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 (\$$\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. |

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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