Spherically symmetric solutions of the multi-dimensional, compressible, isentropic Euler equations

Abstract

In this note, we prove that the solutions obtained to the spherically symmetric Euler equations in the recent works [2, 3] are weak solutions of the multi-dimensional compressible Euler equations. This follows from new uniform estimates made on the artificial viscosity approximations up to the origin, removing previous restrictions on the admissible test functions and ruling out formation of an artificial boundary layer at the origin. The uniform estimates may be of independent interest as concerns the possible rate of blow-up of the density and velocity at the origin for spherically symmetric flows.