Regular and Chaotic Dynamics

, Volume 16, Issue 6, pp 602-622

The Vlasov kinetic equation, dynamics of continuum and turbulence

  • Valery V. KozlovAffiliated withV.A. Steklov Mathematical Institute, Russian Academy of Sciences Email author 

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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.


kinetic Vlasov’s equation Euler’s equation continuum turbulence

MSC2010 numbers

37A60 82B30 82C05