Structural Stability of Prandtl Boundary Layers in the Entire Subsonic Regime

Abstract

Despite the physical significance of the compressible Navier–Stokes equations in the presence of strong boundary layers, rigorous mathematical theories in this area remain at an early stage of development. In this paper, we establish the structural stability of shear flow boundary layer profiles for the two-dimensional steady compressible Navier–Stokes equations. The stability estimates are uniform across the entire subsonic regime. As a byproduct, we provide the first rigorous justification of the low Mach number limit in the presence of Prandtl-type boundary layers. The proof relies on the quasi-compressible-Stokes iteration introduced in [41], combining a frequency-dependent analysis of the density-velocity coupling, and the identification of structural cancellations in higher-order estimates.