Global existence for coupled systems of nonlinear wave and Klein–Gordon equations in three space dimensions
Global existence for coupled systems of nonlinear wave and Klein–Gordon equations in three space dimensions
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DOI：
10.1007/s00209-010-0808-0
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发表时间：
2009-08
影响因子：
0.8
通讯作者：
S. Katayama
中科院分区：
文献类型：
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作者：
S. Katayama
本文考虑三维空间中具有二次非线性项的波动方程和Klein-Gordon方程耦合组的Cauchy问题。在一定的条件下，包括波方程之间自相互作用的零条件下，我们证明了小振幅解的整体存在性。我们的条件比Georgiev为这类耦合系统引入的强零条件弱得多。因此，我们的结果适用于某些物理系统，如Dirac-Klein-Gordon方程，Dirac-Proca方程和Klein-Gordon-Zakharov方程。
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.