id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-430	Begout, Pascal	Finite time extinction for a damped nonlinear Schrodinger equation in the whole space	2020	18	.pdf	application/pdf	8164	636	87	By (4.17), (4.22), (4.23), Remark 2.9 and Hölder’s inequality (recalling that 2m < m+ 1 < 2), we obtain u ∈ L∞loc ( [0,∞);H2(RN ) ) ∩ L∞loc ( [0,∞);L2m(RN ) ) , (4.24) u ∈ C ( [0,∞);L2(RN ) ) ∩ L∞loc ( [0,∞);L2m(RN ) ) ↪→ C ( [0,∞);Lm+1(RN ) ) . (4.25) Recalling that u ∈ W 1,∞ loc ( [0,∞);L2(RN ) ) , by (4.24) and the embedding 3) of Lemma A.4, we have u ∈ C ( [0,∞);H1(RN ) ) .	cache/ejde-430.pdf	txt/ejde-430.txt