报告人：周玉龙（中山大学数学学院副教授、博士生导师）
时间：1月14日16:30-17:10
地点:36-507
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() 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.
个人简介：周玉龙，中山大学数学学院副教授，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，研究成果发表在 Commun. Math. Phys., Arch. Ration. Mech. Anal., Adv. Math., Math. Ann., Ann. Inst. H. Poincaré Anal. Non Linéaire, J. Funct. Anal., SIAM J. Math. Anal., SIAM J. Control Optim. 等期刊上。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]、国家自然科学基金面上项目等。入选第八批“广东特支计划”青年拔尖人才、2023年度“广东省科学技术协会青年科技人才培育计划”。
