Appears in collection : Summer School 2023 - New trends in mathematical fluid dynamics

We study the time evolution of an incompressible fluid (both inviscid and viscous) with axial symmetry without swirl, when the initial vorticity is very concentrated in N disjoint rings. We show that in a suitable limit, in which the thickness of the rings (and the viscosity, in the viscous case) tends 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.