Modified wave operators for the Wave-Klein-Gordon system

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.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

We study a simplified model for the global nonlinear stability of the Minkowski space-time for self-gravitating massive fields by considering a coupled Wave-Klein-Gordon system in 3D. The large-time asymptotic behavior of solutions to such systems is investigated and modified wave operators are proven for small and smooth data with mild decay at infinity. The key novelty lies in the observation that the asymptotic dynamics are determined by the resonant interactions.