报告题目：Landau damping, collisionless limit, and stability threshold for the Vlasov-Poisson equation with nonlinear Fokker-Planck collisions

报告人：訾瑞昭（华中师范大学）

报告时间：2024年06月29日10:10-12:10

报告地点：数学与统计学院312

邀请单位：福州大学数学与统计学院，江飞，林雪云

报告内容简介：

In this talk, we consider the Vlasov-Poisson-Fokker-Planck (VPFP) equation with a small collision frequency $0<\nu\ll1$, 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-$\frac{1}{s}$ class and obtain that the stability threshold for the Gevrey-$\frac{1}{s}$ class with $s>s_k$ can not be larger than $\gamma=\frac{1-3s_k}{3-3s_k}$ for $s_k\in[0,\frac{1}{3}]$. Moreover, we show that for Gevrey-$\frac{1}{s}$ with $s>3$, and for $t\ll\nu^{-\frac{1}{3}}$, the solution to VPFP converges to the solution to Vlasov-Poisson equation without collision. This is based on a joint work with Prof. Weiren Zhao and Prof. Jacob Bedrossian.

报告人简介：

訾瑞昭，教授，华中师范大学首批“桂子青年学者”。主要从事流体中的偏微分方程解的适定性与稳定性的研究。在Mathematische Annalen，Archive for Rational Mechanics and Analysis, Journal de Mathématiques Pures et Appliquées, Journal of Functional Analysis, Annales de l'Institut Henri Poincaré–Analyse non linéaire, SIAM Journal on Mathematical Analysis等国际期刊上发表论文30余篇。先后主持国家自然科学基金青年科学基金项目及面上项目各一项，2022年获得国家自然科学基金优秀青年科学基金资助。