Geodesic
Asymptotic solutions of Navier--Stokes equations and topological invariants of vector fields and Liouville foliations
Teoretičeskaâ i matematičeskaâ fizika, Tome 180 (2014) no. 2, pp. 245-263

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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.
Mots-clés : hydrodynamic equation, topology of Liouville foliations.
Keywords: localized vortex 
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     author = {V. P. Maslov and A. I. Shafarevich},
     title = {Asymptotic solutions of {Navier--Stokes} equations and topological invariants of vector fields and {Liouville} foliations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {245--263},
     publisher = {mathdoc},
     volume = {180},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_180_2_a6/}
}
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V. P. Maslov; A. I. Shafarevich. Asymptotic solutions of Navier--Stokes equations and topological invariants of vector fields and Liouville foliations. Teoretičeskaâ i matematičeskaâ fizika, Tome 180 (2014) no. 2, pp. 245-263. http://geodesic.mathdoc.fr/item/TMF_2014_180_2_a6/