标题：Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off

报告人：李维喜教授

地点：数学与计算机科学学院4号楼302室

时间：2019年03月15日上午8：30

摘要： In this talk we study the Gevrey regularization effect for the spatially inhomogeneous Boltzmann equation without angular cutoff. This equation is partially elliptic in the velocity direction and degenerates in the spatial variable. We consider the nonlinear Cauchy problem for the fluctuation around the Maxwellian distribution and prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with Gevrey index depending on the angular singularity. Our proof relies on the symbolic calculus for the collision operator and the global subelliptic estimate for the Cauchy problem of linearized Boltzmann operator.

李维喜于2008年博士毕业于武汉大学，师从陈化教授。现为武汉大学数学与统计学院教授，国家优秀青年基金获得者。李维喜教授主要从事偏微分方程的研究，特别是在退化椭圆方程的正则性，流体力学方程的边界层分析，以及谱分析等方面做出了一系列出色的工作，并发表在《Adv.Math.》, 《Comm. Partial Differential Equations》, 《J. Eur. Math. Soc.》, 《J. Nonlinear Sci.》, 《J. Math. Pures Appl.》, 《SIAM J. Math. Anal.》与《J Differ. Equations》等杂志上20多篇。