标题： Klein-Gordon-Schrödinger系统的长时间行为 显示英文标题

标题： Large Time Behavior of the Klein-Gordon-Schrödinger system

摘要： 我们建立了三维空间中带有小且局部化初值的 Klein-Gordon-Schrödinger 系统的整体存在性和散射性。 该系统由带有二次非线性的耦合半线性 Schrödinger 方程和 Klein-Gordon 方程组成。 此模型源于研究具有库仑势的平移不变平衡态附近由 Hartree 方程产生的等离子体振荡。 我们的证明依赖于时空共振方法。 主要困难来自二维的时空共振集以及缺乏零形式结构。 显示英文摘要

摘要： We establish the global existence and scattering for small and localized solutions of the Klein-Gordon-Schr\"{o}dinger system in three dimensions. The system consists of coupled semilinear Schr\"{o}dinger and Klein-Gordon equations with quadratic nonlinearities. This model is motivated by the study of plasma oscillations arising from the Hartree equation near a translation-invariant equilibrium with the Coulomb potential. Our proof relies on the space-time resonance method. The main difficulty comes from the two dimensional space-time resonant set and the absence of null form structure.