| 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 ($∖rho$) = $∖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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