V. V. Kozlov, “The Vlasov kinetic equation, dynamics of continuum and turbulence”, Nelin. Dinam., 6:3 (2010), 489

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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]

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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2010, Volume 6, Number 3, Pages 489–512 (Mi nd20)

This article is cited in 6 scientific papers (total in 6 papers)

The Vlasov kinetic equation, dynamics of continuum and turbulence

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (276 kB) Citations (6)

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Abstract: We consider a continuum of interacting particles whose evolution is governed by the Vlasov kinetic equation. An infinite sequence of equations of motion for this medium (in the Eulerian description) is derived and its general properties are explored. An important example is a collisionless gas, which exhibits irreversible behavior. Though individual particles interact via a potential, the dynamics of the continuum bears dissipative features. Applicability of the Vlasov equations to the modeling of small-scale turbulence is discussed.

Keywords: kinetic Vlasov's equation, Euler's equation, continuum, turbulence.

Received: 20.07.2010

Bibliographic databases:

Document Type: Article

UDC: 517

MSC: 37A60, 82B30, 82C05

Language: Russian

Citation: V. V. Kozlov, “The Vlasov kinetic equation, dynamics of continuum and turbulence”, Nelin. Dinam., 6:3 (2010), 489–512

Citation in format AMSBIB

\Bibitem{Koz10}

\by V.~V.~Kozlov

\paper The Vlasov kinetic equation, dynamics of continuum and turbulence

\jour Nelin. Dinam.

\yr 2010

\vol 6

\issue 3

\pages 489--512

\mathnet{http://mi.mathnet.ru/nd20}

\elib{https://elibrary.ru/item.asp?id=15223023}

Linking options:

https://www.mathnet.ru/eng/nd20

https://www.mathnet.ru/eng/nd/v6/i3/p489

This publication is cited in the following 6 articles:

V. I. Bogachev, S. V. Shaposhnikov, “Nonlinear Fokker–Planck–Kolmogorov equations”, Russian Math. Surveys, 79:5 (2024), 751–805
V. V. Vedenyapin, “Uravnenie Vlasova–Maksvella–Einshteina”, Preprinty IPM im. M. V. Keldysha, 2018, 188, 20 pp.
V. V. Vedenyapin, M. A. Negmatov, N. N. Fimin, “Vlasov-type and Liouville-type equations, their microscopic, energetic and hydrodynamical consequences”, Izv. Math., 81:3 (2017), 505–541
Manita O.A., Romanov M.S., Shaposhnikov S.V., “on Uniqueness of Solutions To Nonlinear Fokker-Planek-Kolmogorov Equations”, Nonlinear Anal.-Theory Methods Appl., 128 (2015), 199–226
Manita O.A., Romanov M.S., Shaposhnikov S.V., “Uniqueness of Probability Solutions To Nonlinear Fokker-Planck-Kolmogorov Equation”, Dokl. Math., 91:2 (2015), 142–146
O. A. Manita, S. V. Shaposhnikov, “Nonlinear parabolic equations for measures”, St. Petersburg Math. J., 25:1 (2014), 43–62

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

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