Contact topology and hydrodynamics III: knotted flowlines

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 $S^3$.

17 pages, 5 figures

Cited by in corpus (6)

• Typical field lines of Beltrami flows and boundary field line behaviour of Beltrami flows on simply connected, compact, smooth manifolds with boundary
• Stratified integrals and unknots in invisid flows
• Bi-invariant metric on volume-preserving diffeomorphisms group of a three-dimensional manifold
• Zero set structure of real analytic Beltrami fields
• Bi-invariant metric on contact diffeomorphisms group
• Existence and structure of symmetric Beltrami flows on compact $3$-manifolds