Geodesic
Derivation of the Hydrodynamic Equations in the Framework of the Bogoliubov Functional Hypothesis
Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 3, pp. 501-512 Cet article a éte moissonné depuis la source Math-Net.Ru

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We generalize the Bogoliubov functional hypothesis to the case of multiparticle interaction depending on both the coordinates and momenta of particles. We illustrate this with the examples of two weakly relativistic models: the Darwin model in the theory of charged particles and the Fock model in the general theory of relativity. For these models, based on the chain of the BBGKY equations, we calculate weakly relativistic corrections to the classical transport coefficients and find the conditions under which there is no bijective relation between the parameters of the local equilibrium distribution and the hydrodynamic variables.
Keywords: Bogoliubov chain, weakly relativistic approximation
Mots-clés : hydrodynamic equations. 
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Yu. N. Orlov. Derivation of the Hydrodynamic Equations in the Framework of the Bogoliubov Functional Hypothesis. Teoretičeskaâ i matematičeskaâ fizika, Tome 134 (2003) no. 3, pp. 501-512. http://geodesic.mathdoc.fr/item/TMF_2003_134_3_a12/

[1] N. N. Bogolyubov, Problemy dinamicheskoi teorii v statisticheskoi fizike, GITTL, M.–L., 1946 | MR

[2] N. N. Bogolyubov, Sb. tr. In-ta matematiki AN USSR, 1948, no. 10, 41 | MR

[3] R. P. Gaida, EChAYa, 13:2 (1982), 427

[4] Yu. N. Orlov, I. P. Pavlotsky, Physica A, 151 (1988), 318 | DOI | Zbl

[5] V. A. Fok, Teoriya prostranstva, vremeni i tyagoteniya, Fizmatlit, M., 1961

[6] S. Chepmen, T. Kouling, Matematicheskaya teoriya neodnorodnykh gazov, IL, M., 1960 | MR

[7] Yu. N. Orlov, I. P. Pavlotsky, Physica A, 184 (1992), 558 | DOI

[8] Yu. N. Orlov, Ravnovesnye funktsii raspredeleniya v postgalileevom priblizhenii, Preprint IPM im. M. V. Keldysha RAN No 23, IPM im. M. V. Keldysha, M., 1992

[9] S. de Groot, V. van Leuven, Kh. van Vert, Relyativistskaya kineticheskaya teoriya, Mir, M., 1983 | MR

[10] Yu. N. Orlov, Uravneniya gidrodinamiki slaborelyativistskoi plazmy, Preprint IPM im. M. V. Keldysha RAN No 73, IPM im. M. V. Keldysha, M., 1995

[11] Yu. N. Orlov, Vyvod uravnenii gidrodinamiki, Preprint IPM im. M. V. Keldysha AN SSSR No 36, IPM im. M. V. Keldysha, M., 1989

[12] I. P. Pavlotskii, Vvedenie v slaborelyativistskuyu statisticheskuyu mekhaniku, Nauka, M., 1987

[13] C. G. Darwin, Phil. Mag., 39 (1920), 357 | DOI

[14] Yu. N. Orlov, I. P. Pavlotskii, DAN SSSR, 304:2 (1989), 329

[15] Yu. N. Orlov, I. P. Pavlotskii, Matem. model., 1:12 (1989), 31 | MR