Abstract:
The compressible Navier-Stokes equations has an important position in the progress of fluid mechanics.In order to research the Vaigant-Kazhikhow model,the methods of related articles in 2D are referenced and the results of the 3D spherically symmetric situation are obtained.It is proved that the global well-posedness of the classical solution to the Cauchy problem of spherically symmetric compressible Navier-Stokes equations in an exterior domain.When the bulk viscosity λ(ρ)=ρβ，β>14/5,it is shown that the solution will not develop the vacuum states in any finite time provided the initial density is uniformly away from vacuum.
