# Global ill-posedness of the isentropic system of gas dynamics

created by chiodaroli on 03 Apr 2013
modified by delellis on 04 Sep 2017

[BibTeX]

Published Paper

Inserted: 3 apr 2013
Last Updated: 4 sep 2017

Journal: Comm. Pure App. Math.
Volume: 68
Number: 7
Pages: 1157-1190
Year: 2015

Abstract:

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.