Steady 3D viscous compressible flows with adiabatic exponent $\gamma\in (1,\infty)$

Abstract

The Navier-Stokes equations for compressible barotropic flow in the stationary three dimensional case are considered. It is assumed that a fluid occupies a bounded domain and satisfies the no-slip boundary condition. The existence of a weak solution under the assumption that the adiabatic exponent satisfies $\gamma>1$ is proved. These results cover the cases of monoatomic, diatomic, and polyatomic gases.