A Complete Global Solution to the Pressure Gradient Equation
Analysis of PDEs
2009-01-26 v1
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.
Cite
@article{arxiv.0901.3701,
title = {A Complete Global Solution to the Pressure Gradient Equation},
author = {Zhen Lei and Yuxi Zheng},
journal= {arXiv preprint arXiv:0901.3701},
year = {2009}
}
Comments
We establish global existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions