分析和微分方程讨论班

报告题目：Derivation of Fokker-Planck-Landau equation from Boltzmann equation by weak-coupling limit

报  告  人：何凌冰 教授（清华大学）

时        间：2026年4月9日，14:00-15:00

地        点：海纳苑2幢204

摘  要： Conventional literature on physical books asserts that starting with any smooth potential function $\Phi(|x|)$, the Boltzmann equation transitions into the Fokker-Planck-Landau equation, which is characterized by a typical diffusion coefficient given by $M_\phi:=\int_0^\infty |\hat{\Phi}(r)|^2r^3dr$, in what is referred to as the weak coupling limit. We provide a rigorous mathematical validation of this assertion through two main approaches: (1) We introduce a novel scaling for the collision kernel of the Boltzmann collision operator, enabling us to frame the weak coupling limit as a well-defined mathematical limit problem. This innovative scaling effectively captures the weak coupling interactions governed by an inverse power law or Coulomb potential. (2) We perform a comprehensive mathematical analysis of the global asymptotic behavior in the weak coupling limit, employing a standard perturbation framework. This approach yields a detailed description of the linearized operator and the asymptotic expansion of the solutions during the limit process. As a result, we present the first rigorous and complete proof of Landau's original derivation. This talk is based on a joint work with L.Desvillettes,  J.-C. Jiang and Y.-L. Zhou.

联系人：王伟（wangw07@zju.edu.cn）