Landau damping, collisionless limit, and stability threshold for the Vlasov-Poisson equation with nonlinear Fokker-Planck collisions
数学专题报告
报告题目(Title)：Landau damping, collisionless limit, and stability threshold for the Vlasov-Poisson equation with nonlinear Fokker-Planck collisions
报告人(Speaker)：訾瑞昭 教授（华中师范大学）
地点(Place)：后主楼1124
时间(Time)：2025年7月8日下午2:30-3:30
邀请人(Inviter)：许孝精
报告摘要
In this talk, we consider the Vlasov-Poisson-Fokker-Planck (VPFP) equation with a small collision frequency , exploring the interplay between the regularity and size of perturbations in the context of the asymptotic stability of the global Maxwellian. Our main result establishes the Landau damping and enhanced dissipation phenomena under the condition that the perturbation of the global Maxwellian falls within the Gevrey- class and obtain that the stability threshold for the Gevrey- class with can not be larger than for . Moreover, we show that for Gevrey- with , and for , the solution to VPFP converges to the solution to Vlasov-Poisson equation without collision. This is based on a joint work with Prof. Jacob Bedrossian and Prof. Weiren Zhao.
