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Knotted vortex filaments in an ideal fluid. (English) Zbl 0686.76014
Summary: Knotted closed-curve solutions of the equation of self-induced vortex motion are studied. It is shown that there are invariant torus knots which translated and rotate as rigid bodies. The general motion of ‘small-amplitude’ torus knots and iterated (cabled) torus knots is described and found to be almost periodic in time, and for some, but not all, initial data, the topology of the knot is shown to be invariant.

MSC:
76B47 Vortex flows for incompressible inviscid fluids
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