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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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