A Complete Global Solution to the Pressure Gradient Equation
نویسندگان
چکیده
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., 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. Keyword: Regularity, vacuum boundary, two dimensional Riemann problem, characteristic decomposition. AMS subject classification: Primary: 35L65, 35J70, 35R35; Secondary: 35J65.
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