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

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.