2020/10/10 by Zhimeng Ouyang, Ouyang, Zhimeng · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Cosmology and Gravitation Theories
paper · pdf · doi:10.48550/arxiv.2010.04882
We consider a coupled Wave-Klein-Gordon system in 3D, which is a simplified model for the global nonlinear stability of the Minkowski space-time for self-gravitating massive fields. In this paper we study the large-time asymptotic behavior of solutions to such systems, and prove modified wave operators for small and smooth data with mild decay at infinity. The key novelty comes from a crucial observation that the asymptotic dynamics are dictated by the resonant interactions. As a consequence, our main results include the derivation of a resonant system with good error bounds, and a detailed description of the asymptotic dynamics of such quasilinear evolution system of hyperbolic and dispersive type.