Global existence and scattering for rough solutions to generalized nonlinear Schrodinger equations on R

被引：17

作者：

Colliander, James ^{[1
]}

Holmer, Justin ^{[2
]}

Visan, Monica

Zhang, Xiaoyi ^{[3
]}

机构：

[1] Univ Toronto, Toronto, ON, Canada

[2] Univ Calif Berkeley, Berkeley, CA 94720 USA

[3] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100864, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2008年 / 7卷 / 03期

关键词：

nonlinear Schrodinger equation; well-posedness; scattering; Morawetz inequality;

D O I：

10.3934/cpaa.2008.7.467

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem for a family of semilinear defocusing Schrodinger equations with monomial nonlinearities in one space dimension. We establish global well-posedness and scattering. Our analysis is based on a four-particle interaction Morawetz estimate giving a priori L-t,x(8) spacetime control on solutions.

引用

页码：467 / 489

页数：23

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