### 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 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

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## Cite this

Lei, Z., & Zheng, Y. (2007). A complete global solution to the pressure gradient equation.

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