On weak(measure valued)-strong uniqueness for Navier-Stokes-Fourier system with Dirichlet boundary condition

TL;DR

This paper introduces a measure-valued solution concept for the compressible Navier-Stokes-Fourier system with Dirichlet boundary conditions and proves a weak-strong uniqueness principle using relative energy methods.

Contribution

It defines a new measure-valued solution framework for the system and establishes a weak-strong uniqueness result under Dirichlet boundary conditions.

Findings

Defined measure-valued solutions based on entropy and energy inequalities.

Proved weak-strong uniqueness using relative energy techniques.

Extended the understanding of solution behavior for heat-conducting fluids.

Abstract

In this paper, our goal is to define a measure valued solution of compressible Navier--Stokes--Fourier system for a heat conducting fluid with Dirichlet boundary condition for temperature in a bounded domain. The definition is based on the weak formulation of entropy inequality and ballistic energy inequality. Moreover, we obtain the weak(measure valued)-strong uniqueness property of this solution with the help of relative energy.