Publication at Faculty of Mathematics and Physics |
2010
Abstract
We consider the steady compressible Navier--Stokes--Fourier system in a bounded three-dimensional domain. We prove the existence of a solution for arbitrarily large data under the assumption that the pressure $p(\rho,\theta) \sim \rho \theta + \rho^\gamma$ for $\gamma >\frac 73$, assuming either the slip or no-slip boundary condition for the velocity and the Newton boundary condition for the temperature.
The regularity of solutions is determined by the basic energy estimates, constructed for the system.