no. 4
An improvement on the Brézis–Gallouët technique for 2D NLS and 1D half-wave equation
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 1069-1079.

We revise the classical approach by Brézis–Gallouët to prove global well-posedness for nonlinear evolution equations. In particular we prove global well-posedness for the quartic NLS on general domains Ω in R2 with initial data in H2(Ω)∩H01(Ω), and for the quartic nonlinear half-wave equation on R with initial data in H1(R).

DOI : 10.1016/j.anihpc.2015.03.004
Mots clés : Half-wave equation, Nonlinear Schrödinger equation, Energy estimates, Global existence 
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     title = {An improvement on the {Br\'ezis{\textendash}Gallou\"et} technique for {2D} {NLS} and {1D} half-wave equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1069--1079},
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Ozawa, Tohru; Visciglia, Nicola. An improvement on the Brézis–Gallouët technique for 2D NLS and 1D half-wave equation. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 1069-1079. doi : 10.1016/j.anihpc.2015.03.004. http://archive.numdam.org/articles/10.1016/j.anihpc.2015.03.004/

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