ALMOST GLOBAL EXISTENCE FOR CUBIC NONLINEAR SCHRODINGER EQUATIONS IN ONE SPACE DIMENSION

被引：9

作者：

Murphy, Jason ^{[1
]}

Pusateri, Fabio ^{[2
]}

机构：

[1] Univ Calif Berkeley, Dept Math, 970 Evans Hall, Berkeley, CA 94720 USA

[2] Princeton Univ, Dept Math, Fine Hall,304 Washington Rd, Princeton, NJ 08544 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 04期

基金：

美国国家科学基金会;

关键词：

Cubic NLS; almost global existence; method of space-time resonances; WAVE-EQUATIONS; ASYMPTOTIC-BEHAVIOR; INITIAL DATA; LARGE TIME; LIFE-SPAN; SCATTERING; BOUNDS; NLS;

D O I：

10.3934/dcds.2017089

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider non-gauge-invariant cubic nonlinear Schrodinger equations in one space dimension. We show that initial data of size epsilon in a weighted Sobolev space lead to solutions with sharp L-x(infinity) decay up to time exp(C-epsilon(-2)). We also exhibit norm growth beyond this time for a specific choice of nonlinearity.

引用

页码：2077 / 2102

页数：26

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