A Complete Global Solution to the Pressure Gradient Equation

Details A Complete Global Solution to the Pressure Gradient Equation A Complete Global Solution to the Pressure Gradient Equation

2009-01-23

arxiv.org/abs/0901.3701v1

Journal of Differential Equations 236 (2007), no. 1, 280--292

Mathematics

Analysis of PDEs

We establish global existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions

Scientific paper

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 [Arch. Rational Mech. Anal., {\bf 155}(2000), 277-298] up to the free boundary of vacuum. We prove that the vacuum boundary where the system is degenerate is the trivial coordinate axes.

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