Time evolution of vortex rings with large radius and very concentrated vorticity

We study the time evolution of an incompressible fluid with an axial symmetry without swirl when the vorticity is sharply concentrated on N annuli of radii ≈ r_0 and thickness ε. We prove that when r_0 = ∣log ε∣^α, α > 2, the vorticity field of the fluid converges as ε → 0 to the point-vortex model, at least for a small but positive time. This result generalizes a previous paper that assumed a power law for the relation between r_0 and ε.