题    目：Some recent study on kinetic equations in perturbative framework

时    间：2024年11月15日（周五）上午9：30-12：30

地    点：数学与统计楼213报告厅

报 告 人：杨彤 教授  武汉数学与智能研究院

摘  要：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.

报告人简介：

杨彤教授现为武汉大学长聘正教授。他于1987年和1990年在中山大学获得学士和硕士学位，1993年博士毕业于美国加州大学戴维斯分校。杨彤教授2022年加盟香港理工大学。他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。2022年当选欧洲人文和自然科学院外籍院士。杨彤教授所获科技奖励包括香港研资局高级研究学者奖(2020)、国家自然科学奖二等奖(2012)、香港裘槎基金会高级研究成就奖(2011)、首届华人数学家大会晨兴数学奖银奖(1998)等。