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A characterization of 3D steady Euler flows using commuting zero-flux homologies
Part of
DANIEL PERALTA-SALAS, ANA RECHTMAN, FRANCISCO TORRES DE LIZAUR
Journal:

Ergodic Theory and Dynamical Systems / Volume 41 / Issue 7 / July 2021

Published online by Cambridge University Press:

18 March 2020, pp. 2166-2181

Print publication:

July 2021
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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 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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A characterization of 3D steady Euler flows using commuting zero-flux homologies