A complete global solution to the pressure gradient equation

Zhen Lei, Yuxi Zheng

Research output: Contribution to journalArticle

19 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)280-292
Number of pages13
JournalJournal of Differential Equations
Volume236
Issue number1
DOIs
StatePublished - May 1 2007

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Pressure Gradient
Pressure gradient
Global Solution
Vacuum
Quadrant
Cauchy Problem
Goursat Problem
Global Smooth Solution
Degenerate Problems
Co-ordinate axis
Gas dynamics
Gas Dynamics
Arch
Arches
Smooth Solution
Free Boundary
Global Existence
Gases

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

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

In: Journal of Differential Equations, Vol. 236, No. 1, 01.05.2007, p. 280-292.

Research output: Contribution to journalArticle

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