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Asymptotic solutions of the Navier-Stokes equations and systems of stretched vortices filling a three-dimensional volume

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Abstract

We construct asymptotic solutions of the Navier-Stokes equations describing periodic systems of vortex filaments entirely filling a three-dimensional volume. Such solutions are related to certain topological invariants of divergence-free vector fields on the two-dimensional torus. The equations describing the evolution of of such a structure are defined on a graph which is the set of trajectories of a divergence-free field.

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  1. Moscow State University, Moscow, Russia

    V. P. Maslov & A. I. Shafarevich

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  2. A. I. Shafarevich
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Maslov, V.P., Shafarevich, A.I. Asymptotic solutions of the Navier-Stokes equations and systems of stretched vortices filling a three-dimensional volume. Math Notes 91, 207–216 (2012). https://doi.org/10.1134/S0001434612010221

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