NONLINEAR SCHRODINGER EQUATION AND FREQUENCY SATURATION

被引：0

作者：

Carles, Remi ^{[1
,2
]}

机构：

[1] CNRS, CC051,Pl Eugene Bataillon, F-34095 Montpellier, France

[2] Univ Montpellier 2, UMR 5149, F-34095 Montpellier, France

来源：

ANALYSIS & PDE | 2012年 / 5卷 / 05期

关键词：

nonlinear Schrodinger equation; well-posedness; approximation; DATA CAUCHY-THEORY; GEOMETRIC OPTICS; ILL-POSEDNESS; APPROXIMATION; INSTABILITY; REGULARITY;

D O I：

10.2140/apde.2012.5.1157

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose an approach that permits to avoid instability phenomena for the nonlinear Schrodinger equations. We show that by approximating the solution in a suitable way, relying on a frequency cut-off, global well-posedness is obtained in any Sobolev space with nonnegative regularity. The error between the exact solution and its approximation can be measured according to the regularity of the exact solution, with different accuracy according to the cases considered.

引用

页码：1157 / 1173

页数：17

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