Local Well-Posedness of Dynamics of Viscous Gaseous Stars

TL;DR

This paper proves the local existence and uniqueness of solutions for the motion of viscous gaseous stars with vacuum boundaries, capturing physical vacuum behavior for a range of adiabatic exponents.

Contribution

It establishes the local well-posedness of strong solutions to the compressible Navier-Stokes-Poisson system with vacuum free boundary in spherical symmetry, including physical vacuum boundary behavior.

Findings

Proves local well-posedness for all  > 6/5

Captures physical vacuum boundary behavior

Applies to spherically symmetric, isentropic gaseous stars

Abstract

We establish the local in time well-posedness of strong solutions to the vacuum free boundary problem of the compressible Navier-Stokes-Poisson system in the spherically symmetric and isentropic motion. Our result captures the physical vacuum boundary behavior of the Lane-Emden star configurations for all adiabatic exponents $\gamma>{6/5}$.