Global dynamics of viscous gaseous stars in a physical vacuum

Abstract

The study of vacuum is important in understanding compressible flows. In particular, physical vacuum, in which the boundary moves with a nontrivial finite normal acceleration, naturally arises in the study of the motion of gaseous stars. In this paper, we analyze the free boundary problem for the three-dimensional compressible Navier--Stokes--Poisson equations with degenerate viscosities for self-gravitating viscous gaseous stars. For the spherically symmetric and barotropic motion, we establish the global well-posedness of classical solutions without any restriction on the size of the initial data. Our solutions obtained here are smooth all the way up to the moving boundary and capture the physical vacuum boundary behavior of the Lane--Emden star configuration.