報告人簡介
楊彤教授的研究領域是偏微分方程和動理學理論。 楊彤教授于2018年和2021年分別當選為歐洲科學院（European Academy of Sciences）外籍院士和發(fā)展中國家科學院（也稱世界科學院）院士，于2021年當選香港科學院院士，并于2022年當選歐洲人文和自然科學院（Academia Europaea）外籍院士。他獲得的科技獎勵包括香港研資局高級研究學者獎（2020年）、國家自然科學獎二等獎（2012年）、香港裘槎基金會高級研究成就獎（2011年）、教育部重大人才計劃講座教授（2005年）、國家杰出青年科學基金海外與港澳青年學者合作基金（2004年）、首屆華人數(shù)學家大會晨興數(shù)學獎銀獎（1998年）等。
內容簡介
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.
