Global $L^{\infty}$ 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 $L^{\infty}$ entropy weak solutions has not yet 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 $L^{\infty}$ bound for the approximate solutions.