Speaker: 王振富，北京大学

Inviter: 随机分析研究中心

Title: Kac’s program for the Landau equation

Language: Chinese

Time & Venue: 2025.09.26 15:00–16:00 南楼613

Abstract: 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).