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arXiv · 1904.00960

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

Daniel Peralta-Salas·Ana Rechtman·Francisco Torres de Lizaur
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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.

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Daniel Peralta-Salas, Ana Rechtman, Francisco Torres de Lizaur. 2019-04-01. A characterization of 3D steady Euler flows using commuting zero-flux homologies. https://arxiv.org/abs/1904.00960

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