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arXiv · 1210.6271

Existence of knotted vortex tubes in steady Euler flows

Alberto Enciso·Daniel Peralta-Salas
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Abstract

We prove the existence of knotted and linked thin vortex tubes for steady solutions to the incompressible Euler equation in R^3. More precisely, given a finite collection of (possibly linked and knotted) disjoint thin tubes in R^3, we show that they can be transformed with a C^m-small diffeomorphism into a set of vortex tubes of a Beltrami field that tends to zero at infinity. The structure of the vortex lines in the tubes is extremely rich, presenting a positive-measure set of invariant tori and infinitely many periodic vortex lines. The problem of the existence of steady knotted vortex tubes can be traced back to Lord Kelvin.

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Alberto Enciso, Daniel Peralta-Salas. 2014-10-23. Existence of knotted vortex tubes in steady Euler flows. https://arxiv.org/abs/1210.6271

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