Year: 2024
Type: article
Abstract: We are interested in establishing global stability results for a system of semilinear wave and Klein-Gordon equations with mixed coupling nonlinearities, that is, we consider all of the possible quadratic nonlinear terms of the type of wave and Klein-Gordon interactions. The main difficulties are due to the absence of derivatives on the wave component in the nonlinearities. By doing a nonlinear transformation on the wave equation, we reveal a hidden null structure. Next, by using the scaling vector field on the wave component only, which is generally avoided, we are able to get good $L^2$-type estimates on the wave component. Then we distinguish high-order and low-order energy of both wave and Klein-Gordon components, which allows us to close the bootstrap argument.
Source: Tohoku Mathematical Journal
DOI: 10.2748/tmj.20230407
Author: Shijie Dong
Institution: Laboratoire Jacques-Louis Lions
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: European Commission
OpenAlex ID: W4287815054