A model of a non-isothermal two phase flow of compressible fluids

TL;DR

This paper presents a thermodynamically consistent model for non-isothermal two-phase flow of compressible fluids, proving global existence of weak solutions through compactness arguments.

Contribution

It introduces a simple yet thermodynamically consistent model incorporating thermal effects and establishes global existence of weak solutions.

Findings

Model admits an entropy balance equation

Proves compactness of weak solutions

Establishes global existence result

Abstract

We introduce a simple model of the time evolution of a binary mixture of compressible fluids including the thermal effects. Despite its apparent simplicity, the model is thermodynamically consistent admitting an entropy balance equation. We introduce a suitable weak formulation of the problem based on a combination of the entropy inequality with the total energy conservation principle. Finally, we show compactness of any bounded family of weak solutions and establish a global existence result.