Contact topology and hydrodynamics III knotted orbits
Joint work with Robert Ghrist.
Trans. Amer. Math. Soc. 352 (2000), 5781-5794.

We employ the relationship between contact structures and Beltrami fields derived in part I of this series to construct steady nonsingular solutions to the Euler equations on a Riemannian 3-sphere whose flowlines trace out closed curves of all possible knot and link types simultaneously. Using careful contact-topological controls, we can make such vector fields real-analytic and transverse to the tight contact structure on 3-sphere.

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