Remarks on spherically symmetric solutions of the compressible Euler equations

Abstract

Some evidence indicates that spherically symmetric solutions of the compressible Euler equations blow up near the origin at some time under certain circumstances (cf. [4,19]). In this paper, we observe a criterion forL∞Cauchy data of arbitrarily large amplitude to ensure the existence ofL∞spherically symmetric solutions in the large, which model outgoing blast waves and large-time asymptotic solutions. The equilibrium states of the solutions and their asymptotic decay to such states are analysed. Some remarks on global spherically symmetric solutions are discussed.