SCATTERING FOR THE KLEIN-GORDON-ZAKHAROV SYSTEM IN TWO DIMENSIONS

讲座题目：SCATTERING FOR THE KLEIN-GORDON-ZAKHAROV SYSTEM IN TWO DIMENSIONS
讲座时间 Datetime:2025年11月4日，星期二，15:00-17:30
地点 Venue: 海琴2号A455
主持人 Host：裴龙 副教授
报告人 Speaker: 董世杰 助理教授
单位 Affiliation: 南方科技大学
报告摘要 Abstract: 
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.
报告人简介：
董世杰，南方科技大学数学系助理教授。其博士毕业于法国索邦大学，后来在复旦大学从事博士后研究。董世杰的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。具体地，董世杰主要研究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。目前在CMP, JFA, AIHP，TAMS等期刊上发表论文20篇。