Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions

Abstract

We consider steady compressible Navier--Stokes--Fourier system in a bounded twodimensional domain. We show the existence of a weak solution for arbitrarily large data for the pressure law $p(\vr,\vt) \sim \vr^\gamma + \vr \vt$ if $\gamma >1$ and $p(\vr,\vt) \sim \vr \ln^\alpha(1+\vr) + \vr \vt$ if $\gamma =1$, $\alpha>0$, depending on the model for the heat flux.

Keywords

• steady compressible Navier--Stokes--Fourier system
• weak solution
• entropy inequality
• Orlicz spaces
• compensated compactness
• renormalized solution