【讲座题目】Hilbert expansion for kinetic equations with non-relativistic Coulomb collision
【主讲人】赵会江教授
【讲座时间】2022年12月8日 15:30-16:30
【腾讯会议】ID：754-777-056
【报告人简介】赵会江，二级教授，国家杰出青年科学基金获得者。现任教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、中国数学会常务理事，《数学物理学报》中英文版副主编、《Kinetic and Related Models》编委。关于双曲守恒律组及相关问题的研究工作分别获得2007年度教育部自然科学奖二等奖和2008年度湖北省自然科学一等奖。
【讲座内容简介】
This talk is concerned with the hydrodynamic limits of both the Landau equation and the Vlasov-Maxwell-Landau system in the whole space. Our main purpose is two-fold: the first one is to give a rigorous derivation of the compressible Euler equations from the Landau equation via the Hilbert expansion; while the second one is to prove, still in the setting of Hilbert expansion, that the unique classical solution of the Vlasov-Maxwell-Landau system converges, which is shown to be globally in time, to the resulting global smooth solution of the Euler-Maxwell system, as the Knudsen number goes to zero. The main ingredient of our analysis is to derive some novel interplay energy estimates on the solutions of the Landau equation and the Vlasov-Maxwell-Landau system which are small perturbations of both a local Maxwellian and a global Maxwellian, respectively.
