Global Ill‐Posedness of the Isentropic System of Gas Dynamics. Issue 7 (15th August 2014) - Chiodaroli, Elisabetta; De Lellis, Camillo; Kreml, Ondřej
<x xml:space="preserve">Abstract</x> We consider the isentropic compressible Euler system in 2 space dimensions with pressure law p (ρ) = ρ2 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. © 2015 Wiley Periodicals, Inc.