On a blow-up criterion for the Navier–Stokes–Fourier system under general equations of state

In this paper we prove a blow-up criterion for the compressible Navier–Stokes-Fourier system for general thermal and caloric equations of state with inhomogeneous boundary conditions for the velocity and the temperature. Assuming only that Gibb’s equation and the thermodynamic stability hold, we show that solutions in a certain regularity class remain regular under the condition that the density, the temperature and the modulus of the velocity are bounded.