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arXiv · 1402.6484

A note on the stationary Euler equations of hydrodynamics

K. Cieliebak·E. Volkov
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Abstract

This note concerns stationary solutions of the Euler equations for an ideal fluid on a closed 3-manifold. We prove that if the velocity field of such a solution has no zeroes and real analytic Bernoulli function, then it can be rescaled to the Reeb vector field of a stable Hamiltonian structure. In particular, such a vector field has a periodic orbit unless the 3-manifold is a torus bundle over the circle. We provide a counterexample showing that the correspondence breaks down without the real analyticity hypothesis.

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K. Cieliebak, E. Volkov. 2014-03-15. A note on the stationary Euler equations of hydrodynamics. https://doi.org/10.1017/etds.2015.50

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