Linear Instability Analysis on Compressible Navier–Stokes Equations with Strong Boundary Layer

A classical problem in fluid mechanics concerns the stability and instability of
different hydrodynamic patterns in various physical settings, particularly in the high
Reynolds number limit of laminar flows with boundary layers. Despite extensive
studies when the fluid is governed by incompressibleNavier-Stokes equations, there
are very few mathematical results on the compressible fluid. This paper aims to
introduce 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 subsonic boundary layers.