A model of radiational gaseous stars

Abstract

We introduce a model concerning radiational gaseous stars and establish the existence theory of stationary solutions to the free boundary problem of hydrostatic equations describing the radiative equilibrium. We also establish in the spherically symmetric case the local well-posedness of the moving boundary problem of the corresponding Navier-Stokes-Fourier-Poisson system and construct a priori estimates of strong and classical solutions. Our results explore the vacuum behavior of density and temperature near the free boundary for the equilibrium and capture such degeneracy in the evolutionary problem.