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

被引：8
|
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.
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页码：2077 / 2102
页数：26
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