论文标题
Wave-Klein-Gordon系统的改良波算子
Modified Wave Operators for the Wave-Klein-Gordon System
论文作者
论文摘要
我们考虑了3D中的耦合波 - klein-gordon系统，这是Minkowski时空的全球非线性稳定性的简化模型，用于自我修复大规模领域。在本文中，我们研究了此类系统解决方案的大量渐近行为，并证明了微小衰变的小型和光滑数据的改良波算子。关键的新颖性来自至关重要的观察，即渐近动力学取决于共振的相互作用。结果，我们的主要结果包括具有良好误差界的谐振系统的推导，以及对这种跨性和色散类型的这种准线性进化系统的渐近动力学的详细描述。
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.
