paper

Global existence for systems of nonlinear wave and Klein-Gordon equations in two space dimensions under a kind of the weak null condition

arXiv:2111.13339 · doi:10.1007/s00028-022-00809-3

Abstract

We consider the coupled systems of nonlinear wave and Klein-Gordon equations in two space dimensions with cubic nonlinearity. For this kind of systems, the small data global existence is already known if the cubic nonlinearity satisfies a certain condition related to the null condition. In this article, our aim is to investigate the small data global existence under a condition related to the weak null condition. We also make a remark on the asymptotic behavior of global solutions.

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