Abstract. 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, in the meantime, we will also discuss some joint work with Chengjie Liu, Yaguang Wang and Feng Xie.

Bio. Tong Yang is a chair professor in Department of Mathematics, City University of Hong Kong. He has been working in the fields of hyperbolic conservation laws, kinetic theory and boundary layer theory. He served as an Editor-in-Chief of Analysis and Applications from 2013 to 2017, and is one of the founding Editors-in-Chief of Kinetic and Related Models launched in 2008. He also serves on several international journals, including the Editorial Advisory Board of London Mathematical Society: Bulletin and Journal, and SIAM Journal on Mathematical Analysis. He is foreign member of the Academia Europaea, member of the European Academy of Sciences, the World Academy of Sciences and the Hong Kong Academy of Sciences. The awards that he has received include the 2nd class State Natural Science Award of China and the Croucher Senior Research Fellowship.