A note on the null condition for quadratic nonlinear Klein-Gordon systems in two space dimensions

被引：19

作者：

Katayama, Soichiro ^{[1
]}

Ozawa, Tohru ^{[2
]}

Sunagawa, Hideaki ^{[3
]}

机构：

[1] Wakayama Univ, Dept Math, Wakayama 6408510, Japan

[2] Waseda Univ, Dept Appl Phys, Shinjuku Ku, Tokyo 1698555, Japan

[3] Osaka Univ, Dept Math, Toyonaka, Osaka 5600043, Japan

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2012年 / 65卷 / 09期

关键词：

SMALL AMPLITUDE SOLUTIONS; GLOBAL EXISTENCE; EQUATIONS; WAVE;

D O I：

10.1002/cpa.21392

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem for quadratic nonlinear Klein-Gordon systems in two space dimensions with masses satisfying the resonance relation. Under the null condition in the sense of J.-M. Delort, D. Fang, and R. Xue (J. Funct. Anal. 211 (2004), no. 2, 288323), we show the global existence of asymptotically free solutions if the initial data are sufficiently small in some weighted Sobolev space. Our proof is based on an algebraic characterization of nonlinearities satisfying the null condition. (c) 2012 Wiley Periodicals, Inc.

引用

页码：1285 / 1302

页数：18

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