On steady solutions to vacuumless Newtonian models of compressible flow

We prove the existence of weak solutions to the steady compressible Navier–Stokes system in the barotropic case for a class of pressure laws that are singular at vacuum. We consider the problem in a bounded domain in with slip boundary conditions. Due to the appropriate construction of approximate solutions used in the proof, the obtained density is bounded away from 0 (and infinity). Owing to a classical result, this implies that the density and gradient of velocity are at least Holder continuous, which does not generally hold for the classical isentropic model of a perfect gas in the presence of vacuum.