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Stratified integrals and unknots in invisid flows

John B. Etnyre·Robert W. Ghrist
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Abstract

We prove that any steady solution to the real analytic Euler equations on a Riemannian 3-sphere must possess a periodic orbit bounding an embedded disc. One key ingredient is an extension of Fomenko's work on the topology of integrable Hamiltonian systems to a degenerate case involving stratified integrals. The result on the Euler equations follows from this when combined with some contact-topological perspectives and a recent result of Hofer, Wyzsocki, and Zehnder.

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John B. Etnyre, Robert W. Ghrist. 1999-05-03. Stratified integrals and unknots in invisid flows. https://arxiv.org/abs/math/9905009

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