A complete global solution to the pressure gradient equation

Zhen Lei, Yuxi Zheng

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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 languageEnglish (US)
Pages (from-to)280-292
Number of pages13
JournalJournal of Differential Equations
Issue number1
StatePublished - May 1 2007

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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