TWO-DIMENSIONAL NONLINEAR SCHRODINGER EQUATION WITH RANDOM RADIAL DATA

被引：49
|
作者：
Deng, Yu [1 ]
机构：
[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA
来源：
ANALYSIS & PDE | 2012年 / 5卷 / 05期
关键词：
nonlinear Schrodinger equation; supercritical NLS; random data; Gibbs measure; global well-posedness; GLOBAL WELL-POSEDNESS; DATA CAUCHY-THEORY; INVARIANT-MEASURES;
D O I：
10.2140/apde.2012.5.913
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study radial solutions of a certain two-dimensional nonlinear Schrodinger (NLS) equation with harmonic potential, which is supercritical with respect to the initial data. By combining the nonlinear smoothing effect of Schrodinger equation with L-p estimates of Laguerre functions, we are able to prove an almost-sure global well-posedness result and the invariance of the Gibbs measure. We also discuss an application to the NLS equation without harmonic potential.
引用
收藏
页码：913 / 960
页数：48
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