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Nelin. Dinam., 2010, Volume 6, Number 3, Pages 489–512 (Mi nd20)  

This article is cited in 5 scientific papers (total in 5 papers)

The Vlasov kinetic equation, dynamics of continuum and turbulence

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences

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.

Full text: PDF file (276 kB)
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UDC: 517
MSC: 37A60, 82B30, 82C05
Received: 20.07.2010

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{http://elibrary.ru/item.asp?id=15223023}


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    This publication is cited in the following articles:
    1. O. A. Manita, S. V. Shaposhnikov, “Nonlinear parabolic equations for measures”, St. Petersburg Math. J., 25:1 (2014), 43–62  mathnet  crossref  mathscinet  zmath  isi  elib
    2. 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  crossref  mathscinet  zmath  isi  scopus
    3. 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  crossref  mathscinet  zmath  isi  elib  scopus
    4. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. V. V. Vedenyapin, “Uravnenie Vlasova–Maksvella–Einshteina”, Preprinty IPM im. M. V. Keldysha, 2018, 188, 20 pp.  mathnet  crossref
  • Нелинейная динамика
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