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

@inproceedings{Cavallaro2021TimeEO,
  title={Time evolution of vortex rings with large radius and very concentrated vorticity},
  author={Guido Cavallaro and Carlo Marchioro},
  year={2021}
}
We study the time evolution of an incompressible fluid with axial symmetry without swirl when the vorticity is sharply concentrated on N annuli of radii ≈ r0 and thickness ε. We prove that when r0 = | 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 r0 and ε. 
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We study the time evolution of an incompressible fluid with axial symmetry without swirl, assuming initial data such that the initial vorticity is very concentrated inside N small disjoint rings of…
Stability of the two-dimensional point vortices in Euler flows
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