报告名称：Optimal convergence estimate of the limit from inverse power potential to hard sphere Boltzmann equation

报告专家：周玉龙 教授

专家所在单位：中山大学数学学院

报告时间：3月14日14：30

报告地点:数统学院201报告厅

专家简介： 周玉龙教授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：The inverse power potential U(r)=r^{-1/s}, 0<s<1, generates the Boltzmann kernel B^s = |v-v_*|^{1-4s} b_s(θ) with an angular singularity as θ → 0. Jang-Kepka-Nota-Velázquez ["Vanishing angular singularity limit to the hardsphere Boltzmann equation", J. Stat. Phys., 190(4), 2023] proved the limit B^s → (1/4)|v-v_*| as s → 0, as well as weak convergence of solutions, but without a rate. In this work we establish the sharp estimate|b_s(θ) − 1/4| ≤ C s θ^{−2−2s}. In particular, this sharp estimate yields the optimal O(s) convergence rate for solutions of the homogeneous Boltzmann equation with large initial data in suitable Sobolev spaces; i.e., for any t ∈ [0, T], we have f^s(t) = f^0(t) + O(s), quantified by the L^1_k norm for k ≥ 2.