Stratified integrals and unknots in invisid flows
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2007-05-23 v1 几何拓扑
摘要
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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引用
@article{arxiv.math/9905009,
title = {Stratified integrals and unknots in invisid flows},
author = {John B. Etnyre and Robert W. Ghrist},
journal= {arXiv preprint arXiv:math/9905009},
year = {2007}
}