The compressible Euler equations for an isothermal gas with spherical symmetry

Abstract

We shall study isothermal gas dynamics with spherical symmetry. In this case, existence theorems have been obtained outside a solid ball. However, little is known for the case including the origin, because the equation has a singularity there. In this paper, we will present discontinuous solutions for this case, by introducing a certain non-homogeneous conservation laws and using a modified Glimm’s scheme.