Stability of the isentropic Riemann solutions of the full multidimensional Euler system

2014/12/05 by Eduard Feireisl, Feireisl, Eduard, Ondřej Kreml +3
Earth and Planetary Sciences · Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #math.AP

paper · pdf · doi:10.48550/arxiv.1412.1903

arxiv created 2014/12/05 · openalex publication_date 2014/12/05 · arxiv updated 2014/12/08 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We consider the complete Euler system describing the time evolution of an inviscid non-isothermal gas. We show that the rarefaction wave solutions of the 1D Riemann problem are stable, in particular unique, in the class of all bounded weak solutions to the associated multi-D problem. This may be seen as a counterpart of the non-uniqueness results of physically admissible solutions emanating from 1D shock waves constructed recently by the method of convex integration.

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