Steady solutions to the Navier-Stokes-Fourier system for dense compressible fluid

Abstract

We establish existence of strong solutions to the stationary Navier-Stokes-Fourier system for compressible flows with density dependent viscosities in regime of heat conducting fluids with very high densities. In comparison to the known results considering the low Mach number case, we work in the $L^p$-setting combining the methods for the weak solutions with the method of decomposition. Moreover, the magnitude of gradient of the density as well as other data are not limited, our only assumption is the given total mass must be sufficiently large.