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We study the domain of existence of a solution to a Riemann problem for thepressure gradient equation in two space dimensions. The Riemann problem is theexpansion of a quadrant of gas of constant state into the other three vacuumquadrants. The global existence of a smooth solution was established in Dai andZhang [Arch. Rational Mech. Anal., {\bf 155}(2000), 277-298] up to the freeboundary of vacuum. We prove that the vacuum boundary where the system isdegenerate is the trivial coordinate axes.

A Complete Global Solution to the Pressure Gradient Equation