On the motion of viscous, compressible and heat-conducting liquids

TL;DR

This paper proves the existence of global weak solutions for a viscous, compressible, heat-conducting fluid with temperature-dependent viscosity, and establishes a weak-strong uniqueness principle for such systems.

Contribution

It introduces a new analysis for fluids with temperature-dependent viscosity coefficients and demonstrates the weak-strong uniqueness property in this context.

Findings

Existence of global-in-time weak solutions

Derivation of a relative energy inequality

Weak-strong uniqueness result

Abstract

We consider a system of equations governing the motion of a viscous, compressible, and heat conducting liquid-like fluid, with a general EOS of Mie-Grueneisen type. In addition, we suppose that the viscosity coefficients may decay to zero for large values of the temperature. We show the existence of global-in-time weak solution, derive a relative energy inequality, and compare the weak solutions with strong one emanating from the same initial data - the weak strong uniqueness property.