报告名称：Global mild solutions of the Landau and non-cutoff Boltzmann equations

主办单位：英国威廉希尔体育公司

报告专家：刘双乾 教授

专家所在单位：华中师范大学 数学与统计学院

报告时间：2020年8月3日(周一)上午9：30-11：30

报告地点：腾讯会议 会议号：900 240 958

专家简介：刘双乾，教授，2009年博士毕业于武汉大学。先后任职于暨南大学和华中师范大学。主要研究方向为动理学方程及其相关宏观模型的数学理论。研究成果发表在Communications on Pure and Applied Mathematics、Communications in Mathematical Physics、Archive for Rational and Mechanics and Analysis、SIAM Journal on Mathematical Analysis等杂志。。

报告摘要：The motion of the particles in the dilute gas can be described by the Landau equation or the non-cutoff Boltzmann equation. It is known that it is very difficult to construct the global well-posedness in Sobolev space for the initial boundary value problems of the kinetic equations in general bounded domains due to the formation of singularity of solutions. In this talk, firstly, we will discuss how to establish the global existence in some sharp regularity space for both the Landau equation and the non-cutoff Boltzmann equation with either the inflow boundary condition or the specular reflection boundary condition in a finite channel, secondly, we will show the solutions tend to the equilibrium around a global Maxwellian with the time sub-exponential decay rates, thirdly, we will present the regularity of the initial data or boundary data can be propagated from the boundary into the interior of the channel along the tangential direction. This is a joint work with R. Duan, S. Sakamoto and R. Strain.

邀请人：陈立