On a nonisothermal ideal gas Navier-Stokes-Fourier equations

TL;DR

This paper studies a non-isothermal compressible Navier-Stokes-Fourier model with density-dependent viscosity, proving the stability of weak solutions in a periodic domain, with pressure related to density and temperature.

Contribution

It establishes the sequential stability of variational weak solutions for a complex non-isothermal model with vacuum conditions, advancing mathematical understanding of such fluid systems.

Findings

Proved stability of weak solutions in a periodic domain.

Handled viscosity that vanishes on vacuum.

Confirmed pressure relation P = R ho heta.

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 sequential stability of variational weak solutions in periodic domain \Omega= T3. The main point is that the pressure is given by P = R\rho\theta.