Hydrodynamic equations for microscopic phase densities

• Authors: Viktor Gerasimenko , Vyacheslav Shtyk , Anatoly Zagorodny
• Languages of publication: EN

Abstracts

EN

Evolution equations for marginal generalized microscopic phase densities are introduced. The evolution equations for average values of microscopic phase densities are derived and a solution of the initial-value problem for the hydrodynamic type hierarchy obtained is constructed.

Keywords

EN

microscopic phase density; observable; BBGKY hierarchy; dual BBGKY hierarchy; hydrodynamic equations

• Journal: Open Physics
• Year: 2011
• Volume: 9
• Issue: 1
• Pages: 71-77

Dates

published

1 - 2 - 2011

online

24 - 9 - 2010

Contributors

author

Viktor Gerasimenko

• Institute of Mathematics NAS of Ukraine, 3, Tereshchenkivs’ka str., Kyiv, 01601, Ukraine,

author

Vyacheslav Shtyk

• Bogolyubov Institute for Theoretical Physics NAS of Ukraine, 14-b, Metrolohichna str., Kyiv, 03680, Ukraine,

author

Anatoly Zagorodny

• Bogolyubov Institute for Theoretical Physics NAS of Ukraine, 14-b, Metrolohichna str., Kyiv, 03680, Ukraine,

References

• [1] Yu.L. Klimontovich, V.P. Silin, Zhurn. Exp. Teor. Fiz. 23, 151 (1952)
• [2] Yu.L. Klimontovich, Statistical Physics (Harwood Acad. Publ., London, 1986)
• [3] R. Balescu, Aspects of Anomalous Transport in Plasmas (Institute of Physics, Bristol, 2005) http://dx.doi.org/10.1201/9781420034684[Crossref]
• [4] Yu.L. Klimontovich, H. Wilhelmsson, I.P. Yakimenko, A.G. Zagorodny, Statistical Theory of Plasma-Molecular Systems (Moscow State Univ. Press, Moscow, 1990)
• [5] A.G. Sitenko, A.G. Zagorodny, Ukr. J. Phys. 45, 446 (2000)
• [6] A. Zagorodny, J. Weiland, Phys. Plasmas 16, 052308 (2009) http://dx.doi.org/10.1063/1.3125306[Crossref]
• [7] N.N. Bogolyubov, Problems of Dynamic Theory in Statistical Physics (FITTL, Moscow, 1946)
• [8] C. Cercignani, V.I. Gerasimenko, D.Ya. Petrina, Many-Particle Dynamics and Kinetic Equations (Kluwer, Amsterdam, 1997) http://dx.doi.org/10.1007/978-94-011-5558-8[Crossref]
• [9] G. Borgioli, V.I. Gerasimenko, Riv. Mat. Univ. Parma 4, 251 (2001)
• [10] D.Ya. Petrina, V.I. Gerasimenko, Uspekhi Mat. Nauk 45, 135 (1990)
• [11] V.I. Gerasimenko, T.V. Ryabukha, M.O. Stashenko, J. Phys. A: Math. Gen. 37, 9861 (2004) http://dx.doi.org/10.1088/0305-4470/37/42/002[Crossref]

Identifiers

DOI

10.2478/s11534-010-0033-9