Global L∞ solutions of the compressible Euler Equations with spherical symmetry
Abstract: We study the compressible Euler equations with spherical symmetry surrounding a solid ball. For the spherically symmetric flow, the global existence of L∞ entropy weak solutions has not yet been obtained except a special case. In this paper, we prove the existence of global solutions in the more general case. We construct approximate solutions by using a modified Godunov scheme. The main point is to obtain an L∞ bound for the approximate solutions.