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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 180, Number 2, Pages 245–263
DOI: https://doi.org/10.4213/tmf8653 (Mi tmf8653) 		 
This article is cited in 8 scientific papers (total in 8 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
Full-text PDF (543 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf8653
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.
Received: 13.02.2014
English version:
Theoretical and Mathematical Physics, 2014, Volume 180, Issue 2, Pages 967–982
DOI: https://doi.org/10.1007/s11232-014-0192-8
Bibliographic databases:
Document Type: Article
Language: Russian
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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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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