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.
References in corpus (10)
- Global existence for coupled systems of nonlinear wave and Klein-Gordon equations in three space dimensions
- Asymptotic pointwise behavior for systems of semilinear wave equations in three space dimensions
- Asymptotic Behavior of the Solution to the Klein-Gordon-Zakharov Model in Dimension Two
- Energy decay for systems of semilinear wave equations with dissipative structure in two space dimensions
- Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: weak coupling case
- Global solutions of non-linear wave-Klein-Gordon system in two space dimension: semi-linear interactions
- Global existence for a system of quasi-linear wave equations in D satisfying the weak null condition
- On Agemi-type structural conditions for a system of semilinear wave equations
- Global solutions of wave-Klein-Gordon system in two spatial dimensions with strong couplings in divergence form
- Two dimensional wave--Klein-Gordon equations with semilinear nonlinearities