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.
\Bibitem{Koz11}
\by Valery V. Kozlov
\paper The Vlasov Kinetic Equation, Dynamics of Continuum and Turbulence
\jour Regul. Chaotic Dyn.
\yr 2011
\vol 16
\issue 6
\pages 602--622
\mathnet{http://mi.mathnet.ru/rcd459}
\crossref{https://doi.org/10.1134/S1560354711060049}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2864537}
\zmath{https://zbmath.org/?q=an:1257.37016}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2011RCD....16..602K}
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https://www.mathnet.ru/eng/rcd459
https://www.mathnet.ru/eng/rcd/v16/i6/p602
This publication is cited in the following 7 articles:
V. I. Bogachev, S. V. Shaposhnikov, “Nonlinear Fokker–Planck–Kolmogorov equations”, Russian Math. Surveys, 79:5 (2024), 751–805
Anatolij K. Prykarpatski, “Quantum Current Algebra in Action: Linearization, Integrability of Classical and Factorization of Quantum Nonlinear Dynamical Systems”, Universe, 8:5 (2022), 288
Ivankiv L.I., Prykarpatsky Ya.A., Samoilenko V.H., Prykarpatski A.K., “Quantum Current Algebra Symmetry and Description of Boltzmann Type Kinetic Equations in Statistical Physics”, Symmetry-Basel, 13:8 (2021), 1452
Prykarpatsky Yarema A, Kycia Radoslaw, Prykarpatski Anatolij K, “On the Bogolubov's chain of kinetic equations, the invariant subspaces and the corresponding Dirac type reduction”, Ann Math Phys, 2021, 074
A. L. Skubachevskii, Y. Tsuzuki, “Classical solutions of the Vlasov–Poisson equations with external magnetic field in a half-space”, Comput. Math. Math. Phys., 57:3 (2017), 541–557
A. L. Skubachevskii, “Vlasov–Poisson equations for a two-component plasma in a homogeneous magnetic field”, Russian Math. Surveys, 69:2 (2014), 291–330
A. R. Karimov, “Coupled electron and ion nonlinear oscillations in a collisionless plasma”, Physics of Plasmas, 20:5 (2013)
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