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

摘要

We are interested in studying the coupled wave and Klein-Gordon equations with null quadratic nonlinearities in R2+1. We aim to establish the small data global existence result, and in addition, we also illustrate the sharp 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 Alinhac's ghost weight method to both the wave and the Klein-Gordon equations. (C) 2021 Elsevier Inc. All rights reserved.