Boundary layer problems for the two-dimensional compressible Navier–Stokes equations

We study the well-posedness of the boundary layer problems for compressible Navier–Stokes equations. Under the non-negative assumption on the laminar flow, we investigate the local spatial existence of solution for the steady equations. Meanwhile, we also obtain the solution for the unsteady case with monotonic laminar flow, which exists for either long time small space interval or short time large space interval. Moreover, the limit of these solutions with vanishing Mach number is considered. Our proof is based on the comparison theory for the degenerate parabolic equations obtained by the Crocco transformation or von Mises transformation.