### 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 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Well-posedness of compressible euler equations in a physical vacuum.** / Jang, Juhi; Masmoudi, Nader.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 68, no. 1, pp. 61-111. https://doi.org/10.1002/cpa.21517

}

TY - JOUR

T1 - Well-posedness of compressible euler equations in a physical vacuum

AU - Jang, Juhi

AU - Masmoudi, Nader

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84911404150&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84911404150&partnerID=8YFLogxK

U2 - 10.1002/cpa.21517

DO - 10.1002/cpa.21517

M3 - Article

AN - SCOPUS:84911404150

VL - 68

SP - 61

EP - 111

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 1

ER -