### Abstract

An interesting problem arising in gas and fluid dynamics is to understand the behavior of vacuum states, namely, the behavior of the system in the presence of vacuum. In this paper, we review and expand some local-in-time well-posedness results for one-dimensional compressible Euler equations for polytropic gases with a range of behaviors at the interface including the physical vacuum case. We also present some sort of ill-posedness results in some other cases. Finally, we present some conjectures about the change of behavior at the interface. This paper is a mixture of rigorous and formal calculations.

Original language | English (US) |
---|---|

Article number | 115625 |

Journal | Journal of Mathematical Physics |

Volume | 53 |

Issue number | 11 |

DOIs | |

State | Published - Nov 27 2012 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*53*(11), [115625]. https://doi.org/10.1063/1.4767369

**Well and ill-posedness for compressible Euler equations with vacuum.** / Jang, Juhi; Masmoudi, Nader.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 53, no. 11, 115625. https://doi.org/10.1063/1.4767369

}

TY - JOUR

T1 - Well and ill-posedness for compressible Euler equations with vacuum

AU - Jang, Juhi

AU - Masmoudi, Nader

PY - 2012/11/27

Y1 - 2012/11/27

N2 - An interesting problem arising in gas and fluid dynamics is to understand the behavior of vacuum states, namely, the behavior of the system in the presence of vacuum. In this paper, we review and expand some local-in-time well-posedness results for one-dimensional compressible Euler equations for polytropic gases with a range of behaviors at the interface including the physical vacuum case. We also present some sort of ill-posedness results in some other cases. Finally, we present some conjectures about the change of behavior at the interface. This paper is a mixture of rigorous and formal calculations.

AB - An interesting problem arising in gas and fluid dynamics is to understand the behavior of vacuum states, namely, the behavior of the system in the presence of vacuum. In this paper, we review and expand some local-in-time well-posedness results for one-dimensional compressible Euler equations for polytropic gases with a range of behaviors at the interface including the physical vacuum case. We also present some sort of ill-posedness results in some other cases. Finally, we present some conjectures about the change of behavior at the interface. This paper is a mixture of rigorous and formal calculations.

UR - http://www.scopus.com/inward/record.url?scp=84870491054&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870491054&partnerID=8YFLogxK

U2 - 10.1063/1.4767369

DO - 10.1063/1.4767369

M3 - Article

AN - SCOPUS:84870491054

VL - 53

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 11

M1 - 115625

ER -