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. 
Global time evolution of concentrated vortex rings
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
∂tω + u · ∇ω = 0 ω(0, x) = ω0(x). We are interested in the cases when the initial vorticity has the form ω0 = ω0,ǫ + ω0p,ǫ, where ω0,ǫ is concentrated near M disjoint points p0m and ω0p,ǫ is a small

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