报告地点：行健楼学术活动室665
邀请人：寿凌云副教授
摘要：For the inverse power law potential $U(r)=r^{-p}$, the Boltzmann kernel has the asymptotic behavior $B(v-v_{*}, \sigma) \sim \theta^{-2-2s}|v-v_{*}|^{\gamma}$ as the deviation angle tends to $0$. Global well-posedness of the Boltzmann equation with such singular kernels has been built in the parameter range $\gamma>-3, 0<s<1$ independently by Gressman-Strain [J. Amer. Math. Soc., 2011] and Alexandre-Morimoto-Ukai-Xu-Yang [J. Funct. Anal., 2012], triggering many other theoretical developments thereafter. In this talk, we consider stronger kinetic singularity and extend the global well-posedness theory to the range $\gamma >-2s -3, 0<s<1$. This range is almost optimal by recalling that the dominant part of the Boltzmann operator behaves like the factional Laplace operator $-(-\Delta)^{s}$ which allows a singularity with exponent $-2s -3$ in 3-dimensional space. Based on the global well-posedness result, we prove the grazing limit from the Boltzmann equation to the Landau equation as $s \to 1$ for any $\gamma>-5$ that includes the Coulomb potential $\gamma=-3$. As a byproduct, the Landau equation is globally well-posed for any $\gamma>-5$. This is a joint work with Prof. Tong Yang.
报告人简介：周玉龙，中山大学副教授、博士生导师，国家高层次人才，长期从事 Boltzmann 方程、Landau 方程等动理学方程的理论研究，在相关领域取得了一系列重要成果，发表于 Adv. Math.、CMP、ARMA、Math. Ann.、AIHPC、JFA、SIAM 等国际知名学术期刊。主持国家重点研发计划“数学和应用研究”青年科学家项目、国家自然科学基金青年科学基金项目（B类）、面上项目、青年项目等，并参与 2 项国家重点研发计划。曾入选第八批“广东特支计划”青年拔尖人才（2025）和“广东省科学技术协会青年科技人才培育计划”（2023）。
