The defocusing quintic NLS in four space dimensions

被引：18

作者：

Dodson, Benjamin ^{[1
]}

Miao, Changxing ^{[2
]}

Murphy, Jason ^{[3
]}

Zheng, Jiqiang ^{[4
]}

机构：

[1] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

[2] Inst Appl Phys & Computat Math, POB 8009, Beijing 100088, Peoples R China

[3] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[4] Univ Nice Sophia Antipolis, F-06108 Nice 02, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2017年 / 34卷 / 03期

基金：

欧洲研究理事会; 美国国家科学基金会;

关键词：

Nonlinear Schrodinger equation; Concentration compactness; Scattering; Interaction Morawetz inequality; NONLINEAR SCHRODINGER-EQUATION; GLOBAL WELL-POSEDNESS; ENERGY-SUPERCRITICAL NLS; RADIAL DATA; CRITICAL H; BLOW-UP; SCATTERING; MASS;

D O I：

10.1016/j.anihpc.2016.05.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the defocusing quintic nonlinear Schrodinger equation in four space dimensions. We prove that any solution that remains bounded in the critical Sobolev space must be global and scatter. We employ a space-localized interaction Morawetz inequality, the proof of which requires us to overcome the logarithmic failure in the double Duhamel argument in four dimensions. (C) 2016 Elsevier Masson SAS. All rights reserved.

引用

页码：759 / 787

页数：29

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