Contact topology and hydrodynamics III: knotted flowlines

Details Contact topology and hydrodynamics III: knotted flowlines Contact topology and hydrodynamics III: knotted flowlines

1999-06-24

arxiv.org/abs/math-ph/9906021v1

Physics

Mathematical Physics

17 pages, 5 figures

Scientific paper

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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