Free Boundary Value Problem for the Spherically Symmetric Compressible Navier-Stokes Equations with a Nonconstant Exterior Pressure

Abstract

This paper is concerned with the free boundary value problem (FBVP) for the spherically symmetric barotropic compressible Navier-Stokes equations (CNS) with density-dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a nonconstant exterior pressure. Under certain assumptions imposed on the initial data, we show that there exists a unique global strong solution which is strictly positive for any finite time and decays pointwise to zero time-asymptotically.