On the dynamics of Navier-Stokes-Fourier equations

TL;DR

This paper proves the global existence of weak solutions for a non-isothermal compressible Navier-Stokes-Fourier model with density-dependent viscosity in three dimensions, without assuming cold pressure, advancing understanding of fluid dynamics near vacuum.

Contribution

It establishes the global existence of weak solutions for a complex Navier-Stokes-Fourier system with density-dependent viscosity and no cold pressure assumption.

Findings

Proved global existence of weak solutions in 3D torus.

Handled density-dependent viscosity vanishing at vacuum.

No additional cold pressure assumption needed.

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 $\Omega=T^{3}$. The main point is that the pressure is given by $P=R\rho \theta$ without additional cold pressure assumption.