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arXiv · 1304.0123

Global ill-posedness of the isentropic system of gas dynamics

Elisabetta Chiodaroli·Camillo De Lellis·Ondrej Kreml
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Abstract

We consider the isentropic compressible Euler system in 2 space dimensions with pressure law $p(ρ) = ρ^2$ 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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Elisabetta Chiodaroli, Camillo De Lellis, Ondrej Kreml. 2013-05-06. Global ill-posedness of the isentropic system of gas dynamics. https://doi.org/10.1002/cpa.21537

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