报告时间：2025年4月7日 14:30开始
报 告 人：姜在红 教授（浙江师范大学）
报告地点：9-113
报告题目：Global well-posedness of Vlasov-Poisson-Boltzmann equations with neutral initial data and small relative entropy
报告摘要：The dynamics of dilute plasma particles such as electrons and ions can be modeled by the fundamental two species Vlasov-Poisson-Boltzmann equations, which describes mutual interactions of plasma particles through collisions in the self-induced electric field. In this paper, we are concerned with global well-posedness of mild solutions to these equations. We establish the global existence and uniqueness of mild solutions to the two species Vlasov-Poisson-Boltzmann equations on the torus for a class of initial data with bounded time-velocity-weighted $L^{\infty}$ norm under a nearly neutral condition, along with smallness conditions on the $L^1_xL^\infty_v$ norm and defects in mass, energy and entropy. These conditions allow the initial data to exhibit large amplitude oscillations. Due to the nonlinear effect of electric field, we consider the problem in $W^{1, \infty}_{x,v}$ with large amplitude data, new difficulty arises when establishing globally uniform $W^{1, \infty}_{x,v}$ bound, which has been overcome based on nearly neutral condition, time-velocity weight function and a logarithmic estimate. Moreover, the long-time behavior of solutions in $W^{1, \infty}_{x,v}$ norm, with exponential decay rates of convergence, is also obtained.
报告人简介：姜在红，浙江师范大学数学科学学院教授，博士生导师。主要从事流体力学及动理学等偏微分方程相关理论的学习和研究。在Archive for Rational Mechanics and Analysis，Journal of Differential Equations，Journal of Nonlinear Science等期刊上发表论文40余篇，曾获中国科学院优秀博士学位论文及全国优秀博士学位论文提名论文等荣誉。主持完成国家自然科学基金2项，浙江省自然科学基金3项。
