  We study the time evolution of a viscous incompressible fluid with axial
symmetry without swirl, when the initial vorticity is very concentrated in $N$
disjoint rings. We show that in a suitable joint limit, in which both the
thickness of the rings and the viscosity tend to zero, the vorticity remains
concentrated in $N$ disjointed rings, each one of them performing a simple
translation along the symmetry axis with constant speed.
