2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217238We 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.We establish global existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensionsAnalysis of PDEs35L65, 35J70text