Global existence for coupled systems of nonlinear wave and Klein–Gordon equations in three space dimensions

被引：1
作者：
Soichiro Katayama
机构：
[1] Wakayama University,Department of Mathematics
来源：
Mathematische Zeitschrift | 2012年 / 270卷
关键词：
Null condition; Wave equation; Klein–Gordon equation; Global existence; 35L70;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider the Cauchy problem for coupled systems of wave and Klein–Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null condition on self-interactions between wave equations. Our condition is much weaker than the strong null condition introduced by Georgiev for this kind of coupled system. Consequently our result is applicable to certain physical systems, such as the Dirac–Klein–Gordon equations, the Dirac–Proca equations, and the Klein–Gordon–Zakharov equations.
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页码：487 / 513
页数：26
相关论文
共 38 条
[1]  
Asakura F.(1986)Existence of a global solution to a semi-linear wave equation with slowly decreasing initial data in three space dimensions Commun. Partial Differ. Equ. 11 1459-1487
[2]  
Bachelot A.(1988)Problème de Cauchy global pour des systèmes de Dirac–Klein–Gordon Ann. Inst. Henri Poincaré 48 387-422
[3]  
Christodoulou D.(1986)Global solutions of nonlinear hyperbolic equations for small initial data Commun. Pure Appl. Math. 39 267-282
[4]  
Georgiev V.(1990)Global solution of the system of wave and Klein–Gordon equations Math. Z. 203 683-698
[5]  
Georgiev V.(1992)Decay estimates for the Klein–Gordon equation Commun. Partial Differ. Equ. 17 1111-1139
[6]  
Hayashi N.(2008)Ratno Bagus Edy Wibowo: Nonlinear scattering for a system of nonlinear Klein–Gordon equations J. Math. Phys. 49 103501-513
[7]  
Naumkin P.I.(2000)Global small amplitude solutions of nonlinear hyperbolic systems with a critical exponent under the null condition SIAM J. Math. Anal. 31 486-268
[8]  
Hoshiga A.(1979)Blow-up of solutions of nonlinear wave equations in three space dimensions Manuscr. Math. 28 235-51
[9]  
Kubo H.(1981)Blow-up of solutions for quasi-linear wave equations in three space dimensions Commun. Pure Appl. Math. 34 29-1078
[10]  
John F.(2004)Global and almost-global existence for systems of nonlinear wave equations with different propagation speeds Differ. Integral Eqs. 17 1043-1862
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