  In this paper, we study the 3D axi-symmetric Navier-Stokes Equations with
swirl. We prove the global regularity of the 3D Navier-Stokes equations for a
family of large anisotropic initial data. Moreover, we obtain a global bound of
the solution in terms of its initial data in some $L^p$ norm. Our results also
reveal some interesting dynamic growth behavior of the solution due to the
interaction between the angular velocity and the angular vorticity fields.
