20241115 周玉龙 On semi-classical limit of spatially homogeneous quantum Boltzmann equation: asymptotic expansion

报告题目：On semi-classical limit of spatially homogeneous quantum Boltzmann equation: asymptotic expansion

报告人：周玉龙教授（中山大学）

时间：11月15日（周五）15:30-16:30

地点：数学学院425

摘要：We will talk about the semi-classical limit the spatially homogeneous quantum Boltzmann equation as the Planck constant tends to zero. For general interaction potential, we prove the following: (1) The spatially homogeneous quantum Boltzmann equations are locally well-posed in some weighted Sobolev spaces with  quantitative estimates uniformly in the Planck constant.(2) The semi-classical limit can be established with an explicit convergence rate. Our proof relies on a detailed analysis of the Uehling-Uhlenbeck operator from both angular cutoff and non-cutoff perspectives.

报告人简介：周玉龙，中山大学数学学院副教授，博士生导师，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Adv. Math.、Arch. Ration. Mech. Anal.、Ann. Inst. H. Poincaré Anal. Non Linéaire、J. Funct. Anal.、SIAM J. Math. Anal.、SIAM J. Control Optim. 等期刊上。现主持国家重点研发计划“数学和应用研究”青年科学家项目，已完成国家自然科学基金青年基金。