Analysis on compressible Navier-Stokes equations with strong boundary layer

It is a classical problem in fluid dynamics about the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds number limit of laminar flow with the boundary layer. However, there are very few mathematical results on the compressible fluid despite the extensive studies when the fluid is governed by the incompressible Navier-Stokes equations. In this talk, we will present a new approach to studying the compressible Navier-Stokes equations in the subsonic and high Reynolds number regime where a subtle quasi-compressible and Stokes iteration is developed. As a byproduct, we show the spectral instability of the subsonic boundary layer. This is a joint project with Zhu Zhang.