A characterization of 3D steady Euler flows using commuting zero-flux homologies

Peralta-Salas, Daniel; Rechtman, Ana; Torres de Lizaur, Francisco

doi:10.1017/etds.2020.25

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A characterization of 3D steady Euler flows using commuting zero-flux homologies

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Torres de Lizaur, Francisco
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1017/etds.2020.25
(Publisher version)

https://doi.org/10.48550/arXiv.1904.00960
(Preprint)

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Peralta-Salas-Rechtman-Torres de Lizaur_A characterization of 3D steady Euler flows using commuting zero-flux homologies_2021.pdf
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Citation

Peralta-Salas, D., Rechtman, A., & Torres de Lizaur, F. (2021). A characterization of 3D steady Euler flows using commuting zero-flux homologies. Ergodic Theory and Dynamical Systems, 41(7), 2166-2181. doi:10.1017/etds.2020.25.

Cite as: https://hdl.handle.net/21.11116/0000-0008-B55F-2

Abstract

We characterize, using commuting zero-flux homologies, those
volume-preserving vector fields on a $3$-manifold that are steady solutions of
the Euler equations for some Riemannian metric. This result extends Sullivan's
homological characterization of geodesible flows in the volume-preserving case.
As an application, we show that the steady Euler flows cannot be constructed
using plugs (as in Wilson's or Kuperberg's constructions). Analogous results in
higher dimensions are also proved.