## Abstract

An important problem in gas and fluid dynamics is to understand the behavior of vacuum states, namely the behavior of the system in the presence of a vacuum. In particular, physical vacuum, in which the boundary moves with a nontrivial finite normal acceleration, naturally arises in the study of the motion of gaseous stars or shallow water. Despite its importance, there are only a few mathematical results available near a vacuum. The main difficulty lies in the fact that the physical systems become degenerate along the vacuum boundary. In this paper, we establish the local-in-time well-posedness of three-dimensional compressible Euler equations for polytropic gases with a physical vacuum by considering the problem as a free boundary problem.

Original language | English (US) |
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Pages (from-to) | 61-111 |

Number of pages | 51 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 68 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2015 |

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics