### Abstract

We prove a priori estimates for the three-dimensional compressible Euler equations with moving physical vacuum boundary, with an equation of state given by p(?) = C_{?}?^{?} for ? > 1. The vacuum condition necessitates the vanishing of the pressure, and hence density, on the dynamic boundary, which creates a degenerate and characteristic hyperbolic free-boundary system to which standard methods of symmetrizable hyperbolic equations cannot be applied. © The Author(s) 2010.

Original language | English |
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Pages (from-to) | 559-587 |

Number of pages | 29 |

Journal | Communications in Mathematical Physics |

Volume | 296 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2010 |

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## Cite this

Coutand, D., Lindblad, H., & Shkoller, S. (2010). A priori estimates for the free-boundary 3d compressible euler equations in physical vacuum.

*Communications in Mathematical Physics*,*296*(2), 559-587. https://doi.org/10.1007/s00220-010-1028-5