DMV-strong uniqueness principle for the compressible Navier-Stokes\n system with potential temperature transport

2021/06/24 by Mária Lukáčová-Medviďová, Lukáčová-Medvid'ová, Mária, Andreas Schömer +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Numerical Analysis (math.NA) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2106.12812

openalex publication_date 2021/06/24 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We establish a DMV-strong uniqueness result for the compressible\nNavier-Stokes system with potential temperature transport. The concept of\ngeneralized, the so-called dissipative measure-valued (DMV), solutions was\nproposed in [7], where their global-in-time existence was proved. Here we show\nthat strong solutions are stable in the class of DMV solutions. More precisely,\na DMV solution coincides with a strong solution emanating from the same initial\ndata as long as the strong solution exists.\n

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