题目：Analytic smoothing effect of a class of ultra-parabolic equations

报告人：徐超江 教授 (南京航空航天大学) 

摘要： 

We study a class of ultra-parabolic equations, it is a high order degenerate parabolic operators of Hormander type, so it is strongly degenerate, but we prove that this class operators possesses the analytic smoothing effect of Cauchy problem, that means, for the initial datum belongs to $L^2$, we prove that the solution is analytic for all spatial variables when $t>$. This class operators contains many kinetic operators such as, Kolmogorov-Fakker-Planck operators, Landau operators and non-cuttoff Boltzmann operators.   

To overcome the degeneracy in the spatial variable, a family of well-chosen vector fields with time-dependent coefficients will play a crucial role, and the analytic regularization effect of weak solutions relies on a quantitative estimate on directional derivatives in these vector fields.

报告人简介：

徐超江，南京航空航天大学特聘教授，国家杰出青年科学基金获得者，国家级人才项目入选者。徐超江教授主要从事偏微分方程微局部分析理论研究，包括非线性退化椭圆方程、Landau 方程、Boltzmann 方程和流体力学边界层理论。在JAMS, CPAM等国际一流杂志发表学术论文100余篇.

报告时间：2023年11月23日（周四）下午4：00-5：00

联系人：酒全森

地点：教二楼913