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Steady Euler Flows on the 3-Sphere and Other Sasakian 3-Manifolds

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Abstract

We present new steady Euler solutions on the (round) 3-sphere, that bifurcate from an ansatz proposed in [11], showing that these previously known solutions are not isolated. We also extend this ansatz to any Sasakian 3-manifold, such as the Heisenberg group and \(SL(2, \mathbb {R})\).

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Notes

  1. Here by pull-back of a vector field X through some mapping \(\varphi \) we mean \((\varphi ^* X^\flat )^\sharp \) and the pull-back of a function f on the codomain is \(f\circ \varphi \) defined on the domain of \(\varphi \).

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  1. Faculty of Physics, University of Bucharest, P.O. Box Mg-11, 077125, Bucharest-Măgurele, Romania

    Radu Slobodeanu

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  1. Radu Slobodeanu
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Correspondence to Radu Slobodeanu.

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Slobodeanu, R. Steady Euler Flows on the 3-Sphere and Other Sasakian 3-Manifolds. Qual. Theory Dyn. Syst. 20, 5 (2021). https://doi.org/10.1007/s12346-020-00440-y

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