A non-linear damping structure and global stability of wave-Klein-Gordon coupled system in $\mathbb{R}^{3+1}$
Analysis of PDEs
2026-04-21 v3
Abstract
This paper establishes the global existence of solutions for a class of wave-Klein-Gordon coupled systems with specific nonlinearities in 3+1-dimensional Minkowski spacetime. The study demonstrates that imposing certain constraints on the coefficients of these specific nonlinear terms induces a damping effect within the system, which is crucial for proving the global existence of solutions. The proof is conducted within the framework of a bootstrap argument, primarily employing the hyperboloidal foliation method and the vector field method.
Keywords
Cite
@article{arxiv.2507.12285,
title = {A non-linear damping structure and global stability of wave-Klein-Gordon coupled system in $\mathbb{R}^{3+1}$},
author = {Yue Ma and Weidong Zhang},
journal= {arXiv preprint arXiv:2507.12285},
year = {2026}
}