Calculus of Variations and Geometric Measure Theory
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E. Chiodaroli - C. De Lellis - O. Kreml

Global ill-posedness of the isentropic system of gas dynamics

created by chiodaroli on 03 Apr 2013
modified by delellis on 05 May 2014


Accepted paper

Inserted: 3 apr 2013
Last Updated: 5 may 2014

Journal: Comm. Pure App. Math.
Year: 2013


We consider the isentropic compressible Euler system in 2 space dimensions with pressure law $p({\rho}) = {\rho}^2$ 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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