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

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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. Maslov^ab, A. I. Shafarevich^a

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

https://www.mathnet.ru/eng/tmf/v180/i2/p245

This publication is cited in the following 8 articles:

R. K. Gaydukov, V. G. Danilov, “Asymptotic Solutions of Flow Problems with Boundary Layer of Double-Deck Structures”, Math. Notes, 112:4 (2022), 523–532
E. Yu. Prosviryakov, “Exact solutions to generalized plane Beltrami–Trkal and Ballabh flows”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 24:2 (2020), 319–330
S. V. Zakharov, “Singular points and asymptotics in the singular Cauchy problem for the parabolic equation with a small parameter”, Comput. Math. Math. Phys., 60:5 (2020), 821–832
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
A. Izosimov, B. Khesin, M. Mousavi, “Coadjoint orbits of symplectic diffeomorphisms of surfaces and ideal hydrodynamics”, Ann. Inst. Fourier, 66:6 (2016), 2385–2433
V. P. Maslov, “On the Role of the Gravity of Earth in a Quasistatic Process”, Math. Notes, 99:3 (2016), 477–479
V. P. Maslov, “New Approach to Classical Thermodynamics”, Math. Notes, 100:1 (2016), 154–185
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

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

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Abstract page:	1219
Full-text PDF :	289
References:	130
First page:	89

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