偏微分方程研讨班：Analytic smoothing effect of Cauchy problem for non-cutoff Boltzmann equation

中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：徐超江 教授 (NUAA, Nanjing)        

题  目：Analytic smoothing effect of Cauchy problem for non-cutoff Boltzmann equation 

时  间：2024.07.23（星期二）10:30-11:30

地  点：数学院南楼N913

摘  要：For the hard potentials case, we prove that the spatially inhomogeneous Boltzmann equation with strong angular singularity admits the analytic smoothing effect, just like its diffusive models such as the Landau and Fokker-Planck equations. Moreover, for the mild angular singularity case, we obtain the optimal Gevrey regularization effect. 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.