Application of the Kac equation to the modeling of turbulence
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 3, pp. 575-584 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The possibility of applying the Kac equation to the simulation of small-scale turbulence is explored. The hypothesis is substantiated that the formation of a flow regime similar to the actual turbulent one can be qualitatively described as based on the analysis of the properties of the Kac equation.
@article{ZVMMF_2010_50_3_a15,
     author = {O. M. Belotserkovskiǐ and N. N. Fimin and V. M. Chech\"etkin},
     title = {Application of the {Kac} equation to the modeling of turbulence},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {575--584},
     year = {2010},
     volume = {50},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_3_a15/}
}
TY  - JOUR
AU  - O. M. Belotserkovskiǐ
AU  - N. N. Fimin
AU  - V. M. Chechëtkin
TI  - Application of the Kac equation to the modeling of turbulence
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 575
EP  - 584
VL  - 50
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_3_a15/
LA  - ru
ID  - ZVMMF_2010_50_3_a15
ER  - 
%0 Journal Article
%A O. M. Belotserkovskiǐ
%A N. N. Fimin
%A V. M. Chechëtkin
%T Application of the Kac equation to the modeling of turbulence
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 575-584
%V 50
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_3_a15/
%G ru
%F ZVMMF_2010_50_3_a15
O. M. Belotserkovskiǐ; N. N. Fimin; V. M. Chechëtkin. Application of the Kac equation to the modeling of turbulence. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 3, pp. 575-584. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_3_a15/

[1] Kac M., “Foundations of kinetic theory”, Proc. Third Berkeley Symp. Math. Statist. and Probability (1954–1955), v. III, Univ. California Press, Berkeley–Los Angeles, 1956, 171–197 | MR

[2] Kats M., Veroyatnost i smezhnye voprosy v fizike, Mir, M., 1965 | Zbl

[3] Cornille H., “Nonlinear Kac model: spatially homogeneous solutions and the Tjon effect”, J. Statist. Phys., 39:1/2 (1985), 181–213 | DOI | MR

[4] Bobylev A. V., “Tochnye resheniya uravneniya Boltsmana”, Dokl. AN SSSR, 225:6 (1975), 1296–1299 | MR | Zbl

[5] Krook M., Wu T. T., “Formation of Maxwellian tails”, Phys. Rev. Letts., 36:19 (1976), 107–109 | DOI

[6] Struminskii B. B., Aerodinamika i molekulyarnaya gazovaya dinamika, Nauka, M., 1985

[7] Struminskii V. V., “Problemy ustoichivosti laminarnykh potokov i perekhoda v turbulentnye techeniya”, Turbulentnye techeniya, Tr. Vses. Simp. po probl. turbulentnosti techenii (Kiev, 16–21 iyunya 1967 g.), Nauka, M., 1970, 11–23

[8] McKean H. P. Jr., “Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas”, Arch. Ration. Mech. and Analys., 21 (1966), 343–367 | DOI | MR

[9] Kogan M. N., Dinamika razrezhennogo gaza. Kineticheskaya teoriya, Nauka, M., 1967

[10] Morita T., Mori H., Tokuyama M., “A scaling method for deriving kinetic equations from the BBGKY hierarchy”, J. Statist. Phys., 18 (1978), 137–153 | DOI | MR

[11] Klimontovich Yu. L., Statisticheskaya fizika, Nauka, M., 1982

[12] Lee P. S., Wu T.-Y., “Boltzmann equation with fluctuations”, Internat. J. Theor. Phys., 7:4 (1973), 267–276 | DOI | MR

[13] Koga T., Vvedenie v kineticheskuyu teoriyu stokhasticheskikh protsessov v gazakh, Nauka, M., 1983

[14] Gurov K. P., Osnovaniya kineticheskoi teorii, Nauka, M., 1966

[15] Birman M. Sh., Solomyak M. Z., Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, Izd-vo LGU, L., 1980 | MR

[16] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[17] Marsden J., McCracken M., Hopf bifurcation and its applications, Springer, New York, 1976 | MR

[18] Ize J., “Bifurcation theory for Fredholm operators”, Mem. Amer. Math. Soc., 7, no. 174, 1976, 1–125 | MR

[19] Ize J., “Obstruction theory and multiparameter Hopf bifurcation”, Trans. Amer. Math. Soc., 289 (1985), 757–792 | DOI | MR | Zbl