Strichartz estimates for partially periodic solutions to Schrodinger equations in 4d and applications

被引：45

作者：

Herr, Sebastian ^{[1
]}

Tataru, Daniel ^{[2
]}

Tzvetkov, Nikolay ^{[3
]}

机构：

[1] Univ Bonn, Math Inst, D-53115 Bonn, Germany

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

[3] Univ Cergy Pontoise, Dept Math, F-95302 Cergy Pontoise, France

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2014年 / 690卷

基金：

美国国家科学基金会;

关键词：

COMPACT MANIFOLDS; WELL-POSEDNESS;

D O I：

10.1515/crelle-2012-0013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the energy critical nonlinear Schrodinger equation on periodic domains of the form R-m x T4-m with m = 0, 1, 2, 3. Assuming that a certain L-4 Strichartz estimate holds for solutions to the corresponding linear Schrodinger equation, we prove that the nonlinear problem is locally well-posed in the energy space. Then we verify that the L-4 estimate holds if m = 2, 3.

引用

页码：65 / 78

页数：14

共 12 条

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[2]

Bourgain J., 2011, MOMENT INEQUALITIES

[3]

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