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^*

^*この研究の対応する著者

先進理工学部

研究成果: Article › 査読

18 被引用数 (Scopus)

抄録

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).

本文言語	English
ページ（範囲）	1069-1079
ページ数	11
ジャーナル	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
巻	33
号	4
DOI	https://doi.org/10.1016/j.anihpc.2015.03.004
出版ステータス	Published - 2016 7月 1

ASJC Scopus subject areas

分析
数理物理学
応用数学

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10.1016/j.anihpc.2015.03.004

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AU - Ozawa, Tohru

AU - Visciglia, Nicola

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

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