Existence and uniqueness of strong stationary solutions for compressible flows

Abstract

This chapter contains a survey of results in the existence theory of strong solutions to the steady compressible Navier-Stokes system. In the first part, the compressible Navier-Stokes equations are studied in bounded domains, both for homogeneous (no inflow) and inhomogeneous (inflow) boundary conditions.

The solutions are constructed in Sobolev spaces. The next part contains the results for unbounded domains, especially for the exterior domains.

Here, not only the question of existence and uniqueness is considered, but also the asymptotic structure near infinity is studied. Due to the different nature of the problems, the two- and three-dimensional problems are treated separately.

Keywords

• compressible Navier-Stokes equations
• compressible Navier-Stokes-Fourier system
• stead solutions
• strong solutions
• regularity
• asymptotic structure