Linear instability analysis on compressible Navier-Stokes equations with strong boundary layer

TL;DR

This paper investigates the spectral instability of subsonic boundary layers in compressible Navier-Stokes equations at high Reynolds numbers, introducing a novel quasi-compressible and Stokes iteration approach.

Contribution

It develops a new analytical method for studying stability in compressible Navier-Stokes equations, addressing a gap in mathematical understanding of compressible fluid boundary layers.

Findings

Spectral instability of subsonic boundary layer established

New quasi-compressible and Stokes iteration method introduced

Provides mathematical insights into compressible boundary layer stability

Abstract

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 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. This paper aims to introduce a new approach to study 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 subsonic boundary layer.