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

Comm. Pure Appl. Math. 68 (2015), no. 7, 1157–1190.