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TMF, 2014, Volume 180, Number 2, Pages 245–263 (Mi tmf8653)  

This article is cited in 3 scientific papers (total in 3 papers)

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

V. P. Maslovab, A. I. Shafarevicha

a M. V. Lomonosov Moscow State University, Moscow, Russia
b National Research University "Higher School of Economics", Moscow, Russia

Abstract: 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.

Keywords: hydrodynamic equation, localized vortex, topology of Liouville foliations

DOI: https://doi.org/10.4213/tmf8653

Full text: PDF file (543 kB)
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English version:
Theoretical and Mathematical Physics, 2014, 180:2, 967–982

Bibliographic databases:

Received: 13.02.2014

Citation: V. P. Maslov, A. I. Shafarevich, “Asymptotic solutions of Navier–Stokes equations and topological invariants of vector fields and Liouville foliations”, TMF, 180:2 (2014), 245–263; Theoret. and Math. Phys., 180:2 (2014), 967–982

Citation in format AMSBIB
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\paper Asymptotic solutions of Navier--Stokes equations and topological invariants of vector fields and Liouville foliations
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  • https://doi.org/10.4213/tmf8653
  • http://mi.mathnet.ru/eng/tmf/v180/i2/p245

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. P. Maslov, A. I. Shafarevich, “Fomenko invariants in the asymptotic theory of the Navier–Stokes equations”, J. Math. Sci., 225:4 (2017), 666–680  mathnet  crossref  mathscinet  elib
    2. A. Izosimov, B. Khesin, M. Mousavi, “Coadjoint orbits of symplectic diffeomorphisms of surfaces and ideal hydrodynamics”, Ann. Inst. Fourier, 66:6 (2016), 2385–2433  crossref  mathscinet  zmath  isi  scopus
    3. V. P. Maslov, “A model of classical thermodynamics based on the partition theory of integers, Earth gravitation, and semiclassical asymptotics I”, Russ. J. Math. Phys., 24:3 (2017), 354–372  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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