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Time evolution of concentrated vortex rings. (English) Zbl 1433.76029
Summary: 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.

##### MSC:
 76B47 Vortex flows for incompressible inviscid fluids 37N10 Dynamical systems in fluid mechanics, oceanography and meteorology 35Q31 Euler equations
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##### References:
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