|Title||Global ill-posedness of the isentropic system of gas dynamics|
|Publication Type||Journal Article|
|Year of Publication||2015|
|Authors||Chiodaroli E., De Lellis C., Kreml O.|
|Journal||Communications on Pure and Applied Mathematics|
|Publisher||Wiley-Blackwell Publishing, Inc.|
|Type of Article||hyperbolic conservation laws|
|Keywords||Applied Mathematics, General Mathematics|
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.