Which measure-valued solutions of the monoatomic gas equations are generated by weak solutions?

2021/09/20 by Dennis Gallenmüller, Gallenmüller, Dennis, Emil Wiedemann +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2109.09513

openalex publication_date 2021/09/20 · openalex created_date 2023/03/16 · openalex updated_date 2026/07/28

Abstract

Contrary to the incompressible case not every measure-valued solution of the compressible Euler equations can be generated by weak solutions or a vanishing viscosity sequence. In the present paper we give sufficient conditions on an admissible measure-valued solution of the isentropic Euler system to be generated by weak solutions. As one of the crucial steps we prove an L^∞-variant of Fonseca and Müller's characterization result for generating A-free Young measures in terms of potential operators. More concrete versions of our results are presented in the case of a solution consisting of two Dirac measures. We conclude by discussing also necessary conditions for generating a measure-valued solution by weak solutions or a vanishing viscosity sequence and will point out that the resulting gap mainly results from obtaining only uniform L^p-bounds for 1

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