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

2022/07/03 by Nilasis Chaudhuri, Chaudhuri, Nilasis · 1 citation
Engineering · Mathematics · #76N10 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Primary: 35Q30 #Secondary: 35B30 #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2207.00991

openalex publication_date 2022/07/03 · openalex created_date 2022/07/07 · openalex updated_date 2026/07/28

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.

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