Geodesic
Eigenfunction method of collision Boltzmann integral in kinetic theory of long wave fluctuations
Teoretičeskaâ i matematičeskaâ fizika, Tome 106 (1996) no. 3, pp. 469-488 Cet article a éte moissonné depuis la source Math-Net.Ru

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Linearized general equations of long wave fluctuation kinetics are solved (by utilizing eigenfunctions and eigenvalues of the linearized collision Boltzmann integral) in the asymptotic field $t \gg \tau_{r}$ ($\tau_{r}$ is a relaxation time). A general form of linearized equations of fluctuation hydrodynamics is obtained. Effective initial conditions for the fluctuation hydrodynamics equations are derived for the case when arbitrary order fluctuations are absent at the initial instant. A time asymptotics of the one – particle distribution function is found in the fluctuation hydrodynamic evolution regime when the fluctations of hydrodynamic quantities play an essential role. It is compared with the early obtained results of the “long hydrodynamic tails” theory. 
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     author = {S. V. Peletminskii and Yu. V. Slusarenko},
     title = {Eigenfunction method of collision {Boltzmann} integral in kinetic theory of long wave fluctuations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {469--488},
     year = {1996},
     volume = {106},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_106_3_a9/}
}
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S. V. Peletminskii; Yu. V. Slusarenko. Eigenfunction method of collision Boltzmann integral in kinetic theory of long wave fluctuations. Teoretičeskaâ i matematičeskaâ fizika, Tome 106 (1996) no. 3, pp. 469-488. http://geodesic.mathdoc.fr/item/TMF_1996_106_3_a9/

[1] Monin A. S., Yaglom A. M., Statisticheskaya gidromekhanika, Ch. 1, 1965; Ч. 2, Наука, М., 1967

[2] Landau L. D., Lifshits E. M., Teoreticheskaya fizika. T. VI. Gidrodinamika, Nauka, M., 1986 | MR

[3] Klimontovich Yu. L., Turbulentnoe dvizhenie i struktura khaosa, Nauka, M., 1990 | MR

[4] Alder B. I., Wainwright T. E., Phys. Rev., A1 (1970), 18 | DOI

[5] Dorfman J. R., Cohen E. G. D., Phys. Rev., A6 (1972), 776 | DOI

[6] Zubarev D. N., Khazanov A. M., TMF, 3:1 (1978), 69 | MR

[7] Peletminskii S. V., Plokhov S. S., Prikhodko V. I., TMF, 46:2 (1981), 263 | MR

[8] Ernst M. H., Dorfman J. R., J. Stat. Phys., 12:4 (1975), 311 | DOI | MR | Zbl

[9] Peletminskii S. V., Sokolovskii A. I., UFZh, 37:11 (1992), 1702

[10] Novikov E. A., ZhETF, 47 (1964), 1919

[11] Moiseev S. S., Tur A. V., Yanovskii V. V., ZhETF, 71 (1976), 1063

[12] Peletminskii S. V., Slyusarenko Yu. V., UFZh, 39:1 (1994), 112 | MR

[13] Morozov V. G., Physica, A 110 (1982), 201 | DOI | Zbl

[14] Slyusarenko Yu. V., UFZh, 28:5 (1983), 774

[15] Zubarev D. N., Morozov V. G., Physica, A120:3 (1983), 411 | DOI | MR

[16] Oppenheim I., Sokolovsky A. I., Tseitlin M. Yu., Physica, A136 (1986), 1 | DOI | MR | Zbl

[17] Klimontovich Yu. L., Kineticheskaya teoriya neidealnogo gaza i neidealnoi plazmy, Nauka, M., 1975 | MR

[18] Klimontovich Yu. L., TMF, 9:1 (1971), 109

[19] Kogan Sh. M., TMF, 10:1 (1972), 143

[20] Grechannyi O. A., Stokhasticheskaya teoriya neobratimykh protsessov, Naukova dumka, Kiev, 1989 | MR

[21] Peletminsky S. V., Slusarenko Yu. V., Physica, A210:1, 2 (1994), 165 | DOI

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

[23] Ivanchenko E. A., Krasilnikov V. V., Slyusarenko Yu. V., Metod sobstvennykh funktsii linearizovannogo operatora stolknovenii i gidrodinamicheskii mekhanizm zatukhaniya vtorichnykh voln, Preprint 81-48 KhFTI AN USSR, Kharkov, 1981

[24] Osager L., Phys. Rev., 37 (1931), 405 ; 38, 2265 | DOI | DOI

[25] Pao Y., Commun. Pure Appl. Math., 27 (1974), 407 | DOI | MR | Zbl

[26] Akhiezer A. I., Peletminskii S. V., Metody statisticheskoi fiziki, Nauka, M., 1977 | MR