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 Regul. Chaotic Dyn., 2001, Volume 6, Issue 3, Pages 235–251 (Mi rcd843)

Kinetics of Collisionless Continuous Medium

V. V. Kozlov

Department of Mechanics and Mathematics, Moscow State University, Vorob'ievy Gory, 119899, Moscow, Russia

Abstract: In this article we develop Poincaré ideas about a heat balance of ideal gas considered as a collisionless continuous medium. We obtain the theorems on diffusion in nondegenerate completely integrable systems. As a corollary we show that for any initial distribution the gas will be eventually irreversibly and uniformly distributed over all volume, although every particle during this process approaches arbitrarily close to the initial position indefinitely many times. However, such individual returnability is not uniform, which results in diffusion in a reversible and conservative system. Balancing of pressure and internal energy of ideal gas is proved, the formulas for limit values of these quantities are given and the classical law for ideal gas in a heat balance is deduced. It is shown that the increase of entropy of gas under the adiabatic extension follows from the law of motion of a collisionless continuous medium.

DOI: https://doi.org/10.1070/RD2001v006n03ABEH000175

Bibliographic databases:

MSC: 37H10, 70F45
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Citation: V. V. Kozlov, “Kinetics of Collisionless Continuous Medium”, Regul. Chaotic Dyn., 6:3 (2001), 235–251

Citation in format AMSBIB
\Bibitem{Koz01} \by V. V. Kozlov \paper Kinetics of Collisionless Continuous Medium \jour Regul. Chaotic Dyn. \yr 2001 \vol 6 \issue 3 \pages 235--251 \mathnet{http://mi.mathnet.ru/rcd843} \crossref{https://doi.org/10.1070/RD2001v006n03ABEH000175} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1860145} \zmath{https://zbmath.org/?q=an:1006.82011} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2001RCD.....6..235K} 

• http://mi.mathnet.ru/eng/rcd843
• http://mi.mathnet.ru/eng/rcd/v6/i3/p235

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

This publication is cited in the following articles:
1. V. V. Kozlov, D. V. Treschev, “Evolution of Measures in the Phase Space of Nonlinear Hamiltonian Systems”, Theoret. and Math. Phys., 136:3 (2003), 1325–1335
2. J. Math. Sci. (N. Y.), 128:2 (2005), 2791–2797
3. V. V. Kozlov, “Kineticheskoe uravnenie Vlasova, dinamika sploshnykh sred i turbulentnost”, Nelineinaya dinam., 6:3 (2010), 489–512
4. V. V. Kozlov, “Polynomial conservation laws for the Lorentz gas and the Boltzmann–Gibbs gas”, Russian Math. Surveys, 71:2 (2016), 253–290
5. A. I. Komech, E. A. Kopylova, “Attractors of nonlinear Hamiltonian partial differential equations”, Russian Math. Surveys, 75:1 (2020), 1–87