Showing papers on "Vector flow published in 1981"
TL;DR: In this paper, the authors studied the orbit structure of a vector field defined on a three-dimensional Riemannian manifold which satisfies the velocity of a stationary solution of Euler's equation for a perfect fluid.
Abstract: 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.