Recent progress on the Prandtl equationand Tollmien-Schlichting wave

Abstract

The Prandtl equation introduced by Prandtl in 1904 is a basic equationdescribling the behavior of the fluid near the boundary. In this talk, I willfirst introduce some recent results on the regularity, long-time behavioland boundary layer separation of the steady Prandtl equation. Then I willintroduce the construction of the Tollmien-Schlichting waves in the subsonicregime, which play a key role during the early stage of the boundary layertransition.

Speaker

章志飞，北京大学数学科学学院博雅特聘教授。他主要从事偏微分方程的理论研究，在流体力学方程的适定性、自由界面问题、液晶模型一致性的数学理论以及流动稳定性等方面取得了一系列重要的研究成果。他已在 Invent Math,CPAM, Annales ENS, Memoirs AMS 等顶尖数学刊物上发表学术论文 110 余篇。他2011 年入选中组部首批青年拔尖人才支持计划、2014年获国家杰出青年科学基金、2022 年国际数学家大会邀请报告。