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Contact topology and hydrodynamics III: knotted flowlines

John Etnyre·Robert Ghrist
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Abstract

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 $S^3$ 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 $S^3$.

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John Etnyre, Robert Ghrist. 1999-06-24. Contact topology and hydrodynamics III: knotted flowlines. https://arxiv.org/abs/math-ph/9906021

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