Global time evolution of concentrated vortex rings

We consider an incompressible fluid with axial symmetry without swirl when the vorticity is sharply concentrated inside $N$ disjoint rings of size $\varepsilon$ and intensity of the order of $|\log\varepsilon|^{ -1}$. We show that in the limit $\varepsilon\to 0$ the movement of each vortex ring converges to a uniform motion along the symmetry axis.