Global ill-posedness of the isentropic system of gas dynamics

2013/04/30 by Elisabetta Chiodaroli, Camillo De Lellis, Ondrej Kreml · 2 citations
Mathematics · #math.AP #msc:35L65 #msc:35D30 #msc:76N15

paper · pdf · doi:10.1002/cpa.21537

30 pages

arxiv created 2013/05/06 · arxiv updated 2014/08/26

Abstract

We consider the isentropic compressible Euler system in 2 space dimensions with pressure law p(ρ) = ρ² and we show the existence of classical Riemann data, i.e. pure jump discontinuities across a line, for which there are infinitely many admissible bounded weak solutions (bounded away from the void). We also show that some of these Riemann data are generated by a 1-dimensional compression wave: our theorem leads therefore to Lipschitz initial data for which there are infinitely many global bounded admissible weak solutions.

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• Path-connectedness of incompressible Euler solutions
• Selection criteria for the compressible Euler equations: numerical study

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