Stationary compressible Navier–Stokes equations with inflow condition in domains with piecewise analytical boundaries

Abstract

We show the existence of strong solutions in Sobolev–Slobodetskii spaces to the stationary compressible Navier–Stokes equations with inflow boundary condition. Our result holds provided a certain condition on the shape of the boundary around the points where characteristics of the continuity equation are tangent to the boundary, which holds in particular for piecewise analytical boundaries. The mentioned situation creates a singularity which limits regularity at such points. We show the existence and uniqueness of regular solutions in a vicinity of given laminar solutions under the assumption that the pressure is a linear function of the density. The proofs require the language of suitable fractional Sobolev spaces. In other words our result is an example where the application of fractional spaces is irreplaceable, although the subject is a classical system.