Global existence of the spherically symmetric flow of a self-gravitating viscous gas

Abstract

In this paper we consider a free-boundary problem for the spherically symmetric flow of a self-gravitating viscous and heat-conductive gas over a rigid sphere. Considering the problem in the Lagrangian-mass coordinate system, we investigate the temporally global existence and behaviour of the solution. Especially, we focus our discussion on the corresponding stationary problem, whose solution gives an asymptotic profile of the solution of the original (time-dependent) problem.