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
收藏
页码：1285 / 1302
页数：18
相关论文
共 50 条
  • [21] Low regularity for the nonlinear Klein-Gordon systems
    Yuan, Jia
    Zhang, Junyong
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (02) : 982 - 998
  • [22] Breather compactons in nonlinear Klein-Gordon systems
    Dinda, PT
    Remoissenet, M
    PHYSICAL REVIEW E, 1999, 60 (05): : 6218 - 6221
  • [23] The Initial Value Problem for the Quadratic Nonlinear Klein-Gordon Equation
    Hayashi, Nakao
    Naumkin, Pavel I.
    ADVANCES IN MATHEMATICAL PHYSICS, 2010, 2010
  • [24] Soliton perturbation theory for the quadratic nonlinear Klein-Gordon equation
    Biswas, Anjan
    Zony, Chenwi
    Zerrad, Essaid
    APPLIED MATHEMATICS AND COMPUTATION, 2008, 203 (01) : 153 - 156
  • [25] Global Existence and Blowup for the Cubic Nonlinear Klein-Gordon Equations in Three Space Dimensions
    Zhang, Jian
    Gan, Zaihui
    Guo, Boling
    ADVANCED NONLINEAR STUDIES, 2010, 10 (02) : 315 - 329
  • [26] A quadratic quasi-linear Klein–Gordon equation in two space dimensions
    Nakao Hayashi
    Pavel I. Naumkin
    Journal of Evolution Equations, 2013, 13 : 253 - 280
  • [27] A note on global existence of solutions to nonlinear Klein-Gordon equations in one space dimension
    Katayama, S
    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1999, 39 (02): : 203 - 213
  • [28] Global existence for nonlinear Klein-Gordon equations in infinite homogeneous waveguides in two dimensions
    Fang, Daoyuan
    Tong, Changqing
    Zhong, Sijia
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 331 (01) : 21 - 37
  • [29] Scattering for the quadratic Klein-Gordon equations
    Guo, Zihua
    Shen, Jia
    NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2020, 27 (03):
  • [30] Endpoint Strichartz estimates for the Klein-Gordon equation in two space dimensions and some applications
    Kato, Jun
    Ozawa, Tohru
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2011, 95 (01): : 48 - 71
12345