报告人：周玉龙 教授
报告题目：On the Boltzmann equation with strong kinetic singularity and its grazing limit to the Landau equation
报告时间：2026年4月15日（周三）上午10：00
报告地点：腾讯会议：156474973
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
周玉龙，中山大学数学学院教授，博士研究生导师，主要从事动理学方程的理论研究，包括Boltzmann方程和Landau方程，取得了一系列高水平成果，如量子Boltzmann方程的适定性和半经典极限，经典Boltzmann方程的Landau逼近，相关成果发表在Adv. Math., Math. Ann., Arch. Ration. Mech. Anal., Commun. Math. Phys., Ann. Inst. H. Poincaré Anal. Non Linéaire, J. Funct. Anal., SIAM J. Math. Anal.等著名期刊上。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）[原优秀青年科学基金项目]、面上项目、青年项目等，参与2项国家重点研发计划。2025年入选第八批“广东特支计划”青年拔尖人才，2023年入选“广东省科学技术协会青年科技人才培育计划”。
报告摘要：
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.
