A viscous solution of the spherical vortex to the Navier-Stokes equations

We deal with the Hill's spherical vortex, which is an exact solution to the Euler equation, and manage the solution to satisfy the incompressible Navier-Stokes(INS) equations with a viscous term. Once we get a viscous solution to the INS equations, we will be able to analyze the flows with discontinuities in vorticity. In the same procedure, we also present a time developing exact solution to the INS equations, which has a rotation on the axis besides the Hill's vortex.