### Abstract

We study the domain of existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions. The Riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum quadrants. The global existence of a smooth solution was established in Dai and Zhang [Z. Dai, T. Zhang, Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics, Arch. Ration. Mech. Anal. 155 (2000) 277-298] up to the free boundary of vacuum. We prove that the vacuum boundary is the coordinate axes.

Original language | English (US) |
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Pages (from-to) | 280-292 |

Number of pages | 13 |

Journal | Journal of Differential Equations |

Volume | 236 |

Issue number | 1 |

DOIs | |

State | Published - May 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Analysis

### Cite this

*Journal of Differential Equations*,

*236*(1), 280-292. https://doi.org/10.1016/j.jde.2007.01.024

}

*Journal of Differential Equations*, vol. 236, no. 1, pp. 280-292. https://doi.org/10.1016/j.jde.2007.01.024

**A complete global solution to the pressure gradient equation.** / Lei, Zhen; Zheng, Yuxi.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A complete global solution to the pressure gradient equation

AU - Lei, Zhen

AU - Zheng, Yuxi

PY - 2007/5/1

Y1 - 2007/5/1

N2 - We study the domain of existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions. The Riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum quadrants. The global existence of a smooth solution was established in Dai and Zhang [Z. Dai, T. Zhang, Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics, Arch. Ration. Mech. Anal. 155 (2000) 277-298] up to the free boundary of vacuum. We prove that the vacuum boundary is the coordinate axes.

AB - We study the domain of existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions. The Riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum quadrants. The global existence of a smooth solution was established in Dai and Zhang [Z. Dai, T. Zhang, Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics, Arch. Ration. Mech. Anal. 155 (2000) 277-298] up to the free boundary of vacuum. We prove that the vacuum boundary is the coordinate axes.

UR - http://www.scopus.com/inward/record.url?scp=33947598124&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33947598124&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2007.01.024

DO - 10.1016/j.jde.2007.01.024

M3 - Article

VL - 236

SP - 280

EP - 292

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 1

ER -