On the dynamics of Navier-Stokes-Fourier equations

Abstract

In this paper we are concerned with a non-isothermal compressible Navier-Stokes-Fourier model with density dependent viscosity that vanish on the vacuum. We prove the global existence of weak solutions with large data in the three-dimensional torus $Ω=T^{3}$. The main point is that the pressure is given by $P=Rρθ$ without additional cold pressure assumption.