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304am永利集团、所2022年系列学术活动(第053场):杨彤 教授 香港城市大学

发表于: 2022-06-28   点击: 

报告题目:Stability Analysis on the Compressible Navier-Stokes Equations with Strong Boundary Layer

报 告 人:杨彤 教授

所在单位:香港城市大学

报告时间:2022年07月07日 16:00-17:00

报告地点:腾讯会议 ID:760-550-900

点击链接入会,或添加至会议列表:https://meeting.tencent.com/dm/7Ob6BALn2IKv

校内联系人:王春朋 wangcp@jlu.edu.cn


报告摘要:Even though there are extensive studies on the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds number limit of laminar flow with boundary layer for the incompressible Navier-Stokes equations, there are much less mathematical results in the compressible setting. In this talk, we will present a new approach to study the compressible Navier-Stokes equations in the subsonic and high Reynolds number regime. The key observation is to introduce two new decompositions that involve quasi-compressible and Stokes approximations. And then an iteration scheme is defined by applying the decompositions for solving the linearized compressible Navier-Stokes equations. As a by-product, an analogue of the classical Orr-Sommerfeld equation is derived in the compressible setting.

With the above analytic tools, we show the spectral instability of subsonic boundary layer that is related to the Tollmien-Schlichting waves with critical Gevrey index 3/2 in the compressible setting that has been well investigated for the incompressible flow.

The talk will mainly focus on some recent joint work with Zhu Zhang.


报告人简介:杨彤,香港城市大学数学系讲座教授,欧洲科学院院士,发展中国家科学院院士,香港科学院院士,美国数学会会士。长期从事非线性偏微分方程的研究,特别是在双曲守恒律和玻尔兹曼方程的研究中作出了重要的创新性工作,产生了重大影响,在JAMS、CPAM、JEMS、Adv. Math.、CMP、ARMA、Ann. I. H. Poincare等重要数学期刊上发表论文200多篇,承担各类项目30多项。担任Analysis and Applications、Kinetic and Related Models、Bulletin of London Mathematical Society、Journal of London Mathematical Society、SIAM Journal on Mathematical Analysis等多个国际著名期刊的主编或编委。2012至2018年任香港城市大学数学系主任,2016至2020年任香港数学会主席。1998年获华人数学家大会晨兴数学银奖,2004年获国家杰出青年基金海外与港澳青年学者合作基金,2005年获教育部长江学者奖励计划讲座教授,2011年获裘槎基金会高级研究成就奖,2012年获国家自然科学二等奖,2019年获高等学校科学研究优秀成果奖自然科学奖一等奖,2020年获香港研资局高级研究学者奖。