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 Volume 68 Pagination 1157–1190 Date Published May Publisher Wiley-Blackwell Publishing, Inc. Type of Article hyperbolic conservation laws ISSN 0010-3640 Keywords Applied Mathematics, General Mathematics Abstract We consider the isentropic compressible Euler system in 2 space dimensions with pressure law p (\$\backslashrho\) = \$\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. Notes Comm. Pure Appl. Math. 68 (2015), no. 7, 1157–1190. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.21537 DOI 10.1002/cpa.21537
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