We survey the derivation of the Boltzmann equation from a mathematical point of view. We discuss our recent progress on a conditional mathematical derivation of the quadratic Boltzmann equation from quantum many-body dynamics. We find that, the limit has to be very weak and rough and happens at a double criticality. In fact, we compute through the local Maxwellian that the regularity cannot be higher at the N-body level. On the other hand, the regularity cannot be lower as the limit happens exactly at the well-posedness threshold of the limiting Boltzmann equation. The condition we assume might be related to the entropy dipping phenomenon recently found by an ITP researcher and collaborators.

报告人简介

陈旭文教授，美国罗切斯特大学大学数学系教授，西蒙斯奖金获得者，长期从事量子多体问题、动理学方程等偏微分方程的数学理论研究，已在国际顶级期刊 Inventiones Mathematicae, Forum of Mathematics PI, Journal of the European Mathematical Society, Peking Mathematical Journal, Annals of PDE, Archive for Rational Mechanics and Analysis, Communications in Mathematical Physics等上发表学术论文近30篇。

邀请人

田矗舜 研究员