On the steady solutions to a model of compressible heat conducting fluid in two space dimensions

Abstrakt

We consider steady compressible Navier--Stokes--Fourier system in a bounded two-dimensional domain with the pressure law $p(\vr,\vt) \sim \vr \vt + \vr \ln^\alpha (1+\vr)$. For the heat flux $\vc{q} \sim -(1+\vt^m) \nabla \vt$ we show the existence of a weak solution provided $\alpha > \max \{1, 1/m\}$, $m>0$.

Klíčová slova

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