	ADP
ap-6142	327	24	ω	ω	NUM
ap-6142	327	25	×	×	NOUN
ap-6142	327	26	(	(	PUNCT
ap-6142	327	27	0	0	NUM
ap-6142	327	28	,	,	PUNCT
ap-6142	327	29	t	t	NOUN
ap-6142	327	30	)	)	PUNCT
ap-6142	327	31	.	.	PUNCT
ap-6142	328	1	if	if	SCONJ
ap-6142	328	2	,	,	PUNCT
ap-6142	328	3	moreover	moreover	ADV
ap-6142	328	4	,	,	PUNCT
ap-6142	328	5	∂tv	∂tv	PROPN
ap-6142	328	6	∈	∈	PROPN
ap-6142	328	7	l1(0	l1(0	PROPN
ap-6142	328	8	,	,	PUNCT
ap-6142	328	9	t	t	PROPN
ap-6142	328	10	;	;	PUNCT
ap-6142	328	11	w−1,2(ω	w−1,2(ω	ADJ
ap-6142	328	12	)	)	PUNCT
ap-6142	328	13	)	)	PUNCT
ap-6142	328	14	and	and	CCONJ
ap-6142	328	15	one	one	NUM
ap-6142	328	16	prescribes	prescribe	VERB
ap-6142	328	17	p	p	PROPN
ap-6142	328	18	∈	∈	PROPN
ap-6142	328	19	l1(0	l1(0	PROPN
ap-6142	328	20	,	,	PUNCT
ap-6142	328	21	t	t	PROPN
ap-6142	328	22	)	)	PUNCT
ap-6142	328	23	then	then	ADV
ap-6142	328	24	the	the	DET
ap-6142	328	25	pressure	pressure	NOUN
ap-6142	328	26	p	p	NOUN
ap-6142	328	27	can	can	AUX
ap-6142	328	28	be	be	AUX
ap-6142	328	29	chosen	choose	VERB
ap-6142	328	30	so	so	SCONJ
ap-6142	328	31	that∫	that∫	NOUN
ap-6142	328	32	ω	ω	PROPN
ap-6142	328	33	p(t	p(t	PROPN
ap-6142	328	34	)	)	PUNCT
ap-6142	328	35	dx	dx	PROPN
ap-6142	328	36	=	=	SYM
ap-6142	328	37	p(t	p(t	PROPN
ap-6142	328	38	)	)	PUNCT
ap-6142	328	39	for	for	ADP
ap-6142	328	40	a.a	a.a	PROPN
ap-6142	328	41	.	.	PROPN
ap-6142	328	42	t	t	PROPN
ap-6142	328	43	∈	∈	PROPN
ap-6142	328	44	(	(	PUNCT
ap-6142	328	45	0	0	NUM
ap-6142	328	46	,	,	PUNCT
ap-6142	328	47	t	t	NOUN
ap-6142	328	48	)	)	PUNCT
ap-6142	328	49	.	.	PUNCT
ap-6142	329	1	suppose	suppose	VERB
ap-6142	329	2	now	now	ADV
ap-6142	329	3	that	that	SCONJ
ap-6142	329	4	the	the	DET
ap-6142	329	5	solution	solution	NOUN
ap-6142	329	6	v	v	NOUN
ap-6142	329	7	has	have	VERB
ap-6142	329	8	these	these	DET
ap-6142	329	9	a	a	DET
ap-6142	329	10	posteriori	posteriori	NOUN
ap-6142	329	11	properties	property	NOUN
ap-6142	329	12	:	:	PUNCT
ap-6142	329	13	v	v	NUM
ap-6142	329	14	∈	∈	PROPN
ap-6142	329	15	l2(0	l2(0	NOUN
ap-6142	329	16	,	,	PUNCT
ap-6142	329	17	t	t	NOUN
ap-6142	329	18	;	;	PUNCT
ap-6142	329	19	w	w	ADP
ap-6142	329	20	2,2(ω	2,2(ω	NUM
ap-6142	329	21	)	)	PUNCT
ap-6142	329	22	)	)	PUNCT
ap-6142	329	23	,	,	PUNCT
ap-6142	329	24	∂tv	∂tv	PROPN
ap-6142	329	25	,	,	PUNCT
ap-6142	329	26	v	v	NOUN
ap-6142	329	27	·	·	PUNCT
ap-6142	330	1	∇v	∇v	ADV
ap-6142	330	2	,	,	PUNCT
ap-6142	330	3	f	f	PROPN
ap-6142	330	4	∈	∈	PROPN
ap-6142	330	5	l2(0	l2(0	NOUN
ap-6142	330	6	,	,	PUNCT
ap-6142	330	7	t	t	NOUN
ap-6142	330	8	;	;	PUNCT
ap-6142	330	9	l2(ω	l2(ω	NOUN
ap-6142	330	10	)	)	PUNCT
ap-6142	330	11	)	)	PUNCT
ap-6142	330	12	and	and	CCONJ
ap-6142	330	13	there	there	PRON
ap-6142	330	14	exists	exist	VERB
ap-6142	330	15	ε3	ε3	ADJ
ap-6142	330	16	>	>	X
ap-6142	330	17	0	0	NUM
ap-6142	330	18	such	such	ADJ
ap-6142	330	19	that	that	SCONJ
ap-6142	330	20	all	all	DET
ap-6142	330	21	φ	φ	PROPN
ap-6142	330	22	∈	∈	PROPN
ap-6142	330	23	v(t	v(t	PROPN
ap-6142	330	24	)	)	PUNCT
ap-6142	330	25	+	+	CCONJ
ap-6142	330	26	v	v	NOUN
ap-6142	330	27	,	,	PUNCT
ap-6142	330	28	whose	whose	DET
ap-6142	330	29	distance	distance	NOUN
ap-6142	330	30	from	from	ADP
ap-6142	330	31	v(t	v(t	NOUN
ap-6142	330	32	)	)	PUNCT
ap-6142	330	33	in	in	ADP
ap-6142	330	34	the	the	DET
ap-6142	330	35	w	w	PROPN
ap-6142	330	36	1,2	1,2	NUM
ap-6142	330	37	–	–	PUNCT
ap-6142	330	38	norm	norm	NOUN
ap-6142	330	39	is	be	AUX
ap-6142	330	40	less	less	ADJ
ap-6142	330	41	than	than	ADP
ap-6142	330	42	ε3	ε3	PROPN
ap-6142	330	43	,	,	PUNCT
ap-6142	330	44	belong	belong	VERB
ap-6142	330	45	to	to	ADP
ap-6142	330	46	kc	kc	PROPN
ap-6142	330	47	t	t	PROPN
ap-6142	330	48	for	for	ADP
ap-6142	330	49	a.a	a.a	PROPN
ap-6142	330	50	.	.	PROPN
ap-6142	330	51	t	t	PROPN
ap-6142	330	52	∈	∈	PROPN
ap-6142	330	53	(	(	PUNCT
ap-6142	330	54	0	0	NUM
ap-6142	330	55	,	,	PUNCT
ap-6142	330	56	t	t	NOUN
ap-6142	330	57	)	)	PUNCT
ap-6142	330	58	.	.	PUNCT
ap-6142	331	1	(	(	PUNCT
ap-6142	331	2	the	the	DET
ap-6142	331	3	last	last	ADJ
ap-6142	331	4	condition	condition	NOUN
ap-6142	331	5	means	mean	VERB
ap-6142	331	6	that	that	SCONJ
ap-6142	331	7	v(t	v(t	NOUN
ap-6142	331	8	)	)	PUNCT
ap-6142	331	9	lies	lie	VERB
ap-6142	331	10	“	"	PUNCT
ap-6142	331	11	uniformly	uniformly	ADV
ap-6142	331	12	”	"	PUNCT
ap-6142	331	13	in	in	ADP
ap-6142	331	14	the	the	DET
ap-6142	331	15	interior	interior	NOUN
ap-6142	331	16	of	of	ADP
ap-6142	331	17	kc	kc	PROPN
ap-6142	331	18	t	t	PROPN
ap-6142	331	19	.	.	PUNCT
ap-6142	331	20	)	)	PUNCT
ap-6142	332	1	then	then	ADV
ap-6142	332	2	one	one	PRON
ap-6142	332	3	can	can	AUX
ap-6142	332	4	prove	prove	VERB
ap-6142	332	5	that	that	SCONJ
ap-6142	332	6	the	the	DET
ap-6142	332	7	distribution	distribution	NOUN
ap-6142	332	8	p	p	NOUN
ap-6142	332	9	is	be	AUX
ap-6142	332	10	regular	regular	ADJ
ap-6142	332	11	and	and	CCONJ
ap-6142	332	12	can	can	AUX
ap-6142	332	13	be	be	AUX
ap-6142	332	14	represented	represent	VERB
ap-6142	332	15	by	by	ADP
ap-6142	332	16	a	a	DET
ap-6142	332	17	function	function	NOUN
ap-6142	332	18	from	from	ADP
ap-6142	332	19	l2(0	l2(0	PROPN
ap-6142	332	20	,	,	PUNCT
ap-6142	332	21	t	t	PROPN
ap-6142	332	22	;	;	PUNCT
ap-6142	332	23	w	w	PROPN
ap-6142	332	24	1,2(ω	1,2(ω	NUM
ap-6142	332	25	)	)	PUNCT
ap-6142	332	26	)	)	PUNCT
ap-6142	332	27	.	.	PUNCT
ap-6142	333	1	moreover	moreover	ADV
ap-6142	333	2	,	,	PUNCT
ap-6142	333	3	one	one	PRON
ap-6142	333	4	can	can	AUX
ap-6142	333	5	also	also	ADV
ap-6142	333	6	find	find	VERB
ap-6142	333	7	a	a	DET
ap-6142	333	8	function	function	NOUN
ap-6142	333	9	ϑ	ϑ	X
ap-6142	333	10	∈	∈	PROPN
ap-6142	333	11	l2(0	l2(0	NOUN
ap-6142	333	12	,	,	PUNCT
ap-6142	333	13	t	t	NOUN
ap-6142	333	14	)	)	PUNCT
ap-6142	333	15	so	so	SCONJ
ap-6142	333	16	that	that	SCONJ
ap-6142	333	17	ν	ν	X
ap-6142	333	18	∂v	∂v	PROPN
ap-6142	333	19	∂n	∂n	PROPN
ap-6142	334	1	−	−	PROPN
ap-6142	334	2	(	(	PUNCT
ap-6142	334	3	p+	p+	NOUN
ap-6142	334	4	ϑ)n	ϑ)n	NOUN
ap-6142	335	1	=	=	SYM
ap-6142	335	2	g	g	PROPN
ap-6142	335	3	(	(	PUNCT
ap-6142	335	4	22	22	NUM
ap-6142	335	5	)	)	PUNCT
ap-6142	335	6	holds	hold	VERB
ap-6142	335	7	a.e	a.e	PROPN
ap-6142	335	8	.	.	PROPN
ap-6142	336	1	in	in	ADP
ap-6142	336	2	γ2×	γ2×	PROPN
ap-6142	336	3	(	(	PUNCT
ap-6142	336	4	0	0	NUM
ap-6142	336	5	,	,	PUNCT
ap-6142	336	6	t	t	NOUN
ap-6142	336	7	)	)	PUNCT
ap-6142	336	8	.	.	PUNCT
ap-6142	337	1	this	this	PRON
ap-6142	337	2	shows	show	VERB
ap-6142	337	3	that	that	SCONJ
ap-6142	337	4	the	the	DET
ap-6142	337	5	concrete	concrete	ADJ
ap-6142	337	6	pressure	pressure	NOUN
ap-6142	337	7	,	,	PUNCT
ap-6142	337	8	obtained	obtain	VERB
ap-6142	337	9	from	from	ADP
ap-6142	337	10	the	the	DET
ap-6142	337	11	variational	variational	ADJ
ap-6142	337	12	inequality	inequality	NOUN
ap-6142	337	13	and	and	CCONJ
ap-6142	337	14	satisfying	satisfy	VERB
ap-6142	337	15	the	the	DET
ap-6142	337	16	outflow	outflow	ADJ
ap-6142	337	17	boundary	boundary	ADJ
ap-6142	337	18	condition	condition	NOUN
ap-6142	337	19	on	on	ADP
ap-6142	337	20	γ2	γ2	PROPN
ap-6142	337	21	×	×	NOUN
ap-6142	337	22	(	(	PUNCT
ap-6142	337	23	0	0	NUM
ap-6142	337	24	,	,	PUNCT
ap-6142	337	25	t	t	PROPN
ap-6142	337	26	)	)	PUNCT
ap-6142	337	27	,	,	PUNCT
ap-6142	337	28	is	be	AUX
ap-6142	337	29	unique	unique	ADJ
ap-6142	337	30	in	in	ADP
ap-6142	337	31	the	the	DET
ap-6142	337	32	sense	sense	NOUN
ap-6142	337	33	that	that	SCONJ
ap-6142	337	34	it	it	PRON
ap-6142	337	35	can	can	AUX
ap-6142	337	36	not	not	PART
ap-6142	337	37	be	be	AUX
ap-6142	337	38	changed	change	VERB
ap-6142	337	39	by	by	ADP
ap-6142	337	40	adding	add	VERB
ap-6142	337	41	an	an	DET
ap-6142	337	42	arbitrary	arbitrary	ADJ
ap-6142	337	43	constant	constant	ADJ
ap-6142	337	44	(	(	PUNCT
ap-6142	337	45	or	or	CCONJ
ap-6142	337	46	a	a	DET
ap-6142	337	47	function	function	NOUN
ap-6142	337	48	of	of	ADP
ap-6142	337	49	t	t	PROPN
ap-6142	337	50	)	)	PUNCT
ap-6142	337	51	.	.	PUNCT
ap-6142	338	1	4	4	X
ap-6142	338	2	.	.	X
ap-6142	338	3	the	the	DET
ap-6142	338	4	navier	navier	NOUN
ap-6142	338	5	–	–	PUNCT
ap-6142	338	6	stokes	stoke	VERB
ap-6142	338	7	inequality	inequality	NOUN
ap-6142	338	8	–	–	PUNCT
ap-6142	338	9	the	the	DET
ap-6142	338	10	steady	steady	ADJ
ap-6142	338	11	case	case	NOUN
ap-6142	338	12	in	in	ADP
ap-6142	338	13	both	both	CCONJ
ap-6142	338	14	the	the	DET
ap-6142	338	15	non	non	ADJ
ap-6142	338	16	-	-	ADJ
ap-6142	338	17	steady	steady	ADJ
ap-6142	338	18	and	and	CCONJ
ap-6142	338	19	steady	steady	ADJ
ap-6142	338	20	cases	case	NOUN
ap-6142	338	21	,	,	PUNCT
ap-6142	338	22	the	the	DET
ap-6142	338	23	solution	solution	NOUN
ap-6142	338	24	’s	’s	PART
ap-6142	338	25	proof	proof	NOUN
ap-6142	338	26	of	of	ADP
ap-6142	338	27	existence	existence	NOUN
ap-6142	338	28	relies	rely	VERB
ap-6142	338	29	on	on	ADP
ap-6142	338	30	the	the	DET
ap-6142	338	31	construction	construction	NOUN
ap-6142	338	32	of	of	ADP
ap-6142	338	33	appropriate	appropriate	ADJ
ap-6142	338	34	approximations	approximation	NOUN
ap-6142	338	35	,	,	PUNCT
ap-6142	338	36	the	the	DET
ap-6142	338	37	estimations	estimation	NOUN
ap-6142	338	38	of	of	ADP
ap-6142	338	39	the	the	DET
ap-6142	338	40	approximations	approximation	NOUN
ap-6142	338	41	that	that	SCONJ
ap-6142	338	42	in	in	ADP
ap-6142	338	43	some	some	DET
ap-6142	338	44	sense	sense	NOUN
ap-6142	338	45	copy	copy	VERB
ap-6142	338	46	a	a	DET
ap-6142	338	47	priori	priori	ADJ
ap-6142	338	48	estimates	estimate	NOUN
ap-6142	338	49	,	,	PUNCT
ap-6142	338	50	the	the	DET
ap-6142	338	51	deduction	deduction	NOUN
ap-6142	338	52	of	of	ADP
ap-6142	338	53	various	various	ADJ
ap-6142	338	54	types	type	NOUN
ap-6142	338	55	of	of	ADP
ap-6142	338	56	convergence	convergence	NOUN
ap-6142	338	57	of	of	ADP
ap-6142	338	58	a	a	DET
ap-6142	338	59	sequence	sequence	NOUN
ap-6142	338	60	(	(	PUNCT
ap-6142	338	61	or	or	CCONJ
ap-6142	338	62	a	a	DET
ap-6142	338	63	subsequence	subsequence	NOUN
ap-6142	338	64	)	)	PUNCT
ap-6142	338	65	of	of	ADP
ap-6142	338	66	approximations	approximation	NOUN
ap-6142	338	67	to	to	ADP
ap-6142	338	68	some	some	DET
ap-6142	338	69	limit	limit	NOUN
ap-6142	338	70	function	function	NOUN
ap-6142	338	71	,	,	PUNCT
ap-6142	338	72	and	and	CCONJ
ap-6142	338	73	the	the	DET
ap-6142	338	74	demonstration	demonstration	NOUN
ap-6142	338	75	that	that	PRON
ap-6142	338	76	the	the	DET
ap-6142	338	77	limit	limit	NOUN
ap-6142	338	78	is	be	AUX
ap-6142	338	79	a	a	DET
ap-6142	338	80	solution	solution	NOUN
ap-6142	338	81	whose	whose	DET
ap-6142	338	82	existence	existence	NOUN
ap-6142	338	83	one	one	PRON
ap-6142	338	84	wants	want	VERB
ap-6142	338	85	to	to	PART
ap-6142	338	86	prove	prove	VERB
ap-6142	338	87	.	.	PUNCT
ap-6142	339	1	as	as	SCONJ
ap-6142	339	2	we	we	PRON
ap-6142	339	3	have	have	AUX
ap-6142	339	4	already	already	ADV
ap-6142	339	5	mentioned	mention	VERB
ap-6142	339	6	in	in	ADP
ap-6142	339	7	subsections	subsection	NOUN
ap-6142	339	8	1.2	1.2	NUM
ap-6142	339	9	and	and	CCONJ
ap-6142	339	10	3.4	3.4	NUM
ap-6142	339	11	,	,	PUNCT
ap-6142	339	12	the	the	DET
ap-6142	339	13	crucial	crucial	ADJ
ap-6142	339	14	part	part	NOUN
ap-6142	339	15	is	be	AUX
ap-6142	339	16	the	the	DET
ap-6142	339	17	derivation	derivation	NOUN
ap-6142	339	18	of	of	ADP
ap-6142	339	19	a	a	DET
ap-6142	339	20	priori	priori	ADJ
ap-6142	339	21	estimates	estimate	NOUN
ap-6142	339	22	.	.	PUNCT
ap-6142	340	1	in	in	ADP
ap-6142	340	2	order	order	NOUN
ap-6142	340	3	to	to	PART
ap-6142	340	4	obtain	obtain	VERB
ap-6142	340	5	appropriate	appropriate	ADJ
ap-6142	340	6	estimates	estimate	NOUN
ap-6142	340	7	,	,	PUNCT
ap-6142	340	8	in	in	ADP
ap-6142	340	9	the	the	DET
ap-6142	340	10	non	non	ADJ
ap-6142	340	11	–	–	ADJ
ap-6142	340	12	steady	steady	ADJ
ap-6142	340	13	case	case	NOUN
ap-6142	340	14	,	,	PUNCT
ap-6142	340	15	one	one	PRON
ap-6142	340	16	can	can	AUX
ap-6142	340	17	apply	apply	VERB
ap-6142	340	18	gronwall	gronwall	ADJ
ap-6142	340	19	–	–	PUNCT
ap-6142	340	20	type	type	NOUN
ap-6142	340	21	inequalities	inequality	NOUN
ap-6142	340	22	in	in	ADP
ap-6142	340	23	order	order	NOUN
ap-6142	340	24	to	to	PART
ap-6142	340	25	obtain	obtain	VERB
ap-6142	340	26	a	a	DET
ap-6142	340	27	uniform	uniform	NOUN
ap-6142	340	28	(	(	PUNCT
ap-6142	340	29	in	in	ADP
ap-6142	340	30	time	time	NOUN
ap-6142	340	31	)	)	PUNCT
ap-6142	340	32	estimate	estimate	NOUN
ap-6142	340	33	of	of	ADP
ap-6142	340	34	the	the	DET
ap-6142	340	35	l2	l2	NOUN
ap-6142	340	36	–	–	PUNCT
ap-6142	340	37	norm	norm	NOUN
ap-6142	340	38	of	of	ADP
ap-6142	340	39	the	the	DET
ap-6142	340	40	solution	solution	NOUN
ap-6142	340	41	and	and	CCONJ
ap-6142	340	42	the	the	DET
ap-6142	340	43	estimate	estimate	NOUN
ap-6142	340	44	of	of	ADP
ap-6142	340	45	∫	∫	PROPN
ap-6142	340	46	t	t	PROPN
ap-6142	340	47	0	0	NUM
ap-6142	340	48	‖∇u‖	‖∇u‖	PROPN
ap-6142	340	49	2	2	NUM
ap-6142	340	50	2	2	NUM
ap-6142	340	51	dt	dt	NOUN
ap-6142	340	52	(	(	PUNCT
ap-6142	340	53	see	see	VERB
ap-6142	340	54	subsection	subsection	NOUN
ap-6142	340	55	3.4	3.4	NUM
ap-6142	340	56	)	)	PUNCT
ap-6142	340	57	.	.	PUNCT
ap-6142	341	1	in	in	ADP
ap-6142	341	2	the	the	DET
ap-6142	341	3	steady	steady	ADJ
ap-6142	341	4	case	case	NOUN
ap-6142	341	5	,	,	PUNCT
ap-6142	341	6	the	the	DET
ap-6142	341	7	estimates	estimate	NOUN
ap-6142	341	8	substantially	substantially	ADV
ap-6142	341	9	depend	depend	VERB
ap-6142	341	10	on	on	ADP
ap-6142	341	11	the	the	DET
ap-6142	341	12	properties	property	NOUN
ap-6142	341	13	of	of	ADP
ap-6142	341	14	the	the	DET
ap-6142	341	15	extended	extended	ADJ
ap-6142	341	16	function	function	NOUN
ap-6142	341	17	v∗ext	v∗ext	PROPN
ap-6142	341	18	,	,	PUNCT
ap-6142	341	19	introduced	introduce	VERB
ap-6142	341	20	in	in	ADP
ap-6142	341	21	subsection	subsection	NOUN
ap-6142	341	22	3.1	3.1	NUM
ap-6142	341	23	.	.	PUNCT
ap-6142	342	1	moreover	moreover	ADV
ap-6142	342	2	,	,	PUNCT
ap-6142	342	3	as	as	SCONJ
ap-6142	342	4	follows	follow	VERB
ap-6142	342	5	from	from	ADP
ap-6142	342	6	estimate	estimate	NOUN
ap-6142	342	7	(	(	PUNCT
ap-6142	342	8	25	25	NUM
ap-6142	342	9	)	)	PUNCT
ap-6142	342	10	,	,	PUNCT
ap-6142	342	11	we	we	PRON
ap-6142	342	12	are	be	AUX
ap-6142	342	13	able	able	ADJ
ap-6142	342	14	to	to	PART
ap-6142	342	15	prove	prove	VERB
ap-6142	342	16	the	the	DET
ap-6142	342	17	existence	existence	NOUN
ap-6142	342	18	of	of	ADP
ap-6142	342	19	the	the	DET
ap-6142	342	20	steady	steady	ADJ
ap-6142	342	21	solution	solution	NOUN
ap-6142	342	22	only	only	ADV
ap-6142	342	23	if	if	SCONJ
ap-6142	342	24	ζ	ζ	X
ap-6142	342	25	(	(	PUNCT
ap-6142	342	26	which	which	PRON
ap-6142	342	27	is	be	AUX
ap-6142	342	28	now	now	ADV
ap-6142	342	29	just	just	ADV
ap-6142	342	30	a	a	DET
ap-6142	342	31	positive	positive	ADJ
ap-6142	342	32	number	number	NOUN
ap-6142	342	33	)	)	PUNCT
ap-6142	342	34	is	be	AUX
ap-6142	342	35	“	"	PUNCT
ap-6142	342	36	sufficiently	sufficiently	ADV
ap-6142	342	37	small	small	ADJ
ap-6142	342	38	”	"	PUNCT
ap-6142	342	39	in	in	ADP
ap-6142	342	40	comparison	comparison	NOUN
ap-6142	342	41	to	to	ADP
ap-6142	342	42	ν	ν	PROPN
ap-6142	342	43	.	.	PUNCT
ap-6142	343	1	(	(	PUNCT
ap-6142	343	2	recall	recall	VERB
ap-6142	343	3	the	the	DET
ap-6142	343	4	ζ	ζ	NOUN
ap-6142	343	5	estimates	estimate	NOUN
ap-6142	343	6	possible	possible	ADJ
ap-6142	343	7	reverse	reverse	ADJ
ap-6142	343	8	flows	flow	NOUN
ap-6142	343	9	on	on	ADP
ap-6142	343	10	the	the	DET
ap-6142	343	11	outflow	outflow	ADJ
ap-6142	343	12	part	part	NOUN
ap-6142	343	13	γ2	γ2	NOUN
ap-6142	343	14	of	of	ADP
ap-6142	343	15	the	the	DET
ap-6142	343	16	boundary	boundary	NOUN
ap-6142	343	17	,	,	PUNCT
ap-6142	343	18	see	see	VERB
ap-6142	343	19	(	(	PUNCT
ap-6142	343	20	13	13	NUM
ap-6142	343	21	)	)	PUNCT
ap-6142	343	22	.	.	PUNCT
ap-6142	343	23	)	)	PUNCT
ap-6142	344	1	the	the	DET
ap-6142	344	2	extended	extend	VERB
ap-6142	344	3	function	function	NOUN
ap-6142	344	4	v∗ext	v∗ext	PROPN
ap-6142	344	5	should	should	AUX
ap-6142	344	6	now	now	ADV
ap-6142	344	7	be	be	AUX
ap-6142	344	8	naturally	naturally	ADV
ap-6142	344	9	time	time	NOUN
ap-6142	344	10	–	–	PUNCT
ap-6142	344	11	independent	independent	ADJ
ap-6142	344	12	,	,	PUNCT
ap-6142	344	13	and	and	CCONJ
ap-6142	344	14	should	should	AUX
ap-6142	344	15	be	be	AUX
ap-6142	344	16	constructed	construct	VERB
ap-6142	344	17	so	so	SCONJ
ap-6142	344	18	that	that	SCONJ
ap-6142	344	19	the	the	DET
ap-6142	344	20	integral	integral	ADJ
ap-6142	344	21	∫	∫	PROPN
ap-6142	344	22	ω	ω	NUM
ap-6142	344	23	u	u	PROPN
ap-6142	344	24	·	·	PUNCT
ap-6142	344	25	∇u	∇u	PROPN
ap-6142	344	26	·	·	PUNCT
ap-6142	344	27	v	v	NUM
ap-6142	344	28	∗	∗	NOUN
ap-6142	344	29	ext	ext	NOUN
ap-6142	344	30	dx	dx	PROPN
ap-6142	344	31	is	be	AUX
ap-6142	344	32	“	"	PUNCT
ap-6142	344	33	sufficiently	sufficiently	ADV
ap-6142	344	34	small	small	ADJ
ap-6142	344	35	”	"	PUNCT
ap-6142	344	36	in	in	ADP
ap-6142	344	37	comparison	comparison	NOUN
ap-6142	344	38	with	with	ADP
ap-6142	344	39	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	344	40	for	for	ADP
ap-6142	344	41	all	all	DET
ap-6142	344	42	u	u	NOUN
ap-6142	344	43	∈	∈	PROPN
ap-6142	344	44	v	v	NOUN
ap-6142	344	45	.	.	PUNCT
ap-6142	345	1	the	the	DET
ap-6142	345	2	reasons	reason	NOUN
ap-6142	345	3	are	be	AUX
ap-6142	345	4	the	the	DET
ap-6142	345	5	same	same	ADJ
ap-6142	345	6	as	as	ADP
ap-6142	345	7	in	in	ADP
ap-6142	345	8	the	the	DET
ap-6142	345	9	case	case	NOUN
ap-6142	345	10	of	of	ADP
ap-6142	345	11	the	the	DET
ap-6142	345	12	steady	steady	ADJ
ap-6142	345	13	navier	navier	NOUN
ap-6142	345	14	–	–	PUNCT
ap-6142	345	15	stokes	stoke	NOUN
ap-6142	345	16	problem	problem	NOUN
ap-6142	345	17	with	with	ADP
ap-6142	345	18	inhomogeneous	inhomogeneous	ADJ
ap-6142	345	19	dirichlet	dirichlet	NOUN
ap-6142	345	20	–	–	PUNCT
ap-6142	345	21	type	type	NOUN
ap-6142	345	22	boundary	boundary	ADJ
ap-6142	345	23	condition	condition	NOUN
ap-6142	345	24	on	on	ADP
ap-6142	345	25	the	the	DET
ap-6142	345	26	whole	whole	ADJ
ap-6142	345	27	boundary	boundary	NOUN
ap-6142	345	28	of	of	ADP
ap-6142	345	29	ω	ω	PROPN
ap-6142	345	30	,	,	PUNCT
ap-6142	345	31	see	see	VERB
ap-6142	345	32	e.g.	e.g.	ADV
ap-6142	345	33	[	[	X
ap-6142	345	34	21	21	NUM
ap-6142	345	35	,	,	PUNCT
ap-6142	345	36	chapter	chapter	NOUN
ap-6142	345	37	ix	ix	X
ap-6142	345	38	]	]	PUNCT
ap-6142	345	39	for	for	ADP
ap-6142	345	40	the	the	DET
ap-6142	345	41	detailed	detailed	ADJ
ap-6142	345	42	explanation	explanation	NOUN
ap-6142	345	43	.	.	PUNCT
ap-6142	346	1	it	it	PRON
ap-6142	346	2	follows	follow	VERB
ap-6142	346	3	from	from	ADP
ap-6142	346	4	the	the	DET
ap-6142	346	5	paper	paper	NOUN
ap-6142	346	6	[	[	X
ap-6142	346	7	14	14	NUM
ap-6142	346	8	]	]	PUNCT
ap-6142	346	9	that	that	SCONJ
ap-6142	346	10	this	this	DET
ap-6142	346	11	condition	condition	NOUN
ap-6142	346	12	of	of	ADP
ap-6142	346	13	“	"	PUNCT
ap-6142	346	14	sufficient	sufficient	ADJ
ap-6142	346	15	smallness	smallness	NOUN
ap-6142	346	16	”	"	PUNCT
ap-6142	346	17	of	of	ADP
ap-6142	346	18	the	the	DET
ap-6142	346	19	aforementioned	aforementioned	ADJ
ap-6142	346	20	integral	integral	NOUN
ap-6142	346	21	is	be	AUX
ap-6142	346	22	in	in	ADP
ap-6142	346	23	fact	fact	NOUN
ap-6142	346	24	not	not	PART
ap-6142	346	25	an	an	DET
ap-6142	346	26	obstacle	obstacle	NOUN
ap-6142	346	27	.	.	PUNCT
ap-6142	347	1	concretely	concretely	ADV
ap-6142	347	2	,	,	PUNCT
ap-6142	347	3	it	it	PRON
ap-6142	347	4	is	be	AUX
ap-6142	347	5	shown	show	VERB
ap-6142	347	6	in	in	ADP
ap-6142	347	7	[	[	X
ap-6142	347	8	14	14	NUM
ap-6142	347	9	]	]	PUNCT
ap-6142	347	10	that	that	SCONJ
ap-6142	347	11	if	if	SCONJ
ap-6142	347	12	v∗	v∗	PROPN
ap-6142	347	13	satisfies	satisfy	VERB
ap-6142	347	14	the	the	DET
ap-6142	347	15	condition	condition	NOUN
ap-6142	347	16	(	(	PUNCT
ap-6142	347	17	?	?	PUNCT
ap-6142	347	18	)	)	PUNCT
ap-6142	348	1	v∗	v∗	PROPN
ap-6142	348	2	can	can	AUX
ap-6142	348	3	be	be	AUX
ap-6142	348	4	extended	extend	VERB
ap-6142	348	5	from	from	ADP
ap-6142	348	6	γ1	γ1	PROPN
ap-6142	348	7	onto	onto	ADP
ap-6142	348	8	the	the	DET
ap-6142	348	9	whole	whole	ADJ
ap-6142	348	10	boundary	boundary	NOUN
ap-6142	348	11	∂ω	∂ω	PROPN
ap-6142	348	12	so	so	SCONJ
ap-6142	348	13	that	that	SCONJ
ap-6142	348	14	the	the	DET
ap-6142	348	15	extended	extended	ADJ
ap-6142	348	16	function	function	NOUN
ap-6142	348	17	belongs	belong	VERB
ap-6142	348	18	to	to	ADP
ap-6142	348	19	w	w	PROPN
ap-6142	348	20	1/2,2(∂ω	1/2,2(∂ω	NUM
ap-6142	348	21	)	)	PUNCT
ap-6142	348	22	is	be	AUX
ap-6142	348	23	equal	equal	ADJ
ap-6142	348	24	to	to	ADP
ap-6142	348	25	zero	zero	NUM
ap-6142	348	26	on	on	ADP
ap-6142	348	27	γ0	γ0	NOUN
ap-6142	348	28	and	and	CCONJ
ap-6142	348	29	its	its	PRON
ap-6142	348	30	flux	flux	NOUN
ap-6142	348	31	through	through	ADP
ap-6142	348	32	∂ω	∂ω	PROPN
ap-6142	348	33	is	be	AUX
ap-6142	348	34	zero	zero	NUM
ap-6142	348	35	,	,	PUNCT
ap-6142	348	36	then	then	ADV
ap-6142	348	37	the	the	DET
ap-6142	348	38	extension	extension	NOUN
ap-6142	348	39	v∗ext	v∗ext	PROPN
ap-6142	348	40	can	can	AUX
ap-6142	348	41	be	be	AUX
ap-6142	348	42	constructed	construct	VERB
ap-6142	348	43	so	so	SCONJ
ap-6142	348	44	that	that	SCONJ
ap-6142	348	45	given	give	VERB
ap-6142	348	46	δ	δ	PROPN
ap-6142	348	47	>	>	X
ap-6142	348	48	0	0	PROPN
ap-6142	348	49	,	,	PUNCT
ap-6142	348	50	v∗ext	v∗ext	PROPN
ap-6142	348	51	∈w	∈w	PROPN
ap-6142	348	52	1,2(ω	1,2(ω	ADV
ap-6142	348	53	)	)	PUNCT
ap-6142	348	54	,	,	PUNCT
ap-6142	348	55	v∗ext	v∗ext	PROPN
ap-6142	348	56	is	be	AUX
ap-6142	348	57	divergence	divergence	NOUN
ap-6142	348	58	–	–	PUNCT
ap-6142	348	59	free	free	ADJ
ap-6142	348	60	and∫	and∫	PROPN
ap-6142	348	61	ω	ω	PROPN
ap-6142	348	62	u1	u1	NOUN
ap-6142	348	63	·	·	PUNCT
ap-6142	348	64	∇u2	∇u2	NUM
ap-6142	348	65	·	·	PUNCT
ap-6142	349	1	v∗ext	v∗ext	NOUN
ap-6142	349	2	dx	dx	PROPN
ap-6142	349	3	≤	≤	PROPN
ap-6142	349	4	δ	δ	PROPN
ap-6142	349	5	‖∇u1‖2	‖∇u1‖2	PUNCT
ap-6142	350	1	‖∇u2‖2	‖∇u2‖2	PROPN
ap-6142	350	2	(	(	PUNCT
ap-6142	350	3	23	23	NUM
ap-6142	350	4	)	)	PUNCT
ap-6142	350	5	for	for	ADP
ap-6142	350	6	all	all	DET
ap-6142	350	7	u1	u1	NOUN
ap-6142	350	8	,	,	PUNCT
ap-6142	350	9	u2	u2	PROPN
ap-6142	350	10	∈	∈	PROPN
ap-6142	350	11	v	v	NOUN
ap-6142	350	12	.	.	PUNCT
ap-6142	351	1	this	this	PRON
ap-6142	351	2	is	be	AUX
ap-6142	351	3	the	the	DET
ap-6142	351	4	analogue	analogue	NOUN
ap-6142	351	5	of	of	ADP
ap-6142	351	6	the	the	DET
ap-6142	351	7	so	so	ADV
ap-6142	351	8	called	call	VERB
ap-6142	351	9	leray	leray	ADJ
ap-6142	351	10	–	–	PUNCT
ap-6142	351	11	hopf	hopf	ADJ
ap-6142	351	12	inequality	inequality	NOUN
ap-6142	351	13	,	,	PUNCT
ap-6142	351	14	see	see	VERB
ap-6142	351	15	[	[	X
ap-6142	351	16	21	21	NUM
ap-6142	351	17	]	]	PUNCT
ap-6142	351	18	.	.	PUNCT
ap-6142	352	1	let	let	VERB
ap-6142	352	2	us	we	PRON
ap-6142	352	3	show	show	VERB
ap-6142	352	4	how	how	SCONJ
ap-6142	352	5	the	the	DET
ap-6142	352	6	a	a	DET
ap-6142	352	7	priori	priori	ADJ
ap-6142	352	8	estimate	estimate	NOUN
ap-6142	352	9	looks	look	VERB
ap-6142	352	10	.	.	PUNCT
ap-6142	353	1	obviously	obviously	ADV
ap-6142	353	2	,	,	PUNCT
ap-6142	353	3	in	in	ADP
ap-6142	353	4	the	the	DET
ap-6142	353	5	steady	steady	ADJ
ap-6142	353	6	case	case	NOUN
ap-6142	353	7	,	,	PUNCT
ap-6142	353	8	ζ	ζ	NOUN
ap-6142	353	9	is	be	AUX
ap-6142	353	10	just	just	ADV
ap-6142	353	11	a	a	DET
ap-6142	353	12	number	number	NOUN
ap-6142	353	13	and	and	CCONJ
ap-6142	353	14	set	set	VERB
ap-6142	353	15	kc	kc	PROPN
ap-6142	353	16	t	t	PROPN
ap-6142	353	17	is	be	AUX
ap-6142	353	18	independent	independent	ADJ
ap-6142	353	19	of	of	ADP
ap-6142	353	20	t.	t.	PROPN
ap-6142	354	1	hence	hence	ADV
ap-6142	354	2	we	we	PRON
ap-6142	354	3	further	far	ADV
ap-6142	354	4	on	on	ADP
ap-6142	354	5	use	use	VERB
ap-6142	354	6	the	the	DET
ap-6142	354	7	notation	notation	NOUN
ap-6142	354	8	kc	kc	PROPN
ap-6142	354	9	instead	instead	ADV
ap-6142	354	10	of	of	ADP
ap-6142	354	11	kc	kc	PROPN
ap-6142	354	12	t	t	PROPN
ap-6142	354	13	.	.	PUNCT
ap-6142	355	1	the	the	DET
ap-6142	355	2	“	"	PUNCT
ap-6142	355	3	steady	steady	ADJ
ap-6142	355	4	state	state	NOUN
ap-6142	355	5	version	version	NOUN
ap-6142	355	6	”	"	PUNCT
ap-6142	355	7	of	of	ADP
ap-6142	355	8	inequality	inequality	NOUN
ap-6142	355	9	(	(	PUNCT
ap-6142	355	10	16	16	NUM
ap-6142	355	11	)	)	PUNCT
ap-6142	355	12	is∫	is∫	PROPN
ap-6142	355	13	ω	ω	NUM
ap-6142	355	14	v	v	NOUN
ap-6142	355	15	·	·	PUNCT
ap-6142	355	16	∇v	∇v	NOUN
ap-6142	355	17	·	·	PUNCT
ap-6142	355	18	(	(	PUNCT
ap-6142	355	19	w	w	NOUN
ap-6142	355	20	−	−	PROPN
ap-6142	355	21	v	v	NOUN
ap-6142	355	22	)	)	PUNCT
ap-6142	355	23	dx+	dx+	NOUN
ap-6142	355	24	∫	∫	PROPN
ap-6142	355	25	ω	ω	PROPN
ap-6142	355	26	ν∇v	ν∇v	X
ap-6142	355	27	·	·	PUNCT
ap-6142	355	28	∇(w	∇(w	ADJ
ap-6142	355	29	−	−	PROPN
ap-6142	355	30	v	v	NOUN
ap-6142	355	31	)	)	PUNCT
ap-6142	355	32	dx	dx	PROPN
ap-6142	355	33	≥	≥	NUM
ap-6142	355	34	〈	〈	PROPN
ap-6142	355	35	f	f	PROPN
ap-6142	355	36	,	,	PUNCT
ap-6142	355	37	w	w	PROPN
ap-6142	355	38	−	−	PROPN
ap-6142	355	39	v〉+	v〉+	NUM
ap-6142	355	40	∫	∫	NOUN
ap-6142	355	41	γ2	γ2	PROPN
ap-6142	355	42	g	g	PROPN
ap-6142	355	43	·	·	PUNCT
ap-6142	355	44	(	(	PUNCT
ap-6142	355	45	w	w	NOUN
ap-6142	355	46	−	−	PROPN
ap-6142	355	47	v	v	NOUN
ap-6142	355	48	)	)	PUNCT
ap-6142	355	49	ds	ds	NOUN
ap-6142	355	50	.	.	PUNCT
ap-6142	356	1	(	(	PUNCT
ap-6142	356	2	24	24	NUM
ap-6142	356	3	)	)	PUNCT
ap-6142	356	4	the	the	DET
ap-6142	356	5	solution	solution	NOUN
ap-6142	356	6	v	v	ADP
ap-6142	356	7	lies	lie	VERB
ap-6142	356	8	inkc	inkc	PROPN
ap-6142	356	9	and	and	CCONJ
ap-6142	356	10	the	the	DET
ap-6142	356	11	inequality	inequality	NOUN
ap-6142	356	12	is	be	AUX
ap-6142	356	13	required	require	VERB
ap-6142	356	14	to	to	PART
ap-6142	356	15	be	be	AUX
ap-6142	356	16	satisfied	satisfied	ADJ
ap-6142	356	17	for	for	ADP
ap-6142	356	18	all	all	DET
ap-6142	356	19	w	w	PROPN
ap-6142	356	20	∈kc	∈kc	NOUN
ap-6142	356	21	.	.	PUNCT
ap-6142	357	1	writing	write	VERB
ap-6142	357	2	v	v	NOUN
ap-6142	357	3	in	in	ADP
ap-6142	357	4	the	the	DET
ap-6142	357	5	form	form	NOUN
ap-6142	357	6	v∗ext	v∗ext	PROPN
ap-6142	357	7	+	+	CCONJ
ap-6142	357	8	u	u	NOUN
ap-6142	357	9	,	,	PUNCT
ap-6142	357	10	where	where	SCONJ
ap-6142	357	11	u	u	PROPN
ap-6142	357	12	∈	∈	PROPN
ap-6142	357	13	v	v	NOUN
ap-6142	357	14	,	,	PUNCT
ap-6142	357	15	using	use	VERB
ap-6142	357	16	inequality	inequality	NOUN
ap-6142	357	17	(	(	PUNCT
ap-6142	357	18	24	24	NUM
ap-6142	357	19	)	)	PUNCT
ap-6142	357	20	with	with	ADP
ap-6142	357	21	96	96	NUM
ap-6142	357	22	vol	vol	NOUN
ap-6142	357	23	.	.	PUNCT
ap-6142	358	1	61	61	NUM
ap-6142	358	2	special	special	ADJ
ap-6142	358	3	issue/2021	issue/2021	NOUN
ap-6142	358	4	modeling	modeling	NOUN
ap-6142	358	5	of	of	ADP
ap-6142	358	6	flows	flow	NOUN
ap-6142	358	7	through	through	ADP
ap-6142	358	8	a	a	DET
ap-6142	358	9	channel	channel	NOUN
ap-6142	358	10	w	w	NOUN
ap-6142	358	11	=	=	SYM
ap-6142	358	12	v∗ext	v∗ext	PROPN
ap-6142	358	13	,	,	PUNCT
ap-6142	358	14	and	and	CCONJ
ap-6142	358	15	applying	apply	VERB
ap-6142	358	16	(	(	PUNCT
ap-6142	358	17	19	19	NUM
ap-6142	358	18	)	)	PUNCT
ap-6142	358	19	,	,	PUNCT
ap-6142	358	20	(	(	PUNCT
ap-6142	358	21	20	20	NUM
ap-6142	358	22	)	)	PUNCT
ap-6142	358	23	and	and	CCONJ
ap-6142	358	24	(	(	PUNCT
ap-6142	358	25	23	23	NUM
ap-6142	358	26	)	)	PUNCT
ap-6142	358	27	,	,	PUNCT
ap-6142	358	28	we	we	PRON
ap-6142	358	29	obtain	obtain	VERB
ap-6142	358	30	∫	∫	PROPN
ap-6142	358	31	ω	ω	NUM
ap-6142	358	32	v	v	PROPN
ap-6142	358	33	·	·	PUNCT
ap-6142	358	34	∇v	∇v	NOUN
ap-6142	358	35	·	·	PUNCT
ap-6142	358	36	(	(	PUNCT
ap-6142	358	37	w	w	NOUN
ap-6142	358	38	−	−	PROPN
ap-6142	358	39	v	v	NOUN
ap-6142	358	40	)	)	PUNCT
ap-6142	358	41	dx+	dx+	NOUN
ap-6142	358	42	∫	∫	PROPN
ap-6142	358	43	ω	ω	PROPN
ap-6142	358	44	ν∇v	ν∇v	X
ap-6142	358	45	·	·	PUNCT
ap-6142	358	46	∇(w	∇(w	ADJ
ap-6142	358	47	−	−	PROPN
ap-6142	358	48	v	v	NOUN
ap-6142	358	49	)	)	PUNCT
ap-6142	358	50	dx	dx	PROPN
ap-6142	358	51	≥	≥	NUM
ap-6142	359	1	〈	〈	PROPN
ap-6142	359	2	f	f	PROPN
ap-6142	359	3	,	,	PUNCT
ap-6142	359	4	w	w	PROPN
ap-6142	359	5	−	−	PROPN
ap-6142	359	6	v〉+	v〉+	NUM
ap-6142	359	7	∫	∫	NOUN
ap-6142	359	8	γ2	γ2	PROPN
ap-6142	359	9	g	g	PROPN
ap-6142	359	10	·	·	PUNCT
ap-6142	359	11	(	(	PUNCT
ap-6142	359	12	w	w	NOUN
ap-6142	359	13	−	−	PROPN
ap-6142	359	14	v	v	NOUN
ap-6142	359	15	)	)	PUNCT
ap-6142	359	16	ds	ds	PROPN
ap-6142	359	17	,	,	PUNCT
ap-6142	359	18	ν	ν	NOUN
ap-6142	359	19	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	360	1	+	+	CCONJ
ap-6142	360	2	∫	∫	PROPN
ap-6142	360	3	ω	ω	X
ap-6142	360	4	(	(	PUNCT
ap-6142	360	5	v∗ext	v∗ext	PROPN
ap-6142	360	6	+	+	CCONJ
ap-6142	360	7	u	u	NOUN
ap-6142	360	8	)	)	PUNCT
ap-6142	360	9	·	·	PUNCT
ap-6142	361	1	∇(v∗ext	∇(v∗ext	PROPN
ap-6142	361	2	+	+	CCONJ
ap-6142	361	3	u	u	NOUN
ap-6142	361	4	)	)	PUNCT
ap-6142	361	5	·	·	PUNCT
ap-6142	362	1	(	(	PUNCT
ap-6142	362	2	v∗ext	v∗ext	NOUN
ap-6142	362	3	+	+	CCONJ
ap-6142	362	4	u	u	NOUN
ap-6142	362	5	)	)	PUNCT
ap-6142	362	6	dx	dx	PROPN
ap-6142	362	7	≤	≤	NUM
ap-6142	363	1	∫	∫	PROPN
ap-6142	364	1	ω	ω	PROPN
ap-6142	365	1	[	[	PUNCT
ap-6142	365	2	ν∇v∗ext	ν∇v∗ext	NOUN
ap-6142	365	3	:	:	PUNCT
ap-6142	365	4	∇u	∇u	PROPN
ap-6142	365	5	+	+	CCONJ
ap-6142	365	6	(	(	PUNCT
ap-6142	365	7	v∗ext	v∗ext	PROPN
ap-6142	365	8	+	+	CCONJ
ap-6142	365	9	u	u	NOUN
ap-6142	365	10	)	)	PUNCT
ap-6142	365	11	·	·	PUNCT
ap-6142	366	1	∇(v∗ext	∇(v∗ext	PROPN
ap-6142	366	2	+	+	CCONJ
ap-6142	366	3	u	u	NOUN
ap-6142	366	4	)	)	PUNCT
ap-6142	366	5	·	·	PUNCT
ap-6142	367	1	v∗ext	v∗ext	NOUN
ap-6142	367	2	]	]	PUNCT
ap-6142	367	3	dx	dx	PROPN
ap-6142	367	4	+	+	CCONJ
ap-6142	367	5	〈	〈	PROPN
ap-6142	367	6	f	f	PROPN
ap-6142	367	7	,	,	PUNCT
ap-6142	367	8	u〉+	u〉+	PROPN
ap-6142	367	9	∫	∫	PROPN
ap-6142	367	10	γ2	γ2	PROPN
ap-6142	367	11	g	g	PROPN
ap-6142	367	12	·	·	PUNCT
ap-6142	367	13	u	u	NOUN
ap-6142	367	14	ds	ds	PROPN
ap-6142	367	15	,	,	PUNCT
ap-6142	367	16	ν	ν	X
ap-6142	367	17	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	367	18	+	+	CCONJ
ap-6142	367	19	1	1	NUM
ap-6142	367	20	2	2	NUM
ap-6142	367	21	∫	∫	NOUN
ap-6142	367	22	γ1	γ1	NOUN
ap-6142	367	23	(	(	PUNCT
ap-6142	367	24	v∗	v∗	PROPN
ap-6142	367	25	·	·	PUNCT
ap-6142	367	26	n	n	CCONJ
ap-6142	367	27	)	)	PUNCT
ap-6142	367	28	|v∗|2	|v∗|2	NUM
ap-6142	367	29	ds	ds	NOUN
ap-6142	367	30	+	+	CCONJ
ap-6142	367	31	1	1	NUM
ap-6142	367	32	2	2	NUM
ap-6142	367	33	∫	∫	NOUN
ap-6142	367	34	γ2	γ2	NOUN
ap-6142	367	35	[	[	PUNCT
ap-6142	367	36	(	(	PUNCT
ap-6142	367	37	v∗	v∗	PROPN
ap-6142	367	38	+	+	CCONJ
ap-6142	367	39	u	u	NOUN
ap-6142	367	40	)	)	PUNCT
ap-6142	367	41	·	·	PUNCT
ap-6142	367	42	n	n	CCONJ
ap-6142	367	43	]	]	PUNCT
ap-6142	367	44	|v∗	|v∗	PROPN
ap-6142	367	45	+	+	CCONJ
ap-6142	367	46	u|2	u|2	PROPN
ap-6142	367	47	ds	ds	ADJ
ap-6142	367	48	≤	≤	NUM
ap-6142	367	49	∫	∫	PROPN
ap-6142	367	50	ω	ω	PROPN
ap-6142	367	51	[	[	PUNCT
ap-6142	367	52	ν∇v∗ext	ν∇v∗ext	PROPN
ap-6142	367	53	:	:	PUNCT
ap-6142	367	54	∇u+	∇u+	PROPN
ap-6142	367	55	v∗ext	v∗ext	PROPN
ap-6142	367	56	·	·	PUNCT
ap-6142	368	1	∇v∗ext	∇v∗ext	PROPN
ap-6142	368	2	·	·	PUNCT
ap-6142	368	3	v∗ext	v∗ext	PROPN
ap-6142	368	4	+	+	CCONJ
ap-6142	368	5	v∗ext	v∗ext	PROPN
ap-6142	368	6	·	·	PUNCT
ap-6142	368	7	∇u	∇u	PROPN
ap-6142	368	8	·	·	PUNCT
ap-6142	368	9	v∗ext	v∗ext	PROPN
ap-6142	368	10	+	+	CCONJ
ap-6142	368	11	u	u	X
ap-6142	368	12	·	·	PUNCT
ap-6142	368	13	∇v∗ext	∇v∗ext	PROPN
ap-6142	368	14	·	·	PUNCT
ap-6142	368	15	v∗ext	v∗ext	PROPN
ap-6142	368	16	+	+	CCONJ
ap-6142	368	17	u	u	PROPN
ap-6142	368	18	·	·	PUNCT
ap-6142	368	19	∇u	∇u	PROPN
ap-6142	368	20	·	·	PUNCT
ap-6142	368	21	v∗ext	v∗ext	NOUN
ap-6142	368	22	]	]	PUNCT
ap-6142	368	23	dx+	dx+	PROPN
ap-6142	368	24	〈	〈	PROPN
ap-6142	368	25	f	f	PROPN
ap-6142	368	26	,	,	PUNCT
ap-6142	368	27	u〉+	u〉+	PROPN
ap-6142	368	28	∫	∫	PROPN
ap-6142	368	29	γ2	γ2	PROPN
ap-6142	368	30	g	g	PROPN
ap-6142	368	31	·	·	PUNCT
ap-6142	368	32	u	u	NOUN
ap-6142	368	33	ds	ds	PROPN
ap-6142	368	34	,	,	PUNCT
ap-6142	368	35	ν	ν	X
ap-6142	368	36	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	368	37	≤	≤	NUM
ap-6142	368	38	−	−	NUM
ap-6142	368	39	1	1	NUM
ap-6142	368	40	2	2	NUM
ap-6142	368	41	∫	∫	NOUN
ap-6142	368	42	γ1	γ1	NOUN
ap-6142	368	43	(	(	PUNCT
ap-6142	368	44	v∗	v∗	PROPN
ap-6142	368	45	·	·	PUNCT
ap-6142	368	46	n	n	CCONJ
ap-6142	368	47	)	)	PUNCT
ap-6142	368	48	|v∗|2	|v∗|2	NUM
ap-6142	368	49	ds	ds	NOUN
ap-6142	368	50	+	+	CCONJ
ap-6142	368	51	1	1	NUM
ap-6142	368	52	2	2	NUM
ap-6142	368	53	∫	∫	NOUN
ap-6142	368	54	γ2	γ2	NOUN
ap-6142	368	55	[	[	PUNCT
ap-6142	368	56	(	(	PUNCT
ap-6142	368	57	v∗	v∗	PROPN
ap-6142	368	58	+	+	CCONJ
ap-6142	368	59	u	u	NOUN
ap-6142	368	60	)	)	PUNCT
ap-6142	368	61	·	·	PUNCT
ap-6142	369	1	n	n	CCONJ
ap-6142	369	2	]	]	PUNCT
ap-6142	369	3	−	−	X
ap-6142	369	4	|v	|v	PROPN
ap-6142	369	5	∗	∗	X
ap-6142	369	6	+	+	CCONJ
ap-6142	369	7	u|2	u|2	PROPN
ap-6142	369	8	ds	ds	ADJ
ap-6142	369	9	+	+	CCONJ
ap-6142	369	10	∫	∫	PROPN
ap-6142	369	11	ω	ω	X
ap-6142	369	12	[	[	PUNCT
ap-6142	369	13	ν∇v∗ext	ν∇v∗ext	PROPN
ap-6142	369	14	:	:	PUNCT
ap-6142	369	15	∇u+	∇u+	PROPN
ap-6142	369	16	v∗ext	v∗ext	PROPN
ap-6142	369	17	·	·	PUNCT
ap-6142	370	1	∇v∗ext	∇v∗ext	PROPN
ap-6142	370	2	·	·	PUNCT
ap-6142	370	3	v∗ext	v∗ext	PROPN
ap-6142	370	4	+	+	CCONJ
ap-6142	370	5	v∗ext	v∗ext	PROPN
ap-6142	370	6	·	·	PUNCT
ap-6142	370	7	∇u	∇u	PROPN
ap-6142	370	8	·	·	PUNCT
ap-6142	370	9	v∗ext	v∗ext	PROPN
ap-6142	370	10	+	+	CCONJ
ap-6142	370	11	u	u	X
ap-6142	370	12	·	·	PUNCT
ap-6142	370	13	∇v∗ext	∇v∗ext	PROPN
ap-6142	370	14	·	·	PUNCT
ap-6142	370	15	v∗ext	v∗ext	PROPN
ap-6142	370	16	]	]	PUNCT
ap-6142	370	17	dx	dx	PROPN
ap-6142	370	18	+	+	CCONJ
ap-6142	370	19	δ	δ	PROPN
ap-6142	370	20	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	371	1	+	+	CCONJ
ap-6142	371	2	〈	〈	PROPN
ap-6142	371	3	f	f	X
ap-6142	371	4	,	,	PUNCT
ap-6142	371	5	u〉+	u〉+	PROPN
ap-6142	371	6	∫	∫	PROPN
ap-6142	371	7	γ2	γ2	PROPN
ap-6142	371	8	g	g	PROPN
ap-6142	371	9	·	·	PUNCT
ap-6142	371	10	u	u	NOUN
ap-6142	371	11	ds	ds	PROPN
ap-6142	371	12	,	,	PUNCT
ap-6142	371	13	≤	≤	NUM
ap-6142	371	14	−1	−1	NOUN
ap-6142	371	15	2	2	NUM
ap-6142	371	16	∫	∫	NOUN
ap-6142	371	17	γ1	γ1	PROPN
ap-6142	371	18	(	(	PUNCT
ap-6142	371	19	v∗	v∗	PROPN
ap-6142	371	20	·	·	PUNCT
ap-6142	371	21	n	n	CCONJ
ap-6142	371	22	)	)	PUNCT
ap-6142	371	23	|v∗|2	|v∗|2	NUM
ap-6142	371	24	ds	ds	NOUN
ap-6142	372	1	+	+	CCONJ
ap-6142	372	2	1	1	NUM
ap-6142	372	3	2	2	NUM
ap-6142	372	4	ζ	ζ	NOUN
ap-6142	372	5	‖v	‖v	NOUN
ap-6142	372	6	∗	∗	NOUN
ap-6142	372	7	+	+	CCONJ
ap-6142	372	8	u‖23	u‖23	NOUN
ap-6142	372	9	;	;	PUNCT
ap-6142	372	10	γ2	γ2	PROPN
ap-6142	372	11	+	+	CCONJ
ap-6142	372	12	∫	∫	PROPN
ap-6142	372	13	ω	ω	X
ap-6142	372	14	[	[	PUNCT
ap-6142	372	15	ν∇v∗ext	ν∇v∗ext	PROPN
ap-6142	372	16	:	:	PUNCT
ap-6142	372	17	∇u+	∇u+	PROPN
ap-6142	372	18	v∗ext	v∗ext	PROPN
ap-6142	372	19	·	·	PUNCT
ap-6142	373	1	∇v∗ext	∇v∗ext	PROPN
ap-6142	373	2	·	·	PUNCT
ap-6142	373	3	v∗ext	v∗ext	PROPN
ap-6142	373	4	+	+	CCONJ
ap-6142	373	5	v∗ext	v∗ext	PROPN
ap-6142	373	6	·	·	PUNCT
ap-6142	373	7	∇u	∇u	PROPN
ap-6142	373	8	·	·	PUNCT
ap-6142	373	9	v∗ext	v∗ext	PROPN
ap-6142	373	10	+	+	CCONJ
ap-6142	373	11	u	u	X
ap-6142	373	12	·	·	PUNCT
ap-6142	373	13	∇v∗ext	∇v∗ext	PROPN
ap-6142	373	14	·	·	PUNCT
ap-6142	373	15	v∗ext	v∗ext	PROPN
ap-6142	373	16	]	]	PUNCT
ap-6142	373	17	dx	dx	PROPN
ap-6142	373	18	+	+	CCONJ
ap-6142	373	19	δ	δ	PROPN
ap-6142	373	20	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	374	1	+	+	CCONJ
ap-6142	374	2	〈	〈	PROPN
ap-6142	374	3	f	f	X
ap-6142	374	4	,	,	PUNCT
ap-6142	374	5	u〉+	u〉+	PROPN
ap-6142	374	6	∫	∫	PROPN
ap-6142	374	7	γ2	γ2	PROPN
ap-6142	374	8	g	g	PROPN
ap-6142	374	9	·	·	PUNCT
ap-6142	374	10	u	u	NOUN
ap-6142	374	11	ds	ds	PROPN
ap-6142	374	12	,	,	PUNCT
ap-6142	374	13	≤	≤	NUM
ap-6142	374	14	−1	−1	NOUN
ap-6142	374	15	2	2	NUM
ap-6142	374	16	∫	∫	NOUN
ap-6142	374	17	γ1	γ1	PROPN
ap-6142	374	18	(	(	PUNCT
ap-6142	374	19	v∗	v∗	PROPN
ap-6142	374	20	·	·	PUNCT
ap-6142	374	21	n	n	CCONJ
ap-6142	374	22	)	)	PUNCT
ap-6142	374	23	|v∗|2	|v∗|2	NUM
ap-6142	374	24	ds	ds	NOUN
ap-6142	374	25	+	+	CCONJ
ap-6142	374	26	ζ	ζ	NOUN
ap-6142	374	27	2	2	NUM
ap-6142	374	28	c6	c6	NOUN
ap-6142	374	29	‖v	‖v	PROPN
ap-6142	374	30	∗	∗	NOUN
ap-6142	374	31	ext	ext	NOUN
ap-6142	374	32	+	+	CCONJ
ap-6142	374	33	u‖21,2	u‖21,2	PROPN
ap-6142	374	34	+	+	CCONJ
ap-6142	374	35	∫	∫	PROPN
ap-6142	374	36	ω	ω	X
ap-6142	374	37	[	[	PUNCT
ap-6142	374	38	ν∇v∗ext	ν∇v∗ext	PROPN
ap-6142	374	39	:	:	PUNCT
ap-6142	374	40	∇u+	∇u+	PROPN
ap-6142	374	41	v∗ext	v∗ext	PROPN
ap-6142	374	42	·	·	PUNCT
ap-6142	375	1	∇v∗ext	∇v∗ext	PROPN
ap-6142	375	2	·	·	PUNCT
ap-6142	375	3	v∗ext	v∗ext	PROPN
ap-6142	375	4	+	+	CCONJ
ap-6142	375	5	v∗ext	v∗ext	PROPN
ap-6142	375	6	·	·	PUNCT
ap-6142	375	7	∇u	∇u	PROPN
ap-6142	375	8	·	·	PUNCT
ap-6142	375	9	v∗ext	v∗ext	PROPN
ap-6142	375	10	+	+	CCONJ
ap-6142	375	11	u	u	X
ap-6142	375	12	·	·	PUNCT
ap-6142	375	13	∇v∗ext	∇v∗ext	PROPN
ap-6142	375	14	·	·	PUNCT
ap-6142	375	15	v∗ext	v∗ext	PROPN
ap-6142	375	16	]	]	PUNCT
ap-6142	375	17	dx	dx	PROPN
ap-6142	375	18	+	+	CCONJ
ap-6142	375	19	δ	δ	PROPN
ap-6142	375	20	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	376	1	+	+	CCONJ
ap-6142	376	2	〈	〈	PROPN
ap-6142	376	3	f	f	X
ap-6142	376	4	,	,	PUNCT
ap-6142	376	5	u〉+	u〉+	PROPN
ap-6142	376	6	∫	∫	PROPN
ap-6142	376	7	γ2	γ2	PROPN
ap-6142	376	8	g	g	PROPN
ap-6142	376	9	·	·	PUNCT
ap-6142	376	10	u	u	NOUN
ap-6142	376	11	ds	ds	PROPN
ap-6142	376	12	,	,	PUNCT
ap-6142	376	13	where	where	SCONJ
ap-6142	376	14	c6	c6	PROPN
ap-6142	376	15	=	=	PUNCT
ap-6142	376	16	c6(ω	c6(ω	NUM
ap-6142	376	17	)	)	PUNCT
ap-6142	376	18	.	.	PUNCT
ap-6142	377	1	writing	write	VERB
ap-6142	377	2	only	only	ADV
ap-6142	377	3	the	the	DET
ap-6142	377	4	terms	term	NOUN
ap-6142	377	5	with	with	ADP
ap-6142	377	6	second	second	ADJ
ap-6142	377	7	powers	power	NOUN
ap-6142	377	8	of	of	ADP
ap-6142	377	9	u	u	NOUN
ap-6142	377	10	,	,	PUNCT
ap-6142	377	11	which	which	PRON
ap-6142	377	12	are	be	AUX
ap-6142	377	13	decisive	decisive	ADJ
ap-6142	377	14	for	for	ADP
ap-6142	377	15	the	the	DET
ap-6142	377	16	estimates	estimate	NOUN
ap-6142	377	17	,	,	PUNCT
ap-6142	377	18	and	and	CCONJ
ap-6142	377	19	involving	involve	VERB
ap-6142	377	20	all	all	DET
ap-6142	377	21	other	other	ADJ
ap-6142	377	22	terms	term	NOUN
ap-6142	377	23	to	to	ADP
ap-6142	377	24	a	a	DET
ap-6142	377	25	generic	generic	ADJ
ap-6142	377	26	constant	constant	ADJ
ap-6142	377	27	c	c	NOUN
ap-6142	377	28	,	,	PUNCT
ap-6142	377	29	we	we	PRON
ap-6142	377	30	obtain	obtain	VERB
ap-6142	377	31	ν	ν	DET
ap-6142	377	32	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	377	33	≤	≤	PUNCT
ap-6142	377	34	δ	δ	PROPN
ap-6142	377	35	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	378	1	+	+	CCONJ
ap-6142	378	2	c7	c7	PROPN
ap-6142	378	3	ζ	ζ	PROPN
ap-6142	378	4	‖∇u‖22	‖∇u‖22	NOUN
ap-6142	379	1	+	+	CCONJ
ap-6142	379	2	c	c	X
ap-6142	379	3	,	,	PUNCT
ap-6142	379	4	(	(	PUNCT
ap-6142	379	5	25	25	NUM
ap-6142	379	6	)	)	PUNCT
ap-6142	379	7	where	where	SCONJ
ap-6142	379	8	c7	c7	PROPN
ap-6142	379	9	=	=	PROPN
ap-6142	379	10	c7(ω	c7(ω	PROPN
ap-6142	379	11	)	)	PUNCT
ap-6142	379	12	.	.	PUNCT
ap-6142	380	1	as	as	SCONJ
ap-6142	380	2	δ	δ	PROPN
ap-6142	380	3	>	>	X
ap-6142	380	4	0	0	NUM
ap-6142	380	5	can	can	AUX
ap-6142	380	6	be	be	AUX
ap-6142	380	7	chosen	choose	VERB
ap-6142	380	8	to	to	PART
ap-6142	380	9	be	be	AUX
ap-6142	380	10	arbitrarily	arbitrarily	ADV
ap-6142	380	11	small	small	ADJ
ap-6142	380	12	,	,	PUNCT
ap-6142	380	13	we	we	PRON
ap-6142	380	14	observe	observe	VERB
ap-6142	380	15	that	that	SCONJ
ap-6142	380	16	these	these	DET
ap-6142	380	17	inequalities	inequality	NOUN
ap-6142	380	18	yield	yield	VERB
ap-6142	380	19	an	an	DET
ap-6142	380	20	a	a	DET
ap-6142	380	21	priori	priori	ADJ
ap-6142	380	22	estimate	estimate	NOUN
ap-6142	380	23	of	of	ADP
ap-6142	380	24	‖∇u‖2	‖∇u‖2	NOUN
ap-6142	380	25	in	in	ADP
ap-6142	380	26	terms	term	NOUN
ap-6142	380	27	of	of	ADP
ap-6142	380	28	v∗	v∗	NOUN
ap-6142	380	29	,	,	PUNCT
ap-6142	380	30	f	f	PROPN
ap-6142	380	31	and	and	CCONJ
ap-6142	380	32	g	g	PROPN
ap-6142	380	33	,	,	PUNCT
ap-6142	380	34	provided	provide	VERB
ap-6142	380	35	that	that	SCONJ
ap-6142	380	36	ζ	ζ	NOUN
ap-6142	380	37	>	>	X
ap-6142	380	38	0	0	NUM
ap-6142	380	39	is	be	AUX
ap-6142	380	40	so	so	ADV
ap-6142	380	41	small	small	ADJ
ap-6142	380	42	that	that	SCONJ
ap-6142	380	43	c7ζ	c7ζ	AUX
ap-6142	380	44	<	<	X
ap-6142	380	45	ν	ν	X
ap-6142	380	46	.	.	PUNCT
ap-6142	381	1	obviously	obviously	ADV
ap-6142	381	2	,	,	PUNCT
ap-6142	381	3	in	in	ADP
ap-6142	381	4	this	this	DET
ap-6142	381	5	case	case	NOUN
ap-6142	381	6	one	one	NOUN
ap-6142	381	7	also	also	ADV
ap-6142	381	8	obtains	obtain	VERB
ap-6142	381	9	an	an	DET
ap-6142	381	10	a	a	DET
ap-6142	381	11	priori	priori	ADJ
ap-6142	381	12	estimate	estimate	NOUN
ap-6142	381	13	of	of	ADP
ap-6142	381	14	‖v‖1,2	‖v‖1,2	ADJ
ap-6142	381	15	≡	≡	PROPN
ap-6142	381	16	‖v∗ext	‖v∗ext	NOUN
ap-6142	381	17	+	+	CCONJ
ap-6142	381	18	u‖1,2	u‖1,2	ADJ
ap-6142	381	19	.	.	PUNCT
ap-6142	382	1	under	under	ADP
ap-6142	382	2	the	the	DET
ap-6142	382	3	aforementioned	aforementioned	ADJ
ap-6142	382	4	condition	condition	NOUN
ap-6142	382	5	on	on	ADP
ap-6142	382	6	ζ	ζ	NOUN
ap-6142	382	7	,	,	PUNCT
ap-6142	382	8	one	one	PRON
ap-6142	382	9	can	can	AUX
ap-6142	382	10	prove	prove	VERB
ap-6142	382	11	the	the	DET
ap-6142	382	12	existence	existence	NOUN
ap-6142	382	13	of	of	ADP
ap-6142	382	14	a	a	DET
ap-6142	382	15	weak	weak	ADJ
ap-6142	382	16	solution	solution	NOUN
ap-6142	382	17	v	v	ADP
ap-6142	382	18	∈kc	∈kc	NOUN
ap-6142	382	19	of	of	ADP
ap-6142	382	20	the	the	DET
ap-6142	382	21	variational	variational	ADJ
ap-6142	382	22	inequality	inequality	NOUN
ap-6142	382	23	(	(	PUNCT
ap-6142	382	24	24	24	NUM
ap-6142	382	25	)	)	PUNCT
ap-6142	382	26	,	,	PUNCT
ap-6142	382	27	applying	apply	VERB
ap-6142	382	28	the	the	DET
ap-6142	382	29	procedure	procedure	NOUN
ap-6142	382	30	sketched	sketched	NOUN
ap-6142	382	31	at	at	ADP
ap-6142	382	32	the	the	DET
ap-6142	382	33	beginning	beginning	NOUN
ap-6142	382	34	of	of	ADP
ap-6142	382	35	this	this	DET
ap-6142	382	36	section	section	NOUN
ap-6142	382	37	.	.	PUNCT
ap-6142	383	1	(	(	PUNCT
ap-6142	383	2	see	see	VERB
ap-6142	383	3	also	also	ADV
ap-6142	383	4	[	[	X
ap-6142	383	5	14	14	NUM
ap-6142	383	6	]	]	PUNCT
ap-6142	383	7	for	for	ADP
ap-6142	383	8	the	the	DET
ap-6142	383	9	construction	construction	NOUN
ap-6142	383	10	of	of	ADP
ap-6142	383	11	appropriate	appropriate	ADJ
ap-6142	383	12	approximations	approximation	NOUN
ap-6142	383	13	and	and	CCONJ
ap-6142	383	14	the	the	DET
ap-6142	383	15	detailed	detailed	ADJ
ap-6142	383	16	derivation	derivation	NOUN
ap-6142	383	17	of	of	ADP
ap-6142	383	18	the	the	DET
ap-6142	383	19	estimates	estimate	NOUN
ap-6142	383	20	on	on	ADP
ap-6142	383	21	the	the	DET
ap-6142	383	22	level	level	NOUN
ap-6142	383	23	of	of	ADP
ap-6142	383	24	approximations	approximation	NOUN
ap-6142	383	25	.	.	PUNCT
ap-6142	384	1	however	however	ADV
ap-6142	384	2	,	,	PUNCT
ap-6142	384	3	the	the	DET
ap-6142	384	4	convex	convex	NOUN
ap-6142	384	5	set	set	NOUN
ap-6142	384	6	,	,	PUNCT
ap-6142	384	7	used	use	VERB
ap-6142	384	8	in	in	ADP
ap-6142	384	9	paper	paper	NOUN
ap-6142	384	10	[	[	X
ap-6142	384	11	14	14	NUM
ap-6142	384	12	]	]	PUNCT
ap-6142	384	13	,	,	PUNCT
ap-6142	384	14	differs	differ	VERB
ap-6142	384	15	from	from	ADP
ap-6142	384	16	kc	kc	PROPN
ap-6142	384	17	used	use	VERB
ap-6142	384	18	here	here	ADV
ap-6142	384	19	.	.	PUNCT
ap-6142	384	20	)	)	PUNCT
ap-6142	385	1	thus	thus	ADV
ap-6142	385	2	,	,	PUNCT
ap-6142	385	3	we	we	PRON
ap-6142	385	4	can	can	AUX
ap-6142	385	5	formulate	formulate	VERB
ap-6142	385	6	the	the	DET
ap-6142	385	7	theorem	theorem	NOUN
ap-6142	385	8	:	:	PUNCT
ap-6142	385	9	theorem	theorem	NOUN
ap-6142	385	10	2	2	NUM
ap-6142	385	11	.	.	PUNCT
ap-6142	386	1	let	let	VERB
ap-6142	386	2	functions	function	NOUN
ap-6142	386	3	v∗	v∗	ADJ
ap-6142	386	4	∈w	∈w	NOUN
ap-6142	386	5	1/2,2(γ1	1/2,2(γ1	NUM
ap-6142	386	6	)	)	PUNCT
ap-6142	386	7	(	(	PUNCT
ap-6142	386	8	satisfying	satisfy	VERB
ap-6142	386	9	condition	condition	NOUN
ap-6142	386	10	(	(	PUNCT
ap-6142	386	11	?	?	PUNCT
ap-6142	386	12	)	)	PUNCT
ap-6142	386	13	)	)	PUNCT
ap-6142	386	14	,	,	PUNCT
ap-6142	386	15	f	f	PROPN
ap-6142	386	16	∈w−1,2(ω	∈w−1,2(ω	NOUN
ap-6142	386	17	)	)	PUNCT
ap-6142	386	18	and	and	CCONJ
ap-6142	386	19	g	g	PROPN
ap-6142	386	20	∈	∈	PROPN
ap-6142	386	21	l4/3(γ2	l4/3(γ2	PROPN
ap-6142	386	22	)	)	PUNCT
ap-6142	386	23	be	be	AUX
ap-6142	386	24	given	give	VERB
ap-6142	386	25	.	.	PUNCT
ap-6142	387	1	let	let	VERB
ap-6142	387	2	number	number	NOUN
ap-6142	387	3	ζ	ζ	NOUN
ap-6142	387	4	be	be	AUX
ap-6142	387	5	so	so	ADV
ap-6142	387	6	small	small	ADJ
ap-6142	387	7	that	that	SCONJ
ap-6142	387	8	c7ζ	c7ζ	AUX
ap-6142	387	9	<	<	X
ap-6142	387	10	ν	ν	X
ap-6142	387	11	.	.	PUNCT
ap-6142	388	1	then	then	ADV
ap-6142	388	2	there	there	PRON
ap-6142	388	3	exists	exist	VERB
ap-6142	388	4	v	v	ADP
ap-6142	388	5	∈	∈	PROPN
ap-6142	388	6	kc	kc	PROPN
ap-6142	388	7	,	,	PUNCT
ap-6142	388	8	such	such	ADJ
ap-6142	388	9	that	that	SCONJ
ap-6142	388	10	the	the	DET
ap-6142	388	11	variational	variational	ADJ
ap-6142	388	12	inequality	inequality	NOUN
ap-6142	388	13	(	(	PUNCT
ap-6142	388	14	24	24	NUM
ap-6142	388	15	)	)	PUNCT
ap-6142	388	16	is	be	AUX
ap-6142	388	17	satisfied	satisfied	ADJ
ap-6142	388	18	for	for	ADP
ap-6142	388	19	all	all	DET
ap-6142	388	20	w	w	PROPN
ap-6142	388	21	∈kc	∈kc	NOUN
ap-6142	388	22	.	.	PUNCT
ap-6142	389	1	recall	recall	VERB
ap-6142	389	2	that	that	SCONJ
ap-6142	389	3	ζ	ζ	NOUN
ap-6142	389	4	is	be	AUX
ap-6142	389	5	used	use	VERB
ap-6142	389	6	in	in	ADP
ap-6142	389	7	the	the	DET
ap-6142	389	8	definition	definition	NOUN
ap-6142	389	9	of	of	ADP
ap-6142	389	10	the	the	DET
ap-6142	389	11	convex	convex	PROPN
ap-6142	389	12	set	set	VERB
ap-6142	389	13	kc	kc	PROPN
ap-6142	389	14	,	,	PUNCT
ap-6142	389	15	see	see	VERB
ap-6142	389	16	(	(	PUNCT
ap-6142	389	17	12	12	NUM
ap-6142	389	18	)	)	PUNCT
ap-6142	389	19	and	and	CCONJ
ap-6142	389	20	(	(	PUNCT
ap-6142	389	21	13	13	NUM
ap-6142	389	22	)	)	PUNCT
ap-6142	389	23	.	.	PUNCT
ap-6142	390	1	the	the	DET
ap-6142	390	2	smaller	small	ADJ
ap-6142	390	3	is	be	AUX
ap-6142	390	4	ζ	ζ	NOUN
ap-6142	390	5	,	,	PUNCT
ap-6142	390	6	the	the	DET
ap-6142	390	7	smaller	small	ADJ
ap-6142	390	8	is	be	AUX
ap-6142	390	9	kc	kc	PROPN
ap-6142	390	10	and	and	CCONJ
ap-6142	390	11	the	the	DET
ap-6142	390	12	narrower	narrow	ADJ
ap-6142	390	13	space	space	NOUN
ap-6142	390	14	is	be	AUX
ap-6142	390	15	left	leave	VERB
ap-6142	390	16	for	for	ADP
ap-6142	390	17	possible	possible	ADJ
ap-6142	390	18	reverse	reverse	NOUN
ap-6142	390	19	flows	flow	NOUN
ap-6142	390	20	on	on	ADP
ap-6142	390	21	γ2	γ2	NOUN
ap-6142	390	22	.	.	PUNCT
ap-6142	391	1	5	5	X
ap-6142	391	2	.	.	X
ap-6142	391	3	conclusion	conclusion	NOUN
ap-6142	391	4	the	the	DET
ap-6142	391	5	paper	paper	NOUN
ap-6142	391	6	provides	provide	VERB
ap-6142	391	7	a	a	DET
ap-6142	391	8	mathematical	mathematical	ADJ
ap-6142	391	9	model	model	NOUN
ap-6142	391	10	of	of	ADP
ap-6142	391	11	flows	flow	NOUN
ap-6142	391	12	through	through	ADP
ap-6142	391	13	a	a	DET
ap-6142	391	14	channel	channel	NOUN
ap-6142	391	15	with	with	ADP
ap-6142	391	16	an	an	DET
ap-6142	391	17	artificial	artificial	ADJ
ap-6142	391	18	boundary	boundary	ADJ
ap-6142	391	19	condition	condition	NOUN
ap-6142	391	20	(	(	PUNCT
ap-6142	391	21	5	5	NUM
ap-6142	391	22	)	)	PUNCT
ap-6142	391	23	on	on	ADP
ap-6142	391	24	the	the	DET
ap-6142	391	25	outflow	outflow	NOUN
ap-6142	391	26	.	.	PUNCT
ap-6142	392	1	both	both	DET
ap-6142	392	2	unsteady	unsteady	ADJ
ap-6142	392	3	and	and	CCONJ
ap-6142	392	4	steady	steady	ADJ
ap-6142	392	5	cases	case	NOUN
ap-6142	392	6	are	be	AUX
ap-6142	392	7	considered	consider	VERB
ap-6142	392	8	.	.	PUNCT
ap-6142	393	1	the	the	DET
ap-6142	393	2	core	core	NOUN
ap-6142	393	3	of	of	ADP
ap-6142	393	4	the	the	DET
ap-6142	393	5	model	model	NOUN
ap-6142	393	6	is	be	AUX
ap-6142	393	7	the	the	DET
ap-6142	393	8	variational	variational	ADJ
ap-6142	393	9	inequalities	inequality	NOUN
ap-6142	393	10	(	(	PUNCT
ap-6142	393	11	16	16	NUM
ap-6142	393	12	)	)	PUNCT
ap-6142	393	13	(	(	PUNCT
ap-6142	393	14	in	in	ADP
ap-6142	393	15	the	the	DET
ap-6142	393	16	unsteady	unsteady	ADJ
ap-6142	393	17	case	case	NOUN
ap-6142	393	18	)	)	PUNCT
ap-6142	393	19	and	and	CCONJ
ap-6142	393	20	(	(	PUNCT
ap-6142	393	21	24	24	NUM
ap-6142	393	22	)	)	PUNCT
ap-6142	393	23	(	(	PUNCT
ap-6142	393	24	in	in	ADP
ap-6142	393	25	the	the	DET
ap-6142	393	26	steady	steady	ADJ
ap-6142	393	27	case	case	NOUN
ap-6142	393	28	)	)	PUNCT
ap-6142	393	29	.	.	PUNCT
ap-6142	394	1	solutions	solution	NOUN
ap-6142	394	2	are	be	AUX
ap-6142	394	3	sought	seek	VERB
ap-6142	394	4	in	in	ADP
ap-6142	394	5	an	an	DET
ap-6142	394	6	appropriate	appropriate	ADJ
ap-6142	394	7	closed	closed	ADJ
ap-6142	394	8	convex	convex	NOUN
ap-6142	394	9	subsets	subset	NOUN
ap-6142	394	10	of	of	ADP
ap-6142	394	11	relevant	relevant	ADJ
ap-6142	394	12	function	function	NOUN
ap-6142	394	13	spaces	space	NOUN
ap-6142	394	14	,	,	PUNCT
ap-6142	394	15	defined	define	VERB
ap-6142	394	16	by	by	ADP
ap-6142	394	17	means	mean	NOUN
ap-6142	394	18	of	of	ADP
ap-6142	394	19	restrictions	restriction	NOUN
ap-6142	394	20	,	,	PUNCT
ap-6142	394	21	imposed	impose	VERB
ap-6142	394	22	on	on	ADP
ap-6142	394	23	possible	possible	ADJ
ap-6142	394	24	reverse	reverse	ADJ
ap-6142	394	25	flows	flow	NOUN
ap-6142	394	26	on	on	ADP
ap-6142	394	27	the	the	DET
ap-6142	394	28	outflow	outflow	NOUN
ap-6142	394	29	.	.	PUNCT
ap-6142	395	1	the	the	DET
ap-6142	395	2	restricting	restrict	VERB
ap-6142	395	3	conditions	condition	NOUN
ap-6142	395	4	bound	bind	VERB
ap-6142	395	5	the	the	DET
ap-6142	395	6	kinetic	kinetic	ADJ
ap-6142	395	7	energy	energy	NOUN
ap-6142	395	8	,	,	PUNCT
ap-6142	395	9	brought	bring	VERB
ap-6142	395	10	back	back	ADV
ap-6142	395	11	to	to	ADP
ap-6142	395	12	ω	ω	NOUN
ap-6142	395	13	through	through	ADP
ap-6142	395	14	γ2	γ2	NOUN
ap-6142	395	15	by	by	ADP
ap-6142	395	16	the	the	DET
ap-6142	395	17	reverse	reverse	NOUN
ap-6142	395	18	flows	flow	NOUN
ap-6142	395	19	.	.	PUNCT
ap-6142	396	1	consequently	consequently	ADV
ap-6142	396	2	,	,	PUNCT
ap-6142	396	3	they	they	PRON
ap-6142	396	4	enable	enable	VERB
ap-6142	396	5	one	one	NUM
ap-6142	396	6	to	to	PART
ap-6142	396	7	derive	derive	VERB
ap-6142	396	8	energy	energy	NOUN
ap-6142	396	9	–	–	PUNCT
ap-6142	396	10	type	type	NOUN
ap-6142	396	11	a	a	DET
ap-6142	396	12	priori	priori	ADJ
ap-6142	396	13	estimates	estimate	NOUN
ap-6142	396	14	.	.	PUNCT
ap-6142	397	1	then	then	ADV
ap-6142	397	2	,	,	PUNCT
ap-6142	397	3	applying	apply	VERB
ap-6142	397	4	a	a	DET
ap-6142	397	5	relatively	relatively	ADV
ap-6142	397	6	standard	standard	ADJ
ap-6142	397	7	technique	technique	NOUN
ap-6142	397	8	(	(	PUNCT
ap-6142	397	9	based	base	VERB
ap-6142	397	10	e.g.	e.g.	ADV
ap-6142	397	11	on	on	ADP
ap-6142	397	12	construction	construction	NOUN
ap-6142	397	13	of	of	ADP
ap-6142	397	14	appropriate	appropriate	ADJ
ap-6142	397	15	approximations	approximation	NOUN
ap-6142	397	16	or	or	CCONJ
ap-6142	397	17	some	some	PRON
ap-6142	397	18	of	of	ADP
ap-6142	397	19	the	the	DET
ap-6142	397	20	fixed	fix	VERB
ap-6142	397	21	point	point	NOUN
ap-6142	397	22	theorems	theorem	NOUN
ap-6142	397	23	)	)	PUNCT
ap-6142	397	24	,	,	PUNCT
ap-6142	397	25	one	one	PRON
ap-6142	397	26	can	can	AUX
ap-6142	397	27	come	come	VERB
ap-6142	397	28	to	to	ADP
ap-6142	397	29	the	the	DET
ap-6142	397	30	conclusion	conclusion	NOUN
ap-6142	397	31	on	on	ADP
ap-6142	397	32	the	the	DET
ap-6142	397	33	existence	existence	NOUN
ap-6142	397	34	of	of	ADP
ap-6142	397	35	solutions	solution	NOUN
ap-6142	397	36	.	.	PUNCT
ap-6142	398	1	this	this	PRON
ap-6142	398	2	confirms	confirm	VERB
ap-6142	398	3	the	the	DET
ap-6142	398	4	sense	sense	NOUN
ap-6142	398	5	of	of	ADP
ap-6142	398	6	the	the	DET
ap-6142	398	7	used	used	ADJ
ap-6142	398	8	model	model	NOUN
ap-6142	398	9	and	and	CCONJ
ap-6142	398	10	associated	associated	ADJ
ap-6142	398	11	variational	variational	ADJ
ap-6142	398	12	inequalities	inequality	NOUN
ap-6142	398	13	,	,	PUNCT
ap-6142	398	14	in	in	ADP
ap-6142	398	15	contrast	contrast	NOUN
ap-6142	398	16	to	to	ADP
ap-6142	398	17	models	model	NOUN
ap-6142	398	18	based	base	VERB
ap-6142	398	19	just	just	ADV
ap-6142	398	20	on	on	ADP
ap-6142	398	21	equations	equation	NOUN
ap-6142	398	22	,	,	PUNCT
ap-6142	398	23	where	where	SCONJ
ap-6142	398	24	the	the	DET
ap-6142	398	25	existence	existence	NOUN
ap-6142	398	26	of	of	ADP
ap-6142	398	27	weak	weak	ADJ
ap-6142	398	28	or	or	CCONJ
ap-6142	398	29	strong	strong	ADJ
ap-6142	398	30	solutions	solution	NOUN
ap-6142	398	31	is	be	AUX
ap-6142	398	32	generally	generally	ADV
ap-6142	398	33	an	an	DET
ap-6142	398	34	open	open	ADJ
ap-6142	398	35	problem	problem	NOUN
ap-6142	398	36	.	.	PUNCT
ap-6142	399	1	except	except	SCONJ
ap-6142	399	2	for	for	ADP
ap-6142	399	3	the	the	DET
ap-6142	399	4	discussion	discussion	NOUN
ap-6142	399	5	on	on	ADP
ap-6142	399	6	various	various	ADJ
ap-6142	399	7	boundary	boundary	ADJ
ap-6142	399	8	conditions	condition	NOUN
ap-6142	399	9	of	of	ADP
ap-6142	399	10	the	the	DET
ap-6142	399	11	“	"	PUNCT
ap-6142	399	12	do	do	AUX
ap-6142	399	13	nothing	nothing	PRON
ap-6142	399	14	”	"	PUNCT
ap-6142	399	15	type	type	NOUN
ap-6142	399	16	(	(	PUNCT
ap-6142	399	17	see	see	VERB
ap-6142	399	18	paragraphs	paragraph	NOUN
ap-6142	399	19	2.2	2.2	NUM
ap-6142	399	20	and	and	CCONJ
ap-6142	399	21	2.3	2.3	NUM
ap-6142	399	22	)	)	PUNCT
ap-6142	399	23	and	and	CCONJ
ap-6142	399	24	some	some	DET
ap-6142	399	25	a	a	DET
ap-6142	399	26	posteriori	posteriori	NOUN
ap-6142	399	27	properties	property	NOUN
ap-6142	399	28	of	of	ADP
ap-6142	399	29	solutions	solution	NOUN
ap-6142	399	30	(	(	PUNCT
ap-6142	399	31	paragraph	paragraph	NOUN
ap-6142	399	32	3.5	3.5	NUM
ap-6142	399	33	)	)	PUNCT
ap-6142	399	34	,	,	PUNCT
ap-6142	399	35	we	we	PRON
ap-6142	399	36	present	present	VERB
ap-6142	399	37	a	a	DET
ap-6142	399	38	detailed	detailed	ADJ
ap-6142	399	39	description	description	NOUN
ap-6142	399	40	of	of	ADP
ap-6142	399	41	a	a	DET
ap-6142	399	42	priori	priori	ADJ
ap-6142	399	43	estimates	estimate	NOUN
ap-6142	399	44	of	of	ADP
ap-6142	399	45	solutions	solution	NOUN
ap-6142	399	46	.	.	PUNCT
ap-6142	400	1	these	these	DET
ap-6142	400	2	estimates	estimate	NOUN
ap-6142	400	3	clarify	clarify	VERB
ap-6142	400	4	,	,	PUNCT
ap-6142	400	5	on	on	ADP
ap-6142	400	6	the	the	DET
ap-6142	400	7	formal	formal	ADJ
ap-6142	400	8	level	level	NOUN
ap-6142	400	9	,	,	PUNCT
ap-6142	400	10	how	how	SCONJ
ap-6142	400	11	the	the	DET
ap-6142	400	12	information	information	NOUN
ap-6142	400	13	that	that	PRON
ap-6142	400	14	the	the	DET
ap-6142	400	15	solutions	solution	NOUN
ap-6142	400	16	belong	belong	VERB
ap-6142	400	17	to	to	ADP
ap-6142	400	18	l∞(0	l∞(0	PRON
ap-6142	400	19	,	,	PUNCT
ap-6142	400	20	t	t	PROPN
ap-6142	400	21	;	;	PUNCT
ap-6142	400	22	l2(ω	l2(ω	NOUN
ap-6142	400	23	)	)	PUNCT
ap-6142	400	24	)	)	PUNCT
ap-6142	400	25	∩	∩	ADJ
ap-6142	400	26	l2(0	l2(0	NOUN
ap-6142	400	27	,	,	PUNCT
ap-6142	400	28	t	t	NOUN
ap-6142	400	29	;	;	PUNCT
ap-6142	400	30	w	w	PROPN
ap-6142	400	31	1,2(ω	1,2(ω	NUM
ap-6142	400	32	)	)	PUNCT
ap-6142	400	33	)	)	PUNCT
ap-6142	400	34	(	(	PUNCT
ap-6142	400	35	in	in	ADP
ap-6142	400	36	the	the	DET
ap-6142	400	37	unsteady	unsteady	ADJ
ap-6142	400	38	case	case	NOUN
ap-6142	400	39	)	)	PUNCT
ap-6142	400	40	orw	orw	VERB
ap-6142	400	41	1,2(ω	1,2(ω	NUM
ap-6142	400	42	)	)	PUNCT
ap-6142	400	43	(	(	PUNCT
ap-6142	400	44	in	in	ADP
ap-6142	400	45	the	the	DET
ap-6142	400	46	steady	steady	ADJ
ap-6142	400	47	case	case	NOUN
ap-6142	400	48	)	)	PUNCT
ap-6142	400	49	directly	directly	ADV
ap-6142	400	50	follows	follow	VERB
ap-6142	400	51	from	from	ADP
ap-6142	400	52	the	the	DET
ap-6142	400	53	used	use	VERB
ap-6142	400	54	variational	variational	ADJ
ap-6142	400	55	inequalities	inequality	NOUN
ap-6142	400	56	,	,	PUNCT
ap-6142	400	57	regardless	regardless	ADV
ap-6142	400	58	of	of	ADP
ap-6142	400	59	other	other	ADJ
ap-6142	400	60	technicalities	technicality	NOUN
ap-6142	400	61	,	,	PUNCT
ap-6142	400	62	connected	connect	VERB
ap-6142	400	63	e.g.	e.g.	ADV
ap-6142	400	64	with	with	ADP
ap-6142	400	65	possible	possible	ADJ
ap-6142	400	66	approximations	approximation	NOUN
ap-6142	400	67	.	.	PUNCT
ap-6142	401	1	analogous	analogous	ADJ
ap-6142	401	2	estimates	estimate	NOUN
ap-6142	401	3	have	have	AUX
ap-6142	401	4	been	be	AUX
ap-6142	401	5	obtained	obtain	VERB
ap-6142	401	6	in	in	ADP
ap-6142	401	7	a	a	PRON
ap-6142	401	8	completely	completely	ADV
ap-6142	401	9	different	different	ADJ
ap-6142	401	10	and	and	CCONJ
ap-6142	401	11	much	much	ADJ
ap-6142	402	1	97	97	NUM
ap-6142	402	2	stanislav	stanislav	X
ap-6142	402	3	kračmar	kračmar	PROPN
ap-6142	402	4	,	,	PUNCT
ap-6142	402	5	jiří	jiří	NOUN
ap-6142	402	6	neustupa	neustupa	PROPN
ap-6142	402	7	acta	acta	PROPN
ap-6142	402	8	polytechnica	polytechnica	PROPN
ap-6142	402	9	more	more	ADV
ap-6142	402	10	technical	technical	ADJ
ap-6142	402	11	way	way	NOUN
ap-6142	402	12	(	(	PUNCT
ap-6142	402	13	i.e.	i.e.	X
ap-6142	402	14	at	at	ADP
ap-6142	402	15	first	first	ADV
ap-6142	402	16	on	on	ADP
ap-6142	402	17	the	the	DET
ap-6142	402	18	level	level	NOUN
ap-6142	402	19	of	of	ADP
ap-6142	402	20	approximations	approximation	NOUN
ap-6142	402	21	and	and	CCONJ
ap-6142	402	22	then	then	ADV
ap-6142	402	23	considering	consider	VERB
ap-6142	402	24	an	an	DET
ap-6142	402	25	appropriate	appropriate	ADJ
ap-6142	402	26	limit	limit	NOUN
ap-6142	402	27	transition	transition	NOUN
ap-6142	402	28	)	)	PUNCT
ap-6142	402	29	in	in	ADP
ap-6142	402	30	papers	paper	NOUN
ap-6142	402	31	[	[	X
ap-6142	402	32	14	14	NUM
ap-6142	402	33	]	]	PUNCT
ap-6142	402	34	and	and	CCONJ
ap-6142	402	35	[	[	X
ap-6142	402	36	15	15	NUM
ap-6142	402	37	]	]	PUNCT
ap-6142	402	38	.	.	PUNCT
ap-6142	403	1	however	however	ADV
ap-6142	403	2	,	,	PUNCT
ap-6142	403	3	it	it	PRON
ap-6142	403	4	must	must	AUX
ap-6142	403	5	be	be	AUX
ap-6142	403	6	noted	note	VERB
ap-6142	403	7	that	that	SCONJ
ap-6142	403	8	while	while	SCONJ
ap-6142	403	9	the	the	DET
ap-6142	403	10	convex	convex	NOUN
ap-6142	403	11	set	set	VERB
ap-6142	403	12	,	,	PUNCT
ap-6142	403	13	corresponding	correspond	VERB
ap-6142	403	14	to	to	ADP
ap-6142	403	15	our	our	PRON
ap-6142	403	16	kc	kc	PROPN
ap-6142	403	17	t	t	PROPN
ap-6142	403	18	,	,	PUNCT
ap-6142	403	19	is	be	AUX
ap-6142	403	20	defined	define	VERB
ap-6142	403	21	in	in	ADP
ap-6142	403	22	a	a	DET
ap-6142	403	23	rather	rather	ADV
ap-6142	403	24	artificial	artificial	ADJ
ap-6142	403	25	way	way	NOUN
ap-6142	403	26	in	in	ADP
ap-6142	403	27	[	[	X
ap-6142	403	28	14	14	NUM
ap-6142	403	29	]	]	PUNCT
ap-6142	403	30	and	and	CCONJ
ap-6142	403	31	[	[	X
ap-6142	403	32	15	15	NUM
ap-6142	403	33	]	]	X
ap-6142	403	34	,	,	PUNCT
ap-6142	403	35	ourkc	ourkc	PROPN
ap-6142	403	36	t	t	PROPN
ap-6142	403	37	has	have	VERB
ap-6142	403	38	a	a	DET
ap-6142	403	39	good	good	ADJ
ap-6142	403	40	physical	physical	ADJ
ap-6142	403	41	sense	sense	NOUN
ap-6142	403	42	.	.	PUNCT
ap-6142	404	1	naturally	naturally	ADV
ap-6142	404	2	,	,	PUNCT
ap-6142	404	3	the	the	DET
ap-6142	404	4	change	change	NOUN
ap-6142	404	5	of	of	ADP
ap-6142	404	6	set	set	NOUN
ap-6142	404	7	kc	kc	PROPN
ap-6142	404	8	t	t	PROPN
ap-6142	404	9	requires	require	VERB
ap-6142	404	10	a	a	DET
ap-6142	404	11	new	new	ADJ
ap-6142	404	12	technique	technique	NOUN
ap-6142	404	13	in	in	ADP
ap-6142	404	14	the	the	DET
ap-6142	404	15	derivation	derivation	NOUN
ap-6142	404	16	of	of	ADP
ap-6142	404	17	approximations	approximation	NOUN
ap-6142	404	18	.	.	PUNCT
ap-6142	405	1	we	we	PRON
ap-6142	405	2	do	do	AUX
ap-6142	405	3	not	not	PART
ap-6142	405	4	present	present	VERB
ap-6142	405	5	any	any	DET
ap-6142	405	6	numerical	numerical	ADJ
ap-6142	405	7	justification	justification	NOUN
ap-6142	405	8	of	of	ADP
ap-6142	405	9	our	our	PRON
ap-6142	405	10	model	model	NOUN
ap-6142	405	11	.	.	PUNCT
ap-6142	406	1	nevertheless	nevertheless	ADV
ap-6142	406	2	,	,	PUNCT
ap-6142	406	3	we	we	PRON
ap-6142	406	4	recall	recall	VERB
ap-6142	406	5	that	that	SCONJ
ap-6142	406	6	corresponding	correspond	VERB
ap-6142	406	7	numerical	numerical	ADJ
ap-6142	406	8	experiments	experiment	NOUN
ap-6142	406	9	,	,	PUNCT
ap-6142	406	10	also	also	ADV
ap-6142	406	11	involving	involve	VERB
ap-6142	406	12	comparison	comparison	NOUN
ap-6142	406	13	between	between	ADP
ap-6142	406	14	various	various	ADJ
ap-6142	406	15	artificial	artificial	ADJ
ap-6142	406	16	boundary	boundary	ADJ
ap-6142	406	17	conditions	condition	NOUN
ap-6142	406	18	on	on	ADP
ap-6142	406	19	the	the	DET
ap-6142	406	20	outflow	outflow	NOUN
ap-6142	406	21	,	,	PUNCT
ap-6142	406	22	suggested	suggest	VERB
ap-6142	406	23	in	in	ADP
ap-6142	406	24	paragraphs	paragraph	NOUN
ap-6142	406	25	2.2	2.2	NUM
ap-6142	406	26	and	and	CCONJ
ap-6142	406	27	2.3	2.3	NUM
ap-6142	406	28	,	,	PUNCT
ap-6142	406	29	would	would	AUX
ap-6142	406	30	be	be	AUX
ap-6142	406	31	very	very	ADV
ap-6142	406	32	desirable	desirable	ADJ
ap-6142	406	33	and	and	CCONJ
ap-6142	406	34	interesting	interesting	ADJ
ap-6142	406	35	.	.	PUNCT
ap-6142	407	1	acknowledgements	acknowledgement	NOUN
ap-6142	407	2	this	this	DET
ap-6142	407	3	work	work	NOUN
ap-6142	407	4	was	be	AUX
ap-6142	407	5	supported	support	VERB
ap-6142	407	6	by	by	ADP
ap-6142	407	7	the	the	DET
ap-6142	407	8	european	european	PROPN
ap-6142	407	9	regional	regional	PROPN
ap-6142	407	10	development	development	PROPN
ap-6142	407	11	fund	fund	PROPN
ap-6142	407	12	–	–	PUNCT
ap-6142	407	13	project	project	NOUN
ap-6142	407	14	“	"	PUNCT
ap-6142	407	15	center	center	NOUN
ap-6142	407	16	for	for	ADP
ap-6142	407	17	advanced	advanced	ADJ
ap-6142	407	18	applied	apply	VERB
ap-6142	407	19	science	science	NOUN
ap-6142	407	20	”	"	PUNCT
ap-6142	407	21	no	no	NOUN
ap-6142	407	22	.	.	PUNCT
ap-6142	407	23	cz.02.1.01/0.0/0.0/16_019/0000778	cz.02.1.01/0.0/0.0/16_019/0000778	PROPN
ap-6142	407	24	.	.	PUNCT
ap-6142	408	1	references	reference	NOUN
ap-6142	408	2	[	[	X
ap-6142	408	3	1	1	NUM
ap-6142	408	4	]	]	PUNCT
ap-6142	408	5	m.	m.	NOUN
ap-6142	408	6	beneš	beneš	NOUN
ap-6142	408	7	,	,	PUNCT
ap-6142	408	8	p.	p.	PROPN
ap-6142	408	9	kučera	kučera	NOUN
ap-6142	408	10	.	.	PUNCT
ap-6142	409	1	solutions	solution	NOUN
ap-6142	409	2	of	of	ADP
ap-6142	409	3	the	the	DET
ap-6142	409	4	navier	navier	NOUN
ap-6142	409	5	–	–	PUNCT
ap-6142	409	6	stokes	stoke	NOUN
ap-6142	409	7	equations	equation	NOUN
ap-6142	409	8	with	with	ADP
ap-6142	409	9	various	various	ADJ
ap-6142	409	10	types	type	NOUN
ap-6142	409	11	of	of	ADP
ap-6142	409	12	boundary	boundary	ADJ
ap-6142	409	13	conditions	condition	NOUN
ap-6142	409	14	.	.	PUNCT
ap-6142	410	1	archiv	archiv	PROPN
ap-6142	410	2	der	der	PROPN
ap-6142	410	3	mathematik	mathematik	PROPN
ap-6142	410	4	98:487–497	98:487–497	PROPN
ap-6142	410	5	,	,	PUNCT
ap-6142	410	6	2012	2012	NUM
ap-6142	410	7	.	.	PUNCT
ap-6142	411	1	doi:10.1007	doi:10.1007	VERB
ap-6142	411	2	/	/	SYM
ap-6142	412	1	s00013	s00013	PROPN
ap-6142	412	2	-	-	PUNCT
ap-6142	412	3	012	012	NUM
ap-6142	412	4	-	-	PUNCT
ap-6142	412	5	0387	0387	NUM
ap-6142	412	6	-	-	PUNCT
ap-6142	412	7	x.	x.	NOUN
ap-6142	413	1	[	[	X
ap-6142	413	2	2	2	NUM
ap-6142	413	3	]	]	PUNCT
ap-6142	413	4	c.-h	c.-h	NOUN
ap-6142	413	5	.	.	PUNCT
ap-6142	414	1	bruneau	bruneau	PROPN
ap-6142	414	2	,	,	PUNCT
ap-6142	414	3	p.	p.	PROPN
ap-6142	414	4	fabrie	fabrie	PROPN
ap-6142	414	5	.	.	PUNCT
ap-6142	415	1	new	new	ADJ
ap-6142	415	2	efficient	efficient	ADJ
ap-6142	415	3	boundary	boundary	ADJ
ap-6142	415	4	conditions	condition	NOUN
ap-6142	415	5	for	for	ADP
ap-6142	415	6	incompressible	incompressible	ADJ
ap-6142	415	7	navier	navier	NOUN
ap-6142	415	8	-	-	PUNCT
ap-6142	415	9	stokes	stoke	NOUN
ap-6142	415	10	equations	equation	NOUN
ap-6142	415	11	:	:	PUNCT
ap-6142	415	12	a	a	DET
ap-6142	415	13	well	well	ADV
ap-6142	415	14	-	-	PUNCT
ap-6142	415	15	posedness	posedness	NOUN
ap-6142	415	16	result	result	NOUN
ap-6142	415	17	.	.	PUNCT
ap-6142	416	1	mathematical	mathematical	ADJ
ap-6142	416	2	modelling	modelling	NOUN
ap-6142	416	3	and	and	CCONJ
ap-6142	416	4	numerical	numerical	ADJ
ap-6142	416	5	analysis	analysis	NOUN
ap-6142	416	6	30(7):815–840	30(7):815–840	NUM
ap-6142	416	7	,	,	PUNCT
ap-6142	416	8	1996	1996	NUM
ap-6142	416	9	.	.	PUNCT
ap-6142	417	1	doi:10.1051	doi:10.1051	NOUN
ap-6142	417	2	/	/	SYM
ap-6142	417	3	m2an/1996300708151	m2an/1996300708151	ADV
ap-6142	417	4	.	.	PUNCT
ap-6142	418	1	[	[	X
ap-6142	418	2	3	3	X
ap-6142	418	3	]	]	PUNCT
ap-6142	418	4	m.	m.	NOUN
ap-6142	418	5	feistauer	feistauer	NOUN
ap-6142	418	6	,	,	PUNCT
ap-6142	418	7	t.	t.	PROPN
ap-6142	418	8	neustupa	neustupa	PROPN
ap-6142	418	9	.	.	PUNCT
ap-6142	419	1	on	on	ADP
ap-6142	419	2	some	some	DET
ap-6142	419	3	aspects	aspect	NOUN
ap-6142	419	4	of	of	ADP
ap-6142	419	5	analysis	analysis	NOUN
ap-6142	419	6	of	of	ADP
ap-6142	419	7	incompressible	incompressible	ADJ
ap-6142	419	8	flow	flow	NOUN
ap-6142	419	9	through	through	ADP
ap-6142	419	10	cascades	cascade	NOUN
ap-6142	419	11	of	of	ADP
ap-6142	419	12	profiles	profile	NOUN
ap-6142	419	13	.	.	PUNCT
ap-6142	420	1	operator	operator	NOUN
ap-6142	420	2	theory	theory	NOUN
ap-6142	420	3	,	,	PUNCT
ap-6142	420	4	advances	advance	NOUN
ap-6142	420	5	and	and	CCONJ
ap-6142	420	6	applications	application	NOUN
ap-6142	420	7	147:257–276	147:257–276	NUM
ap-6142	420	8	,	,	PUNCT
ap-6142	420	9	2004	2004	NUM
ap-6142	420	10	.	.	PUNCT
ap-6142	421	1	[	[	X
ap-6142	421	2	4	4	NUM
ap-6142	421	3	]	]	PUNCT
ap-6142	421	4	m.	m.	NOUN
ap-6142	421	5	feistauer	feistauer	NOUN
ap-6142	421	6	,	,	PUNCT
ap-6142	421	7	t.	t.	PROPN
ap-6142	421	8	neustupa	neustupa	PROPN
ap-6142	421	9	.	.	PUNCT
ap-6142	422	1	on	on	ADP
ap-6142	422	2	non	non	ADJ
ap-6142	422	3	-	-	ADJ
ap-6142	422	4	stationary	stationary	ADJ
ap-6142	422	5	viscous	viscous	ADJ
ap-6142	422	6	incompressible	incompressible	ADJ
ap-6142	422	7	flow	flow	NOUN
ap-6142	422	8	through	through	ADP
ap-6142	422	9	a	a	DET
ap-6142	422	10	cascade	cascade	NOUN
ap-6142	422	11	of	of	ADP
ap-6142	422	12	profiles	profile	NOUN
ap-6142	422	13	.	.	PUNCT
ap-6142	423	1	mathematical	mathematical	ADJ
ap-6142	423	2	methods	method	NOUN
ap-6142	423	3	in	in	ADP
ap-6142	423	4	the	the	DET
ap-6142	423	5	applied	apply	VERB
ap-6142	423	6	sciences	science	NOUN
ap-6142	423	7	29(16):1907–1941	29(16):1907–1941	ADP
ap-6142	423	8	,	,	PUNCT
ap-6142	423	9	2006	2006	NUM
ap-6142	423	10	.	.	PUNCT
ap-6142	424	1	doi:10.1002	doi:10.1002	NOUN
ap-6142	424	2	/	/	SYM
ap-6142	424	3	mma.755	mma.755	PROPN
ap-6142	424	4	.	.	PUNCT
ap-6142	425	1	[	[	X
ap-6142	425	2	5	5	NUM
ap-6142	425	3	]	]	PUNCT
ap-6142	425	4	m.	m.	NOUN
ap-6142	425	5	feistauer	feistauer	NOUN
ap-6142	425	6	,	,	PUNCT
ap-6142	425	7	t.	t.	PROPN
ap-6142	425	8	neustupa	neustupa	PROPN
ap-6142	425	9	.	.	PUNCT
ap-6142	426	1	on	on	ADP
ap-6142	426	2	the	the	DET
ap-6142	426	3	existence	existence	NOUN
ap-6142	426	4	of	of	ADP
ap-6142	426	5	a	a	DET
ap-6142	426	6	weak	weak	ADJ
ap-6142	426	7	solution	solution	NOUN
ap-6142	426	8	of	of	ADP
ap-6142	426	9	viscous	viscous	ADJ
ap-6142	426	10	incompressible	incompressible	ADJ
ap-6142	426	11	flow	flow	NOUN
ap-6142	426	12	past	past	ADP
ap-6142	426	13	a	a	DET
ap-6142	426	14	cascade	cascade	NOUN
ap-6142	426	15	of	of	ADP
ap-6142	426	16	profiles	profile	NOUN
ap-6142	426	17	with	with	ADP
ap-6142	426	18	an	an	DET
ap-6142	426	19	arbitrarily	arbitrarily	ADV
ap-6142	426	20	large	large	ADJ
ap-6142	426	21	inflow	inflow	NOUN
ap-6142	426	22	.	.	PUNCT
ap-6142	427	1	journal	journal	NOUN
ap-6142	427	2	of	of	ADP
ap-6142	427	3	mathematical	mathematical	ADJ
ap-6142	427	4	fluid	fluid	ADJ
ap-6142	427	5	mechanics	mechanic	NOUN
ap-6142	427	6	15(15):701–715	15(15):701–715	NUM
ap-6142	427	7	,	,	PUNCT
ap-6142	427	8	2013	2013	NUM
ap-6142	427	9	.	.	PUNCT
ap-6142	428	1	doi:10.1007	doi:10.1007	VERB
ap-6142	428	2	/	/	SYM
ap-6142	428	3	s00021	s00021	NOUN
ap-6142	428	4	-	-	PUNCT
ap-6142	428	5	013	013	NUM
ap-6142	428	6	-	-	PUNCT
ap-6142	428	7	0135	0135	NUM
ap-6142	428	8	-	-	PUNCT
ap-6142	428	9	4	4	NUM
ap-6142	428	10	.	.	PUNCT
ap-6142	429	1	[	[	X
ap-6142	429	2	6	6	NUM
ap-6142	429	3	]	]	PUNCT
ap-6142	429	4	j.	j.	PROPN
ap-6142	429	5	g.	g.	PROPN
ap-6142	429	6	heywood	heywood	PROPN
ap-6142	429	7	,	,	PUNCT
ap-6142	429	8	r.	r.	PROPN
ap-6142	429	9	rannacher	rannacher	PROPN
ap-6142	429	10	,	,	PUNCT
ap-6142	429	11	s.	s.	PROPN
ap-6142	429	12	turek	turek	PROPN
ap-6142	429	13	.	.	PUNCT
ap-6142	430	1	artificial	artificial	ADJ
ap-6142	430	2	boundaries	boundary	NOUN
ap-6142	430	3	and	and	CCONJ
ap-6142	430	4	flux	flux	NOUN
ap-6142	430	5	and	and	CCONJ
ap-6142	430	6	pressure	pressure	NOUN
ap-6142	430	7	conditions	condition	NOUN
ap-6142	430	8	for	for	ADP
ap-6142	430	9	the	the	DET
ap-6142	430	10	incompressible	incompressible	ADJ
ap-6142	430	11	navier	navier	NOUN
ap-6142	430	12	–	–	PUNCT
ap-6142	430	13	stokes	stokes	PROPN
ap-6142	430	14	equations	equation	NOUN
ap-6142	430	15	.	.	PUNCT
ap-6142	431	1	international	international	ADJ
ap-6142	431	2	journal	journal	PROPN
ap-6142	431	3	for	for	ADP
ap-6142	431	4	numerical	numerical	ADJ
ap-6142	431	5	methods	method	NOUN
ap-6142	431	6	in	in	ADP
ap-6142	431	7	fluids	fluid	NOUN
ap-6142	431	8	22(5):325–352	22(5):325–352	NUM
ap-6142	431	9	,	,	PUNCT
ap-6142	431	10	1996	1996	NUM
ap-6142	431	11	.	.	PUNCT
ap-6142	432	1	doi:10.1002/(sici)10970363(19960315)22:5<325::aid	doi:10.1002/(sici)10970363(19960315)22:5<325::aid	NOUN
ap-6142	432	2	-	-	PUNCT
ap-6142	432	3	fld307>3.0.co;2	fld307>3.0.co;2	NOUN
ap-6142	432	4	-	-	PUNCT
ap-6142	432	5	y.	y.	NOUN
ap-6142	433	1	[	[	X
ap-6142	433	2	7	7	X
ap-6142	433	3	]	]	PUNCT
ap-6142	433	4	t.	t.	PROPN
ap-6142	433	5	neustupa	neustupa	PROPN
ap-6142	433	6	.	.	PUNCT
ap-6142	434	1	a	a	DET
ap-6142	434	2	steady	steady	ADJ
ap-6142	434	3	flow	flow	NOUN
ap-6142	434	4	through	through	ADP
ap-6142	434	5	a	a	DET
ap-6142	434	6	plane	plane	NOUN
ap-6142	434	7	cascade	cascade	NOUN
ap-6142	434	8	of	of	ADP
ap-6142	434	9	profiles	profile	NOUN
ap-6142	434	10	with	with	ADP
ap-6142	434	11	an	an	DET
ap-6142	434	12	arbitrarily	arbitrarily	ADV
ap-6142	434	13	large	large	ADJ
ap-6142	434	14	inflow	inflow	NOUN
ap-6142	434	15	–	–	PUNCT
ap-6142	434	16	the	the	DET
ap-6142	434	17	mathematical	mathematical	ADJ
ap-6142	434	18	model	model	NOUN
ap-6142	434	19	,	,	PUNCT
ap-6142	434	20	existence	existence	NOUN
ap-6142	434	21	of	of	ADP
ap-6142	434	22	a	a	DET
ap-6142	434	23	weak	weak	ADJ
ap-6142	434	24	solution	solution	NOUN
ap-6142	434	25	.	.	PUNCT
ap-6142	435	1	applied	apply	VERB
ap-6142	435	2	mathematics	mathematic	NOUN
ap-6142	435	3	and	and	CCONJ
ap-6142	435	4	computation	computation	NOUN
ap-6142	435	5	272:687–691	272:687–691	NUM
ap-6142	435	6	,	,	PUNCT
ap-6142	435	7	2016	2016	NUM
ap-6142	435	8	.	.	PUNCT
ap-6142	436	1	doi:10.1016	doi:10.1016	PROPN
ap-6142	436	2	/	/	SYM
ap-6142	436	3	j.amc.2015.05.066	j.amc.2015.05.066	PROPN
ap-6142	436	4	.	.	PUNCT
ap-6142	437	1	[	[	X
ap-6142	437	2	8	8	X
ap-6142	437	3	]	]	PUNCT
ap-6142	437	4	t.	t.	PROPN
ap-6142	437	5	neustupa	neustupa	PROPN
ap-6142	437	6	.	.	PUNCT
ap-6142	438	1	the	the	DET
ap-6142	438	2	weak	weak	ADJ
ap-6142	438	3	solvability	solvability	NOUN
ap-6142	438	4	of	of	ADP
ap-6142	438	5	the	the	DET
ap-6142	438	6	steady	steady	ADJ
ap-6142	438	7	problem	problem	NOUN
ap-6142	438	8	modelling	model	VERB
ap-6142	438	9	the	the	DET
ap-6142	438	10	flow	flow	NOUN
ap-6142	438	11	of	of	ADP
ap-6142	438	12	a	a	DET
ap-6142	438	13	viscous	viscous	ADJ
ap-6142	438	14	incompressible	incompressible	ADJ
ap-6142	438	15	heat	heat	NOUN
ap-6142	438	16	–	–	PUNCT
ap-6142	438	17	conductive	conductive	ADJ
ap-6142	438	18	fluid	fluid	NOUN
ap-6142	438	19	through	through	ADP
ap-6142	438	20	the	the	DET
ap-6142	438	21	profile	profile	ADJ
ap-6142	438	22	cascade	cascade	NOUN
ap-6142	438	23	.	.	PUNCT
ap-6142	439	1	international	international	ADJ
ap-6142	439	2	journal	journal	PROPN
ap-6142	439	3	of	of	ADP
ap-6142	439	4	numerical	numerical	ADJ
ap-6142	439	5	methods	method	NOUN
ap-6142	439	6	for	for	ADP
ap-6142	439	7	heat	heat	NOUN
ap-6142	439	8	&	&	CCONJ
ap-6142	439	9	fluid	fluid	ADJ
ap-6142	439	10	flow	flow	NOUN
ap-6142	439	11	27(7):1451–1466	27(7):1451–1466	NUM
ap-6142	439	12	,	,	PUNCT
ap-6142	439	13	2017	2017	NUM
ap-6142	439	14	.	.	PUNCT
ap-6142	440	1	doi:10.1108	doi:10.1108	PROPN
ap-6142	440	2	/	/	SYM
ap-6142	440	3	hff-03	hff-03	PROPN
ap-6142	440	4	-	-	PUNCT
ap-6142	440	5	2016	2016	NUM
ap-6142	440	6	-	-	PUNCT
ap-6142	440	7	0104	0104	NUM
ap-6142	440	8	.	.	PUNCT
ap-6142	441	1	[	[	X
ap-6142	441	2	9	9	NUM
ap-6142	441	3	]	]	PUNCT
ap-6142	441	4	p.	p.	NOUN
ap-6142	441	5	kučera	kučera	PROPN
ap-6142	441	6	,	,	PUNCT
ap-6142	441	7	z.	z.	PROPN
ap-6142	441	8	skalák	skalák	PROPN
ap-6142	441	9	.	.	PUNCT
ap-6142	442	1	local	local	ADJ
ap-6142	442	2	solutions	solution	NOUN
ap-6142	442	3	to	to	ADP
ap-6142	442	4	the	the	DET
ap-6142	442	5	navier	navier	NOUN
ap-6142	442	6	–	–	PUNCT
ap-6142	442	7	stokes	stoke	NOUN
ap-6142	442	8	equations	equation	NOUN
ap-6142	442	9	with	with	ADP
ap-6142	442	10	mixed	mixed	ADJ
ap-6142	442	11	boundary	boundary	ADJ
ap-6142	442	12	conditions	condition	NOUN
ap-6142	442	13	.	.	PUNCT
ap-6142	443	1	acta	acta	PROPN
ap-6142	443	2	applicandae	applicandae	PROPN
ap-6142	443	3	mathematicae	mathematicae	PROPN
ap-6142	443	4	54:275–288	54:275–288	PROPN
ap-6142	443	5	,	,	PUNCT
ap-6142	443	6	1998	1998	NUM
ap-6142	443	7	.	.	PUNCT
ap-6142	444	1	doi:10.1023	doi:10.1023	NOUN
ap-6142	444	2	/	/	SYM
ap-6142	445	1	a:1006185601807	a:1006185601807	X
ap-6142	445	2	.	.	PUNCT
ap-6142	446	1	[	[	X
ap-6142	446	2	10	10	NUM
ap-6142	446	3	]	]	PUNCT
ap-6142	446	4	p.	p.	NOUN
ap-6142	446	5	kučera	kučera	PROPN
ap-6142	446	6	.	.	PUNCT
ap-6142	447	1	basic	basic	ADJ
ap-6142	447	2	properties	property	NOUN
ap-6142	447	3	of	of	ADP
ap-6142	447	4	the	the	DET
ap-6142	447	5	non	non	ADJ
ap-6142	447	6	-	-	ADJ
ap-6142	447	7	steady	steady	ADJ
ap-6142	447	8	navier	navier	NOUN
ap-6142	447	9	–	–	PUNCT
ap-6142	447	10	stokes	stoke	VERB
ap-6142	447	11	equations	equation	NOUN
ap-6142	447	12	with	with	ADP
ap-6142	447	13	mixed	mixed	ADJ
ap-6142	447	14	boundary	boundary	ADJ
ap-6142	447	15	conditions	condition	NOUN
ap-6142	447	16	in	in	ADP
ap-6142	447	17	a	a	DET
ap-6142	447	18	bounded	bounded	ADJ
ap-6142	447	19	domain	domain	NOUN
ap-6142	447	20	.	.	PUNCT
ap-6142	448	1	ann	ann	PROPN
ap-6142	448	2	univ	univ	PROPN
ap-6142	448	3	ferrara	ferrara	PROPN
ap-6142	448	4	55:289–308	55:289–308	PROPN
ap-6142	448	5	,	,	PUNCT
ap-6142	448	6	2009	2009	NUM
ap-6142	448	7	.	.	PUNCT
ap-6142	449	1	[	[	X
ap-6142	449	2	11	11	NUM
ap-6142	449	3	]	]	PUNCT
ap-6142	449	4	m.	m.	NOUN
ap-6142	449	5	braack	braack	NOUN
ap-6142	449	6	,	,	PUNCT
ap-6142	449	7	p.	p.	PROPN
ap-6142	449	8	b.	b.	PROPN
ap-6142	449	9	mucha	mucha	PROPN
ap-6142	449	10	.	.	PUNCT
ap-6142	450	1	directional	directional	PROPN
ap-6142	450	2	do	do	AUX
ap-6142	450	3	-	-	PUNCT
ap-6142	450	4	nothing	nothing	PRON
ap-6142	450	5	condition	condition	NOUN
ap-6142	450	6	for	for	ADP
ap-6142	450	7	the	the	DET
ap-6142	450	8	navier	navier	NOUN
ap-6142	450	9	-	-	PUNCT
ap-6142	450	10	stokes	stokes	PROPN
ap-6142	450	11	equations	equation	NOUN
ap-6142	450	12	.	.	PUNCT
ap-6142	451	1	journal	journal	NOUN
ap-6142	451	2	of	of	ADP
ap-6142	451	3	computational	computational	ADJ
ap-6142	451	4	mathematics	mathematic	NOUN
ap-6142	451	5	32(5):507–521	32(5):507–521	NUM
ap-6142	451	6	,	,	PUNCT
ap-6142	451	7	2014	2014	NUM
ap-6142	451	8	.	.	PUNCT
ap-6142	452	1	doi:10.4208	doi:10.4208	NOUN
ap-6142	452	2	/	/	SYM
ap-6142	453	1	jcm.1405	jcm.1405	PROPN
ap-6142	453	2	-	-	PUNCT
ap-6142	453	3	m4347	m4347	PROPN
ap-6142	453	4	.	.	PUNCT
ap-6142	454	1	[	[	X
ap-6142	454	2	12	12	NUM
ap-6142	454	3	]	]	PUNCT
ap-6142	454	4	m.	m.	NOUN
ap-6142	454	5	lanzendörfer	lanzendörfer	NOUN
ap-6142	454	6	,	,	PUNCT
ap-6142	454	7	j.	j.	PROPN
ap-6142	454	8	stebel	stebel	PROPN
ap-6142	454	9	.	.	PUNCT
ap-6142	455	1	on	on	ADP
ap-6142	455	2	pressure	pressure	NOUN
ap-6142	455	3	boundary	boundary	ADJ
ap-6142	455	4	conditions	condition	NOUN
ap-6142	455	5	for	for	ADP
ap-6142	455	6	steady	steady	ADJ
ap-6142	455	7	flows	flow	NOUN
ap-6142	455	8	of	of	ADP
ap-6142	455	9	incompressible	incompressible	ADJ
ap-6142	455	10	fluids	fluid	NOUN
ap-6142	455	11	with	with	ADP
ap-6142	455	12	pressure	pressure	NOUN
ap-6142	455	13	and	and	CCONJ
ap-6142	455	14	shear	shear	NOUN
ap-6142	455	15	rate	rate	NOUN
ap-6142	455	16	dependent	dependent	ADJ
ap-6142	455	17	viscosities	viscosity	NOUN
ap-6142	455	18	.	.	PUNCT
ap-6142	456	1	applications	application	NOUN
ap-6142	456	2	of	of	ADP
ap-6142	456	3	mathematics	mathematics	NOUN
ap-6142	456	4	56(3):265–285	56(3):265–285	PROPN
ap-6142	456	5	,	,	PUNCT
ap-6142	456	6	2011	2011	NUM
ap-6142	456	7	.	.	PUNCT
ap-6142	457	1	doi:10.1007	doi:10.1007	VERB
ap-6142	457	2	/	/	SYM
ap-6142	457	3	s10492	s10492	NOUN
ap-6142	457	4	-	-	PUNCT
ap-6142	457	5	011	011	NUM
ap-6142	457	6	-	-	PUNCT
ap-6142	457	7	0016	0016	NUM
ap-6142	457	8	-	-	PUNCT
ap-6142	457	9	1	1	NUM
ap-6142	457	10	.	.	PUNCT
ap-6142	458	1	[	[	X
ap-6142	458	2	13	13	NUM
ap-6142	458	3	]	]	PUNCT
ap-6142	458	4	s.	s.	PROPN
ap-6142	458	5	kračmar	kračmar	PROPN
ap-6142	458	6	,	,	PUNCT
ap-6142	458	7	j.	j.	PROPN
ap-6142	458	8	neustupa	neustupa	PROPN
ap-6142	458	9	.	.	PUNCT
ap-6142	459	1	modelling	modelling	NOUN
ap-6142	459	2	of	of	ADP
ap-6142	459	3	flows	flow	NOUN
ap-6142	459	4	of	of	ADP
ap-6142	459	5	a	a	DET
ap-6142	459	6	viscous	viscous	ADJ
ap-6142	459	7	incompressible	incompressible	ADJ
ap-6142	459	8	fluid	fluid	NOUN
ap-6142	459	9	through	through	ADP
ap-6142	459	10	a	a	DET
ap-6142	459	11	channel	channel	NOUN
ap-6142	459	12	by	by	ADP
ap-6142	459	13	means	mean	NOUN
ap-6142	459	14	of	of	ADP
ap-6142	459	15	variational	variational	ADJ
ap-6142	459	16	inequalities	inequality	NOUN
ap-6142	459	17	.	.	PUNCT
ap-6142	460	1	zamm	zamm	PROPN
ap-6142	460	2	74(6):637–639	74(6):637–639	PROPN
ap-6142	460	3	,	,	PUNCT
ap-6142	460	4	1994	1994	NUM
ap-6142	460	5	.	.	PUNCT
ap-6142	461	1	[	[	X
ap-6142	461	2	14	14	NUM
ap-6142	461	3	]	]	X
ap-6142	461	4	s.	s.	PROPN
ap-6142	461	5	kračmar	kračmar	PROPN
ap-6142	461	6	,	,	PUNCT
ap-6142	461	7	j.	j.	PROPN
ap-6142	461	8	neustupa	neustupa	PROPN
ap-6142	461	9	.	.	PUNCT
ap-6142	462	1	a	a	DET
ap-6142	462	2	weak	weak	ADJ
ap-6142	462	3	solvability	solvability	NOUN
ap-6142	462	4	of	of	ADP
ap-6142	462	5	a	a	DET
ap-6142	462	6	steady	steady	ADJ
ap-6142	462	7	variational	variational	ADJ
ap-6142	462	8	inequality	inequality	NOUN
ap-6142	462	9	of	of	ADP
ap-6142	462	10	the	the	DET
ap-6142	462	11	navier	navier	NOUN
ap-6142	462	12	–	–	PUNCT
ap-6142	462	13	stokes	stoke	NOUN
ap-6142	462	14	type	type	NOUN
ap-6142	462	15	with	with	ADP
ap-6142	462	16	mixed	mixed	ADJ
ap-6142	462	17	boundary	boundary	ADJ
ap-6142	462	18	conditions	condition	NOUN
ap-6142	462	19	.	.	PUNCT
ap-6142	463	1	nonlinear	nonlinear	ADJ
ap-6142	463	2	analysis	analysis	NOUN
ap-6142	463	3	:	:	PUNCT
ap-6142	463	4	theory	theory	NOUN
ap-6142	463	5	,	,	PUNCT
ap-6142	463	6	methods	method	NOUN
ap-6142	463	7	&	&	CCONJ
ap-6142	463	8	applications	application	NOUN
ap-6142	463	9	47(6):4169–4180	47(6):4169–4180	NUM
ap-6142	463	10	,	,	PUNCT
ap-6142	463	11	2001	2001	NUM
ap-6142	463	12	.	.	PUNCT
ap-6142	464	1	proceedings	proceeding	NOUN
ap-6142	464	2	of	of	ADP
ap-6142	464	3	the	the	DET
ap-6142	464	4	third	third	ADJ
ap-6142	464	5	world	world	NOUN
ap-6142	464	6	congress	congress	PROPN
ap-6142	464	7	of	of	ADP
ap-6142	464	8	nonlinear	nonlinear	ADJ
ap-6142	464	9	analysts	analyst	NOUN
ap-6142	464	10	,	,	PUNCT
ap-6142	464	11	doi:10.1016	doi:10.1016	PROPN
ap-6142	464	12	/	/	SYM
ap-6142	464	13	s0362	s0362	PROPN
ap-6142	464	14	-	-	PUNCT
ap-6142	464	15	546x(01)00534	546x(01)00534	PROPN
ap-6142	464	16	-	-	PUNCT
ap-6142	464	17	x.	x.	NOUN
ap-6142	465	1	[	[	X
ap-6142	465	2	15	15	NUM
ap-6142	465	3	]	]	X
ap-6142	465	4	s.	s.	PROPN
ap-6142	465	5	kračmar	kračmar	PROPN
ap-6142	465	6	,	,	PUNCT
ap-6142	465	7	j.	j.	PROPN
ap-6142	465	8	neustupa	neustupa	PROPN
ap-6142	465	9	.	.	PUNCT
ap-6142	466	1	modeling	modeling	NOUN
ap-6142	466	2	of	of	ADP
ap-6142	466	3	the	the	DET
ap-6142	466	4	unsteady	unsteady	ADJ
ap-6142	466	5	flow	flow	NOUN
ap-6142	466	6	through	through	ADP
ap-6142	466	7	a	a	DET
ap-6142	466	8	channel	channel	NOUN
ap-6142	466	9	with	with	ADP
ap-6142	466	10	an	an	DET
ap-6142	466	11	artificial	artificial	ADJ
ap-6142	466	12	outflow	outflow	NOUN
ap-6142	466	13	condition	condition	NOUN
ap-6142	466	14	by	by	ADP
ap-6142	466	15	the	the	DET
ap-6142	466	16	navier	navier	NOUN
ap-6142	466	17	–	–	PUNCT
ap-6142	466	18	stokes	stokes	PROPN
ap-6142	466	19	variational	variational	ADJ
ap-6142	466	20	inequality	inequality	NOUN
ap-6142	466	21	.	.	PUNCT
ap-6142	467	1	mathematische	mathematische	PROPN
ap-6142	467	2	nachrichten	nachrichten	PROPN
ap-6142	467	3	291(11–12):1801–1814	291(11–12):1801–1814	NUM
ap-6142	467	4	,	,	PUNCT
ap-6142	467	5	2018	2018	NUM
ap-6142	467	6	.	.	PUNCT
ap-6142	468	1	doi:10.1002	doi:10.1002	NOUN
ap-6142	468	2	/	/	SYM
ap-6142	468	3	mana.201700228	mana.201700228	PROPN
ap-6142	468	4	.	.	PUNCT
ap-6142	469	1	[	[	X
ap-6142	469	2	16	16	NUM
ap-6142	469	3	]	]	X
ap-6142	469	4	p.	p.	NOUN
ap-6142	469	5	deuring	deuring	NOUN
ap-6142	469	6	,	,	PUNCT
ap-6142	469	7	s.	s.	PROPN
ap-6142	469	8	kračmar	kračmar	PROPN
ap-6142	469	9	.	.	PUNCT
ap-6142	470	1	artificial	artificial	ADJ
ap-6142	470	2	boundary	boundary	ADJ
ap-6142	470	3	conditions	condition	NOUN
ap-6142	470	4	for	for	ADP
ap-6142	470	5	the	the	DET
ap-6142	470	6	oseen	oseen	NOUN
ap-6142	470	7	system	system	NOUN
ap-6142	470	8	in	in	ADP
ap-6142	470	9	3d	3d	NUM
ap-6142	470	10	exterior	exterior	ADJ
ap-6142	470	11	domains	domain	NOUN
ap-6142	470	12	.	.	PUNCT
ap-6142	471	1	analysis	analysis	NOUN
ap-6142	471	2	20:65–90	20:65–90	NUM
ap-6142	471	3	,	,	PUNCT
ap-6142	471	4	2012	2012	NUM
ap-6142	471	5	.	.	PUNCT
ap-6142	472	1	[	[	X
ap-6142	472	2	17	17	NUM
ap-6142	472	3	]	]	X
ap-6142	472	4	p.	p.	NOUN
ap-6142	472	5	deuring	deuring	NOUN
ap-6142	472	6	,	,	PUNCT
ap-6142	472	7	s.	s.	PROPN
ap-6142	472	8	kračmar	kračmar	PROPN
ap-6142	472	9	.	.	PUNCT
ap-6142	473	1	exterior	exterior	ADJ
ap-6142	473	2	stationary	stationary	ADJ
ap-6142	473	3	navier	navier	NOUN
ap-6142	473	4	-	-	PUNCT
ap-6142	473	5	stokes	stoke	NOUN
ap-6142	473	6	flows	flow	NOUN
ap-6142	473	7	in	in	ADP
ap-6142	473	8	3d	3d	NUM
ap-6142	473	9	with	with	ADP
ap-6142	473	10	non	non	ADJ
ap-6142	473	11	-	-	ADJ
ap-6142	473	12	zero	zero	ADJ
ap-6142	473	13	velocity	velocity	NOUN
ap-6142	473	14	at	at	ADP
ap-6142	473	15	infinity	infinity	NOUN
ap-6142	473	16	:	:	PUNCT
ap-6142	473	17	approximation	approximation	NOUN
ap-6142	473	18	by	by	ADP
ap-6142	473	19	flows	flow	NOUN
ap-6142	473	20	in	in	ADP
ap-6142	473	21	bounded	bounded	ADJ
ap-6142	473	22	domains	domain	NOUN
ap-6142	473	23	.	.	PUNCT
ap-6142	474	1	mathematische	mathematische	PROPN
ap-6142	474	2	nachrichten	nachrichten	NUM
ap-6142	474	3	269–270:86–115	269–270:86–115	PROPN
ap-6142	474	4	,	,	PUNCT
ap-6142	474	5	2004	2004	NUM
ap-6142	474	6	.	.	PUNCT
ap-6142	475	1	doi:10.1002	doi:10.1002	NOUN
ap-6142	475	2	/	/	SYM
ap-6142	475	3	mana.200310167	mana.200310167	PROPN
ap-6142	475	4	.	.	PUNCT
ap-6142	476	1	[	[	X
ap-6142	476	2	18	18	NUM
ap-6142	476	3	]	]	X
ap-6142	476	4	r.	r.	NOUN
ap-6142	476	5	temam	temam	NOUN
ap-6142	476	6	.	.	PUNCT
ap-6142	477	1	navier	navier	NOUN
ap-6142	477	2	-	-	PUNCT
ap-6142	477	3	stokes	stokes	PROPN
ap-6142	477	4	equations	equation	NOUN
ap-6142	477	5	.	.	PUNCT
ap-6142	478	1	north	north	NOUN
ap-6142	478	2	-	-	PUNCT
ap-6142	478	3	holland	holland	PROPN
ap-6142	478	4	,	,	PUNCT
ap-6142	478	5	amsterdam	amsterdam	PROPN
ap-6142	478	6	,	,	PUNCT
ap-6142	478	7	1977	1977	NUM
ap-6142	478	8	.	.	PUNCT
ap-6142	479	1	[	[	X
ap-6142	479	2	19	19	NUM
ap-6142	479	3	]	]	X
ap-6142	479	4	j.	j.	PROPN
ap-6142	479	5	l.	l.	PROPN
ap-6142	479	6	lions	lions	PROPN
ap-6142	479	7	,	,	PUNCT
ap-6142	479	8	e.	e.	PROPN
ap-6142	479	9	magenes	magenes	PROPN
ap-6142	479	10	.	.	PUNCT
ap-6142	480	1	nonhomogeneous	nonhomogeneous	ADJ
ap-6142	480	2	boundary	boundary	ADJ
ap-6142	480	3	value	value	NOUN
ap-6142	480	4	problems	problem	NOUN
ap-6142	480	5	and	and	CCONJ
ap-6142	480	6	applications	application	NOUN
ap-6142	480	7	i.	i.	NOUN
ap-6142	480	8	springer	springer	PROPN
ap-6142	480	9	–	–	PUNCT
ap-6142	480	10	verlag	verlag	PROPN
ap-6142	480	11	,	,	PUNCT
ap-6142	480	12	new	new	PROPN
ap-6142	480	13	york	york	PROPN
ap-6142	480	14	,	,	PUNCT
ap-6142	480	15	1972	1972	NUM
ap-6142	480	16	.	.	PUNCT
ap-6142	481	1	doi:10.1007/978	doi:10.1007/978	ADJ
ap-6142	481	2	-	-	PUNCT
ap-6142	481	3	3	3	NUM
ap-6142	481	4	-	-	PUNCT
ap-6142	481	5	642	642	NUM
ap-6142	481	6	-	-	PUNCT
ap-6142	481	7	65161	65161	NUM
ap-6142	481	8	-	-	SYM
ap-6142	481	9	8	8	NUM
ap-6142	481	10	.	.	PUNCT
ap-6142	482	1	[	[	X
ap-6142	482	2	20	20	NUM
ap-6142	482	3	]	]	PUNCT
ap-6142	482	4	i.	i.	NOUN
ap-6142	482	5	ekeland	ekeland	PROPN
ap-6142	482	6	,	,	PUNCT
ap-6142	482	7	r.	r.	NOUN
ap-6142	482	8	temam	temam	NOUN
ap-6142	482	9	.	.	PUNCT
ap-6142	483	1	convex	convex	VERB
ap-6142	483	2	analysis	analysis	NOUN
ap-6142	483	3	and	and	CCONJ
ap-6142	483	4	variational	variational	ADJ
ap-6142	483	5	problems	problem	NOUN
ap-6142	483	6	.	.	PUNCT
ap-6142	484	1	north	north	NOUN
ap-6142	484	2	holland	holland	PROPN
ap-6142	484	3	publishing	publishing	PROPN
ap-6142	484	4	company	company	NOUN
ap-6142	484	5	,	,	PUNCT
ap-6142	484	6	amsterdam	amsterdam	PROPN
ap-6142	484	7	–	–	PUNCT
ap-6142	484	8	oxford	oxford	PROPN
ap-6142	484	9	–	–	PUNCT
ap-6142	484	10	new	new	PROPN
ap-6142	484	11	york	york	PROPN
ap-6142	484	12	,	,	PUNCT
ap-6142	484	13	1976	1976	NUM
ap-6142	484	14	.	.	PUNCT
ap-6142	485	1	doi:10.1137/1.9781611971088.bm	doi:10.1137/1.9781611971088.bm	NOUN
ap-6142	485	2	.	.	PUNCT
ap-6142	486	1	[	[	X
ap-6142	486	2	21	21	NUM
ap-6142	486	3	]	]	X
ap-6142	486	4	g.	g.	PROPN
ap-6142	486	5	p.	p.	PROPN
ap-6142	486	6	galdi	galdi	PROPN
ap-6142	486	7	.	.	PUNCT
ap-6142	487	1	an	an	DET
ap-6142	487	2	introduction	introduction	NOUN
ap-6142	487	3	to	to	ADP
ap-6142	487	4	the	the	DET
ap-6142	487	5	mathematical	mathematical	ADJ
ap-6142	487	6	theory	theory	NOUN
ap-6142	487	7	of	of	ADP
ap-6142	487	8	the	the	DET
ap-6142	487	9	navier	navier	NOUN
ap-6142	487	10	–	–	PUNCT
ap-6142	487	11	stokes	stoke	NOUN
ap-6142	487	12	equations	equation	NOUN
ap-6142	487	13	,	,	PUNCT
ap-6142	487	14	steady	steady	ADJ
ap-6142	487	15	–	–	PUNCT
ap-6142	487	16	state	state	NOUN
ap-6142	487	17	problems	problem	NOUN
ap-6142	487	18	.	.	PUNCT
ap-6142	488	1	springer	springer	NOUN
ap-6142	488	2	–	–	PUNCT
ap-6142	488	3	verlag	verlag	PROPN
ap-6142	488	4	,	,	PUNCT
ap-6142	488	5	2nd	2nd	ADJ
ap-6142	488	6	edn	edn	PROPN
ap-6142	488	7	.	.	PUNCT
ap-6142	488	8	,	,	PUNCT
ap-6142	488	9	2011	2011	NUM
ap-6142	488	10	.	.	PUNCT
ap-6142	489	1	[	[	X
ap-6142	489	2	22	22	NUM
ap-6142	489	3	]	]	PUNCT
ap-6142	489	4	j.	j.	PROPN
ap-6142	489	5	l.	l.	PROPN
ap-6142	489	6	lions	lions	PROPN
ap-6142	489	7	.	.	PUNCT
ap-6142	490	1	quelques	quelques	PROPN
ap-6142	490	2	méthodes	méthode	NOUN
ap-6142	490	3	de	de	X
ap-6142	490	4	résolution	résolution	PROPN
ap-6142	490	5	des	des	X
ap-6142	490	6	problèmes	problèmes	PROPN
ap-6142	490	7	âux	âux	PROPN
ap-6142	490	8	limites	limites	PROPN
ap-6142	490	9	non	non	X
ap-6142	490	10	linéaire	linéaire	NOUN
ap-6142	490	11	.	.	PUNCT
ap-6142	491	1	dunod	dunod	PROPN
ap-6142	491	2	,	,	PUNCT
ap-6142	491	3	gauthier	gauthier	PROPN
ap-6142	491	4	–	–	PUNCT
ap-6142	491	5	villars	villar	NOUN
ap-6142	491	6	,	,	PUNCT
ap-6142	491	7	paris	paris	PROPN
ap-6142	491	8	,	,	PUNCT
ap-6142	491	9	1969	1969	NUM
ap-6142	491	10	.	.	PUNCT
ap-6142	492	1	[	[	X
ap-6142	492	2	23	23	NUM
ap-6142	492	3	]	]	PUNCT
ap-6142	492	4	j.	j.	PROPN
ap-6142	492	5	marschall	marschall	PROPN
ap-6142	492	6	.	.	PUNCT
ap-6142	493	1	the	the	DET
ap-6142	493	2	trace	trace	NOUN
ap-6142	493	3	of	of	ADP
ap-6142	493	4	sobolev	sobolev	NOUN
ap-6142	493	5	–	–	PUNCT
ap-6142	493	6	slobodeckij	slobodeckij	PROPN
ap-6142	493	7	spaces	space	VERB
ap-6142	493	8	on	on	ADP
ap-6142	493	9	lipschitz	lipschitz	NOUN
ap-6142	493	10	domains	domain	NOUN
ap-6142	493	11	.	.	PUNCT
ap-6142	494	1	manuscipta	manuscipta	PROPN
ap-6142	494	2	mathematica	mathematica	PROPN
ap-6142	494	3	58:47–65	58:47–65	PROPN
ap-6142	494	4	,	,	PUNCT
ap-6142	494	5	1987	1987	NUM
ap-6142	494	6	.	.	PUNCT
ap-6142	495	1	doi:10.1007	doi:10.1007	PROPN
ap-6142	495	2	/	/	SYM
ap-6142	495	3	bf01169082	bf01169082	PROPN
ap-6142	495	4	.	.	PUNCT
ap-6142	496	1	98	98	NUM
ap-6142	496	2	http://dx.doi.org/10.1007/s00013-012-0387-x	http://dx.doi.org/10.1007/s00013-012-0387-x	NOUN
ap-6142	496	3	http://dx.doi.org/10.1051/m2an/1996300708151	http://dx.doi.org/10.1051/m2an/1996300708151	PROPN
ap-6142	496	4	http://dx.doi.org/10.1002/mma.755	http://dx.doi.org/10.1002/mma.755	VERB
ap-6142	496	5	http://dx.doi.org/10.1007/s00021-013-0135-4	http://dx.doi.org/10.1007/s00021-013-0135-4	PRON
ap-6142	496	6	http://dx.doi.org/10.1002/(sici)1097-0363(19960315)22:5<325::aid-fld307>3.0.co;2-y	http://dx.doi.org/10.1002/(sici)1097-0363(19960315)22:5<325::aid-fld307>3.0.co;2-y	PUNCT
ap-6142	496	7	http://dx.doi.org/10.1002/(sici)1097-0363(19960315)22:5<325::aid-fld307>3.0.co;2-y	http://dx.doi.org/10.1002/(sici)1097-0363(19960315)22:5<325::aid-fld307>3.0.co;2-y	INTJ
ap-6142	496	8	http://dx.doi.org/10.1016/j.amc.2015.05.066	http://dx.doi.org/10.1016/j.amc.2015.05.066	PROPN
ap-6142	496	9	http://dx.doi.org/10.1108/hff-03-2016-0104	http://dx.doi.org/10.1108/hff-03-2016-0104	PROPN
ap-6142	496	10	http://dx.doi.org/10.1023/a:1006185601807	http://dx.doi.org/10.1023/a:1006185601807	PROPN
ap-6142	496	11	http://dx.doi.org/10.4208/jcm.1405-m4347	http://dx.doi.org/10.4208/jcm.1405-m4347	PROPN
ap-6142	496	12	http://dx.doi.org/10.1007/s10492-011-0016-1	http://dx.doi.org/10.1007/s10492-011-0016-1	PROPN
ap-6142	496	13	http://dx.doi.org/10.1016/s0362-546x(01)00534-x	http://dx.doi.org/10.1016/s0362-546x(01)00534-x	PRON
ap-6142	496	14	http://dx.doi.org/10.1002/mana.201700228	http://dx.doi.org/10.1002/mana.201700228	PROPN
ap-6142	496	15	http://dx.doi.org/10.1002/mana.200310167	http://dx.doi.org/10.1002/mana.200310167	PUNCT
ap-6142	496	16	http://dx.doi.org/10.1007/978-3-642-65161-8	http://dx.doi.org/10.1007/978-3-642-65161-8	PROPN
ap-6142	496	17	http://dx.doi.org/10.1137/1.9781611971088.bm	http://dx.doi.org/10.1137/1.9781611971088.bm	PROPN
ap-6142	496	18	http://dx.doi.org/10.1007/bf01169082	http://dx.doi.org/10.1007/bf01169082	PROPN
ap-6142	496	19	acta	acta	PROPN
ap-6142	496	20	polytechnica	polytechnica	PROPN
ap-6142	496	21	61(si):89–98	61(si):89–98	NUM
ap-6142	496	22	,	,	PUNCT
ap-6142	496	23	2021	2021	NUM
ap-6142	496	24	1	1	NUM
ap-6142	496	25	introduction	introduction	NOUN
ap-6142	496	26	1.1	1.1	NUM
ap-6142	496	27	the	the	DET
ap-6142	496	28	considered	consider	VERB
ap-6142	496	29	initial	initial	ADJ
ap-6142	496	30	–	–	PUNCT
ap-6142	496	31	boundary	boundary	ADJ
ap-6142	496	32	value	value	NOUN
ap-6142	496	33	problem	problem	NOUN
ap-6142	496	34	1.2	1.2	NUM
ap-6142	496	35	on	on	ADP
ap-6142	496	36	some	some	DET
ap-6142	496	37	previous	previous	ADJ
ap-6142	496	38	related	related	ADJ
ap-6142	496	39	existential	existential	ADJ
ap-6142	496	40	results	result	NOUN
ap-6142	496	41	2	2	NUM
ap-6142	496	42	several	several	ADJ
ap-6142	496	43	boundary	boundary	ADJ
ap-6142	496	44	conditions	condition	NOUN
ap-6142	496	45	of	of	ADP
ap-6142	496	46	the	the	DET
ap-6142	496	47	`	`	PUNCT
ap-6142	496	48	`	`	PUNCT
ap-6142	496	49	do	do	VERB
ap-6142	496	50	nothing	nothing	PRON
ap-6142	496	51	''	''	PUNCT
ap-6142	496	52	type	type	NOUN
ap-6142	496	53	2.1	2.1	NUM
ap-6142	496	54	three	three	NUM
ap-6142	496	55	equivalent	equivalent	ADJ
ap-6142	496	56	forms	form	NOUN
ap-6142	496	57	of	of	ADP
ap-6142	496	58	the	the	DET
ap-6142	496	59	dynamic	dynamic	ADJ
ap-6142	496	60	stress	stress	NOUN
ap-6142	496	61	tensor	tensor	NOUN
ap-6142	496	62	in	in	ADP
ap-6142	496	63	equation	equation	NOUN
ap-6142	496	64	(	(	PUNCT
ap-6142	496	65	1	1	NUM
ap-6142	496	66	)	)	PUNCT
ap-6142	496	67	2.2	2.2	NUM
ap-6142	496	68	variational	variational	ADJ
ap-6142	496	69	formulations	formulation	NOUN
ap-6142	496	70	of	of	ADP
ap-6142	496	71	the	the	DET
ap-6142	496	72	initial	initial	ADJ
ap-6142	496	73	–	–	PUNCT
ap-6142	496	74	boundary	boundary	ADJ
ap-6142	496	75	value	value	NOUN
ap-6142	496	76	problem	problem	NOUN
ap-6142	496	77	2.3	2.3	NUM
ap-6142	496	78	the	the	DET
ap-6142	496	79	momentum	momentum	NOUN
ap-6142	496	80	equation	equation	NOUN
ap-6142	496	81	with	with	ADP
ap-6142	496	82	the	the	DET
ap-6142	496	83	bernoulli	bernoulli	PROPN
ap-6142	496	84	pressure	pressure	NOUN
ap-6142	496	85	2.4	2.4	NUM
ap-6142	496	86	which	which	DET
ap-6142	496	87	artificial	artificial	ADJ
ap-6142	496	88	boundary	boundary	ADJ
ap-6142	496	89	condition	condition	NOUN
ap-6142	496	90	is	be	AUX
ap-6142	496	91	the	the	DET
ap-6142	496	92	best	good	ADJ
ap-6142	496	93	?	?	PUNCT
ap-6142	497	1	3	3	NUM
ap-6142	497	2	the	the	DET
ap-6142	497	3	navier	navier	NOUN
ap-6142	497	4	–	–	PUNCT
ap-6142	497	5	stokes	stoke	VERB
ap-6142	497	6	inequality	inequality	NOUN
ap-6142	497	7	–	–	PUNCT
ap-6142	497	8	the	the	DET
ap-6142	497	9	non	non	ADJ
ap-6142	497	10	-	-	ADJ
ap-6142	497	11	steady	steady	ADJ
ap-6142	497	12	case	case	NOUN
ap-6142	497	13	3.1	3.1	NUM
ap-6142	497	14	notation	notation	NOUN
ap-6142	497	15	3.2	3.2	NUM
ap-6142	497	16	a	a	DET
ap-6142	497	17	formal	formal	ADJ
ap-6142	497	18	derivation	derivation	NOUN
ap-6142	497	19	of	of	ADP
ap-6142	497	20	the	the	DET
ap-6142	497	21	variational	variational	ADJ
ap-6142	497	22	inequality	inequality	NOUN
ap-6142	497	23	3.3	3.3	NUM
ap-6142	497	24	definition	definition	NOUN
ap-6142	497	25	of	of	ADP
ap-6142	497	26	the	the	DET
ap-6142	497	27	initial	initial	ADJ
ap-6142	497	28	–	–	PUNCT
ap-6142	497	29	boundary	boundary	ADJ
ap-6142	497	30	value	value	NOUN
ap-6142	497	31	problem	problem	NOUN
ap-6142	497	32	(	(	PUNCT
ap-6142	497	33	p	p	NOUN
ap-6142	497	34	)	)	PUNCT
ap-6142	497	35	3.4	3.4	NUM
ap-6142	497	36	the	the	DET
ap-6142	497	37	principle	principle	NOUN
ap-6142	497	38	of	of	ADP
ap-6142	497	39	the	the	DET
ap-6142	497	40	proof	proof	NOUN
ap-6142	497	41	and	and	CCONJ
ap-6142	497	42	a	a	DET
ap-6142	497	43	priori	priori	ADJ
ap-6142	497	44	estimates	estimate	NOUN
ap-6142	497	45	3.5	3.5	NUM
ap-6142	497	46	remark	remark	NOUN
ap-6142	497	47	4	4	NUM
ap-6142	497	48	the	the	DET
ap-6142	497	49	navier	navier	NOUN
ap-6142	497	50	–	–	PUNCT
ap-6142	497	51	stokes	stoke	VERB
ap-6142	497	52	inequality	inequality	NOUN
ap-6142	497	53	–	–	PUNCT
ap-6142	497	54	the	the	DET
ap-6142	497	55	steady	steady	ADJ
ap-6142	497	56	case	case	NOUN
ap-6142	497	57	5	5	NUM
ap-6142	497	58	conclusion	conclusion	NOUN
ap-6142	497	59	acknowledgements	acknowledgement	NOUN
ap-6142	497	60	references	reference	NOUN