Journal of Mathematical Fluid Mechanics ( IF 0.970 ) Pub Date : 2020-02-24 , DOI: 10.1007/s00021-020-0482-x
Paolo Buttà, Carlo Marchioro

We study the time evolution of an incompressible fluid with axisymmetry without swirl when the vorticity is sharply concentrated. In particular, we consider N disjoint vortex rings of size $$\varepsilon$$ and intensity of the order of $$|\log \varepsilon |^{ -1}$$. We show that in the limit $$\varepsilon \rightarrow 0$$, when the density of vorticity becomes very large, the movement of each vortex ring converges to a simple translation, at least for a small but positive time.

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