Temporally global solution to the equations for a spherically symmetric viscous radiative and reactive gas over the rigid core

In this paper, we consider a system of classical model equations describing a motion of gaseous star, spherically symmetric, with a free-surface and a rigid core in the center under the influence of gaseous self-gravitation and potential force of the core. In addition to it, we investigate the above model equations in the physically more realistic situation: the presence of radiation and reacting process. By introducing Lagrangian mass coordinate, this free-boundary problem is reduced to the one in a fixed domain. Based on the fundamental local existence result and a priori estimates, we can construct a unique global classical solution.