报告题目：Hilbert expansion for some nonrelativistic kinetic equation

报 告 人：赵会江教授，武汉大学

报告时间：2024年6月16日下午 4点

报告地点：格物楼数学研究中心528报告厅

报告摘要：Vlasov-Maxwell-Boltzmann (VMB) system are fundamental models in dilute collisional plasmas. In this talk, we are concerned with the hydrodynamic limits of both the VML and the non-cutoff VMB systems in the entire space. Our primary objective is to rigorously prove that, within the framework of Hilbert expansion, the unique classical solution of the VML or non-cutoff VMB system converges globally over time to the smooth global solution of the Euler-Maxwell system as the Knudsen number approaches zero.  

The core of our analysis hinges on deriving novel interplay energy estimates for the solutions of these two systems, concerning both a local Maxwellian and a global Maxwellian, respectively. Our findings address a problem in the hydrodynamic limit for Landau-type equations and non-cutoff Boltzmann-type equations with a magnetic field. Furthermore, the approach developed can be seamlessly extended to assess the validity of the Hilbert expansion for other types of kinetic equations.

报告人简介：赵会江，教授，博士生导师，国家基金委创新研究群体项目“偏微分方程”牵头人，国家杰出青年科学基金获得者。现任武汉大学数学与统计学院院长，兼任教育部高等学校数学类专业教学指导委员会委员，国务院学位委员会第八届学科评议组成员，武汉市数学学会理事长，湖北省数学学会副理事长，《数学物理学报》中英文版副主编，《Kinetic and Related Models》等期刊编委。赵会江教授长期从事非线性偏微分方程，特别是动理学方程及相关的宏观模型数学理论的研究，在动理学方程定解问题的适定性以及其解和相关的宏观模型解的关系等问题的研究上取得了一些有意义的研究进展。