Global $L^{\infty}$ solutions of the compressible Euler equations with damping and spherical symmetry

Abstract

We study the Euler equations of compressible isentropic gas dynamics with damping and spherical symmetry. For spherically symmetric flow, the global existence of the weak entropy $L^{\infty}$ solutions with damping isn’t still obtained. In this paper, we prove the existence of global solutions with small $L^{\infty}$ data. We construct the approximate solutions by using modified Godunov scheme. A $L^{\infty}$ bound for the approximate solutions can be obtained with the aid of the presence of the damping term.