Sharp weights in the Cauchy problem for nonlinear Schrodinger equations with potential

被引：10

作者：

Carles, Remi ^{[1
,2
]}

机构：

[1] CNRS, F-34095 Montpellier, France

[2] Univ Montpellier, Math CC 051, F-34095 Montpellier, France

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2015年 / 66卷 / 04期

关键词：

Nonlinear Schrodinger equation; Unbounded potential; Cauchy problem; FUNDAMENTAL SOLUTION; SMOOTHING PROPERTY;

D O I：

10.1007/s00033-015-0501-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We review different properties related to the Cauchy problem for the (nonlinear) Schrodinger equation with a smooth potential. For energy-subcritical nonlinearities and at most quadratic potentials, we investigate the necessary decay in space in order for the Cauchy problem to be locally (and globally) well posed. The characterization of the minimal decay is different in the case of super-quadratic potentials.

引用

页码：2087 / 2094

页数：8

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