A non-linear damping structure and global stability of wave-Klein-Gordon coupled system in $\mathbb{R}^{3+1}$

Yue Ma; Weidong Zhang

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arXiv · 2507.12285

A non-linear damping structure and global stability of wave-Klein-Gordon coupled system in $\mathbb{R}^{3+1}$

Yue Ma·Weidong Zhang

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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.

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Yue Ma, Weidong Zhang. 2025-07-16. A non-linear damping structure and global stability of wave-Klein-Gordon coupled system in $\mathbb{R}^{3+1}$. https://arxiv.org/abs/2507.12285

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