报告人简介

杨彤教授的研究领域是偏微分方程和动理学理论。 杨彤教授于2018年和2021年分别当选为欧洲科学院（European Academy of Sciences）外籍院士和发展中国家科学院（也称世界科学院）院士，于2021年当选香港科学院院士，并于2022年当选欧洲人文和自然科学院（Academia Europaea）外籍院士。他获得的科技奖励包括香港研资局高级研究学者奖（2020年）、国家自然科学奖二等奖（2012年）、香港裘槎基金会高级研究成就奖（2011年）、教育部重大人才计划讲座教授（2005年）、国家杰出青年科学基金海外与港澳青年学者合作基金（2004年）、首届华人数学家大会晨兴数学奖银奖（1998年）等。

内容简介

There are two basic models in Kinetic theory, the Boltzmann equation and the Landau equation. Between these two models, the grazing limit of the Boltzmann equation to Landau equation is well-known and has been justified by using cutoff near the grazing angle with some suitable scaling. In the first part of the talk, we will present a new approach by applying a natural scaling on the Boltzmann equation and an improved well-posedness theory for the Boltzmann equation without angular cutoff in the regime with an optimal range of parameters to justify the grazing limit. In the second part of the talk, we will focus on the well-posedness of the Landau equation in some critical function spaces that capture its essential structure of scaling invariance. The talk is based on some recent joint works with Yu-Long Zhou on the first topic and Ke Chen and Quoc-Hung Nguyen on the second topic.