Endpoint Strichartz estimates for the Klein-Gordon equation in two space dimensions and some applications

被引：10

作者：

Kato, Jun ^{[1
,2
]}

Ozawa, Tohru ^{[3
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Nagoya, Aichi 4648602, Japan

[2] NYU, Courant Inst, New York, NY 10012 USA

[3] Waseda Univ, Dept Appl Phys, Tokyo 1698555, Japan

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2011年 / 95卷 / 01期

关键词：

Klein-Gordon equation; Strichartz estimate; Endpoint estimate; Angular regularity; LINEAR EVOLUTION-EQUATIONS; SMALL AMPLITUDE SOLUTIONS; NONLINEAR DIRAC-EQUATION; GLOBAL EXISTENCE; NONRELATIVISTIC LIMIT; SCHRODINGER; BEHAVIOR; FORMS;

D O I：

10.1016/j.matpur.2010.10.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the endpoint Strichartz estimates for the Klein-Gordon equation in mixed norms on the polar coordinates in two space dimensions. As an application, similar endpoint estimates for the Schrodinger equation in two space dimensions are shown by using the non-relativistic limit. The existence of global solutions for the cubic nonlinear Klein-Gordon equation in two space dimensions for small data is also shown. (C) 2010 Elsevier Masson SAS. All rights reserved.

引用

页码：48 / 71

页数：24

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