报告人：何凌冰（清华大学）
时间：2025年3月24日下午3：30-4：30
地点：36-507
报告摘要：It is widely accepted that in the weak coupling regime, the Fokker-Planck-Landau equation is the primary effective model for charged particles. This talk aims to support this assertion by deriving the Fokker-Planck-Landau equation from the quantum Boltzmann equation using a semi-classical limit. We approach this derivation in two distinct contexts:
1) Weak Convergence of Solutions: We demonstrate that the weak solutions of the Boltzmann equation converge weakly to the H-solution of the Landau equation for any radical initial data.
2) Asymptotic Expansion: We establish an asymptotic expansion formula that describes the limiting behavior for a short time with regular initial data.
Through these analyses, we provide a comprehensive framework linking the quantum Boltzmann equation to the Fokker-Planck-Landau equation, reinforcing its significance as a fundamental model in the study of charged particle dynamics in weakly interacting systems.
报告人简介：何凌冰，清华大学数学系教授、博士研究生导师。主要研究方向为Boltzmann方程及Landau方程解的正则性传播和渐进性行为。在Ann. Sci. Éc. Norm. Supér、 Math. Ann.、 Ann. PDE、 Arch. Ration. Mech. Anal.、Comm. Math. Phys.、SIAM J. Math. Anal.、J. Funct. Anal.、 J. Stat. Phys.等国际主流数学杂志发表论文30余篇。
