报告题目：Gevrey regularity of mild solutions to the non-cutoff Boltzmann equation

报告人：李维喜 教授

时间：6月10日下午 15：30 （周四）

地点：实训楼 308会议室

摘要：For the Cauchy problem on the non-cutoff Boltzmann equation in torus, we establish the global-in-time Gevrey smoothness in velocity and space variables for a class of low-regularity mild solutions near Maxwellians with the Gevrey index depending only on the angular singularity. This together with the work of Duan-Liu-Sakamoto-Strain (CPAM,2021) provides a self-contained well-posedness theory for both existence and regularity of global solutions for initial data of low regularity in the framework of perturbations. For the proof we treat in a subtle way the commutator between the regularization operators and the Boltzmann collision operator involving rough coefficients, and this enables us to combine the classical Ho ̈rmander’s hypoelliptic techniques together with the global symbolic calculus established for the linearized Boltzmann operator so as to improve the regularity of solutions at positive time.  Joint work with Renjun Duan and Lvqiao Liu.

个人简介：李维喜，武汉大学数学与统计学院教授、博士生导师，主要从事偏微分方程的研究，特别是在流体力学方程的边界层分析，退化椭圆方程的正则性，以及谱分析等方面做出了一系列出色的工作。主持国家自然科学基金项目多项(2014年国家优秀青年基金)，霍英东教育基金（2015）及武汉大学珞珈青年学者（2013）获得者，至今已在JEMS,CPAM等高水平期刊发表论文30余篇。