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arXiv · 0901.3701

A Complete Global Solution to the Pressure Gradient Equation

Zhen Lei·Yuxi Zheng
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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 [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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Zhen Lei, Yuxi Zheng. 2009-01-23. A Complete Global Solution to the Pressure Gradient Equation. https://arxiv.org/abs/0901.3701

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