Before revision: In this paper, we present strong numerical evidences that the 3D  axisymmetric Navier-Stokes equations with degenerate variable diffusion coefficients and smooth initial data of finite energy develop a potential finite time locally self-similar singularity at the origin.
After revision: In this paper, we present strong numerical evidences that the 3D axisymmetric Navier-Stokes equations with degenerate diffusion coefficients and smooth initial data of finite energy develop a potential finite time locally self-similar singularity at the origin.