An improvement on the Brézis–Gallouët technique for 2D NLS and 1D half-wave equation

Tohru Ozawa; Nicola Visciglia

doi:10.1016/j.anihpc.2015.03.004

An improvement on the Brézis–Gallouët technique for 2D NLS and 1D half-wave equation

Tohru Ozawa, Nicola Visciglia^*

^*Corresponding author for this work

School of Advanced Science and Engineering

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

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).

Original language	English
Pages (from-to)	1069-1079
Number of pages	11
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	33
Issue number	4
DOIs	https://doi.org/10.1016/j.anihpc.2015.03.004
Publication status	Published - 2016 Jul 1

Keywords

Energy estimates
Global existence
Half-wave equation
Nonlinear Schrödinger equation

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

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10.1016/j.anihpc.2015.03.004

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title = "An improvement on the Br{\'e}zis–Gallou{\"e}t technique for 2D NLS and 1D half-wave equation",

abstract = "We revise the classical approach by Br{\'e}zis–Gallou{\"e}t 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).",

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author = "Tohru Ozawa and Nicola Visciglia",

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AU - Ozawa, Tohru

AU - Visciglia, Nicola

PY - 2016/7/1

Y1 - 2016/7/1

N2 - 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).

AB - 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).

KW - Energy estimates

KW - Global existence

KW - Half-wave equation

KW - Nonlinear Schrödinger equation

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JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

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ER -

An improvement on the Brézis–Gallouët technique for 2D NLS and 1D half-wave equation

Abstract

Keywords

ASJC Scopus subject areas

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