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Regular version of the site

Article

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

Mathematical notes. 2012. Vol. 91. No. 2. P. 207-216.
Maslov V., Шафаревич А. И.

We construct asymptotic solutions of the Navier-Stokes equations describing  periodic systems of vortex filaments 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 such a structure are defined on a graph which is the set of trajectories of a divergence-free field.