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

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...

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Bibliographic Details
Published in:arXiv.org 2020-02
Main Authors: Peralta-Salas, Daniel, Rechtman, Ana, Torres de Lizaur, Francisco
Format: Article
Language:English
Subjects:
Euler-Lagrange equation
Fields (mathematics)
Homology
Plugs
Three dimensional flow
Online Access:Get full text
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Summary: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.
ISSN:2331-8422