Global solutions of wave-Klein-Gordon system in two spatial dimensions with strong couplings in divergence form
Analysis of PDEs
2020-10-20 v1 Mathematical Physics
Differential Geometry
math.MP
Abstract
In this paper we established the global well-posedness theorem for a special type of wave-Klein-Gordon system that have the strong coupling terms in divergence form on the right hand side of its wave equation. We cope with the problem by constructing an auxiliary system with the shifted primitives of the original unknowns. The result is then applied directly on Klein-Gordon-Zakharov system in 2+1 space-time with general small-localized-regular initial data. In the end of this paper, we also give a preliminary answer to the question of global stability of a class of totally geodesic the wave maps in 2+1 dimensional case.
Keywords
Cite
@article{arxiv.2010.08951,
title = {Global solutions of wave-Klein-Gordon system in two spatial dimensions with strong couplings in divergence form},
author = {Senhao Duan and Yue Ma},
journal= {arXiv preprint arXiv:2010.08951},
year = {2020}
}