Global strong solutions to radial symmetric compressible Navier–Stokes equations with free boundary

Abstract

In this paper, we consider the two-dimensional barotropic compressible Navier–Stokes equations with stress free boundary condition imposed on the free surface. As the viscosity coefficients satisfies μ(ρ)=2μ, λ(ρ)=ρβ, β>1, we establish the existence of global strong solution for arbitrarily large spherical symmetric initial data even if the density vanishes across the free boundary. In particular, we show that the density is strictly positive and bounded from the above and below in any finite time if the initial density is strictly positive, and the free boundary propagates along the particle path and expand outwards at an algebraic rate.