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

Chiodaroli, Elisabetta; De Lellis, Camillo; Kreml, Ondřej (2015). Global III-posedness of the isentropic system of gas dynamics. Communications on Pure and Applied Mathematics, 68(7):1157-1190.

## Abstract

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

## Citations

8 citations in Web of Science®
9 citations in Scopus®

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 15 May 2015 27 Jan 2016 11:15 16 May 2016 00:00 Wiley-Blackwell Publishing, Inc. 0010-3640 https://doi.org/10.1002/cpa.21537
Permanent URL: https://doi.org/10.5167/uzh-116672

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