The topology of stationary curl parallel solutions of Euler’s equations
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We study the orbit structure of a vector fieldV defined on a three-dimensional Riemannian manifold which satisfiesV ^ curlV=0. Such a vector field represents the velocity of a stationary solution of Euler’s equation for a perfect fluid. In addition to several other results, we show that if the vector field admits a first integral, then each level set is toroidal and the induced flow on the level set is either periodic or conditionally periodic.
KeywordsVector Field Contact Structure Geodesic Flow Identity Bundle Riemannian Volume
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