报告题目: Kac’s program for the Landau equation

报告人：王振富（北京大学）

邀请人&主持人：黄辉

报告时间与地点：12月23号晚上8点， Zoom 会议：932 2377 1616，密码：728318

报告摘要: We study the derivation of the spatially homogeneous Landau equation from the mean-field limit of a conservative N -particle system, obtained by passing to the grazing limit on Kac’s walk in his program for the Boltzmann equation. Our result covers the full range of interaction potentials, including the physically important Coulomb case. This provides the first resolution of propagation of chaos for a many-particle system approximating the Landau equation with Coulomb interactions, and the first extension of Kac’s program to the Landau equation in the soft potential regime. The convergence is established in weak, Wasserstein, and entropic senses,together with strong L1 convergence. To handle the singularity of soft potentials, we extend the duality approach of Bresch-Duerinckx-Jabin and establish key functional inequalities, including an extended commutator estimate and a new second-order Fisher information estimate. Based on a joint work with Xuanrui Feng (PKU).

报告人介绍：王振富，2017年博士毕业于美国马里兰大学，之后在美国宾夕法尼亚大学任Hans Radmacher讲师。2020年10月起加入北京大学北京国际数学研究中心，任助理教授，研究员。主要研究领域为多体系统的平均场极限和动理学方程的分析与应用。主要研究成果发表于Invent. Math., Duke Math. J., ARMA，JMPA, JFA等重要数学杂志。2021年获基金委首届海外优秀青年基金资助，2024年主持国家重点研发计划青年科学家项目。