Scattering For THE Klein-Gordon-Zakharov System in Two Dimensions
数学专题报告
报告题目(Title)：Scattering For THE Klein-Gordon-Zakharov System in Two Dimensions
报告人(Speaker)：董世杰（南方科技大学）
地点(Place)：后主楼1223
时间(Time)：2025年9月6日（周六）下午2:30-3:30
邀请人(Inviter)：徐桂香
报告摘要
We study the Klein-Gordon–Zakharov system in two spatial dimensions, an important model in plasma physics. For small, smooth, and spatially localized initial data, we establish the global existence of solutions and characterize their sharp long-time behavior, including sharp time decay and scattering properties. A particularly interesting phenomenon is that the Klein-Gordon component exhibits modified scattering for certain initial data, while for others it undergoes linear scattering—a dichotomy highlighting delicate long-range interaction effects.
The major obstacles are lack of symmetry and weak decay of the solution in two dimensions. To overcome these, we introduce a novel nonlinear transformation of the wave component and reinterpret the nonlinear coupling as a perturbation of the mass term in the Klein-Gordon equation. The proof employs a combination of physical space and frequency space methods.
主讲人简介
董世杰，南方科技大学数学系助理教授。博士毕业于法国索邦大学（原巴黎六大），复旦大学从事博士后研究。主要研究方向为物理以及几何中波动类型偏微分方程的定性分析。主要研究Dirac-Klein-Gordon方程，Klein-Gordon-Zakharov方程，波映照方程等波动类型的非线性方程。在CMP, TAMS, JFA, AIHP等著名学术期刊发表10余篇学术论文。
