Theoretical and Mathematical Physics

, Volume 180, Issue 2, pp 967–982 | Cite as

Asymptotic solutions of Navier-Stokes equations and topological invariants of vector fields and Liouville foliations

  • V. P. MaslovEmail author
  • A. I. Shafarevich


We construct asymptotic solutions of the Navier-Stokes equations. Such solutions describe periodic systems of localized vortices and are related to topological invariants of divergence-free vector fields on two-dimensional cylinders or tori and to the Fomenko invariants of Liouville foliations. The equations describing the evolution of a vortex system are given on a graph that is a set of trajectories of the divergence-free field or a set of Liouville tori.


hydrodynamic equation localized vortex topology of Liouville foliations 


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© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Higher School of EconomicsMoscowRussia
  2. 2.Lomonosov Moscow State UniversityMoscowRussia

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