Energy-Critical NLS with Quadratic Potentials

被引：25

作者：

Killip, Rowan ^{[1
]}

Visan, Monica ^{[1
,2
]}

Zhang, Xiaoyi ^{[3
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[2] Inst Adv Study, Princeton, NJ 08540 USA

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

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2009年 / 34卷 / 12期

基金：

美国国家科学基金会;

关键词：

Energy critical; Nonlinear Schrodinger equation; NONLINEAR SCHRODINGER-EQUATION; GLOBAL WELL-POSEDNESS; CAUCHY-PROBLEM; SCATTERING; WELLPOSEDNESS; EXISTENCE;

D O I：

10.1080/03605300903328109

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the defocusing [image omitted]-critical nonlinear Schrodinger equation in all dimensions (n epsilon 3) with a quadratic potential [image omitted]. We show global well-posedness for radial initial data obeying delta u0(x), xu0(x)L2. In view of the potential V, this is the natural energy space. In the repulsive case, we also prove scattering. We follow the approach pioneered by Bourgain and Tao in the case of no potential; indeed, we include a proof of their results that incorporates a couple of simplifications discovered while treating the problem with quadratic potential.

引用

页码：1531 / 1565

页数：35

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