  In this paper, we prove the local well-posedness of 3-D axi-symmetric
Navier-Stokes system with initial data in the critical Lebesgue spaces. We also
obtain the global well-posedness result with small initial data. Furthermore,
with the initial swirl component of the velocity being sufficiently small in
the almost critical spaces, we can still prove the global well-posedness of the
system.
