## Global Ill-Posedness of the Isentropic System of Gas Dynamics

We consider the isentropic compressible Euler system in 2 space dimensions with pressure law p () = (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. (c) 2015 Wiley Periodicals, Inc.

Published in:
Communications On Pure And Applied Mathematics, 68, 7, 1157-1190
Year:
2015
Publisher:
Hoboken, Wiley-Blackwell
ISSN:
0010-3640
Laboratories: