Derivation of Fokker-Planck-Landau
equation from Boltzmann equation
by weak-coupling limit
报告专家：何凌冰 教授（清华大学）
报告时间：4月23日（周四）16:30-17:30
报告地点：国家天元数学西南中心401
报告摘要：
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.
邀请人：程建峰
