Steady compressible Navier-Stokes-Fourier system for monoatomic gas and its generalizations

Abstrakt

We consider steady compressible Navier--Stokes--Fourier system for a gas with pressure $p$ and internal energy $e$ related by the constitutive law $p=(\gamma-1) \vr e$, $\gamma }1$. We show that for any $\gamma}\frac 32$ there exists a variational entropy solution (i.e. solution satisfying the weak formulation of balance of mass and momentum, entropy inequality and global balance of total energy).

This result includes the model for monoatomic gas ($\gamma = \frac 53$). If $\gamma } \frac 53$, these solutions also fulfill the weak formulation of the pointwise total energy balance.

Klíčová slova

• steady compressible Navier--Stokes--Fourier system
• weak solution
• entropy variational solution
• entropy inequality
• compensated compactness