Global solution to the wave and Klein-Gordon system under null condition in dimension two

Abstract

We are interested in studying the coupled wave and Klein-Gordon equations with null quadratic nonlinearities in ${\mathbb{R}}^{2+1}$. We want to establish the small data global existence result, and in addition, we also demonstrate the pointwise asymptotic behaviour of the solution to the coupled system. The initial data are not required to have compact support, and this is achieved by applying the Alinhac's ghost weight method to both the wave and the Klein-Gordon equations.

20 pages; all comments are welcome

References in corpus (5)

• Global existence for coupled systems of nonlinear wave and Klein-Gordon equations in three 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
• Almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems in two space dimensions
• Stability of a class of semilinear waves in $2+1$ dimension under null condition

Cited by in corpus (3)

• Asymptotic Behavior of the Solution to the Klein-Gordon-Zakharov Model in Dimension Two
• Two dimensional wave--Klein-Gordon equations with semilinear nonlinearities
• Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: A prototype of strong coupling case