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

Details 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

2009-08-28

arxiv.org/abs/0908.4137v3

Mathematische Zeitschrift 270 (2012), 487-513

Mathematics

Analysis of PDEs

31 pages. The final version

Scientific paper

10.1007/s00209-010-0808-0

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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