Geodesic
Renormalization group in the theory of fully developed turbulence. Problem of the infrared relevant corrections to the Navier–Stokes equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 1, pp. 47-63 
N. V. Antonov; S. V. Borisenok; V. I. Girina. Renormalization group in the theory of fully developed turbulence. Problem of the infrared relevant corrections to the Navier–Stokes equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 1, pp. 47-63. http://geodesic.mathdoc.fr/item/TMF_1996_107_1_a4/
@article{TMF_1996_107_1_a4,
     author = {N. V. Antonov and S. V. Borisenok and V. I. Girina},
     title = {Renormalization group in the theory of fully developed turbulence. {Problem} of the infrared relevant corrections to the {Navier{\textendash}Stokes} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {47--63},
     year = {1996},
     volume = {107},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_107_1_a4/}
}
TY  - JOUR
AU  - N. V. Antonov
AU  - S. V. Borisenok
AU  - V. I. Girina
TI  - Renormalization group in the theory of fully developed turbulence. Problem of the infrared relevant corrections to the Navier–Stokes equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1996
SP  - 47
EP  - 63
VL  - 107
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1996_107_1_a4/
LA  - ru
ID  - TMF_1996_107_1_a4
ER  - 
%0 Journal Article
%A N. V. Antonov
%A S. V. Borisenok
%A V. I. Girina
%T Renormalization group in the theory of fully developed turbulence. Problem of the infrared relevant corrections to the Navier–Stokes equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1996
%P 47-63
%V 107
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1996_107_1_a4/
%G ru
%F TMF_1996_107_1_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

Within the framework of the RG approach to the theory of fully developed turbulence we consider the problem of possible IR relevant corrections to the Navier–Stokes equation. We formulate an exact criterium of the “actual IR relevance” of the corrections. In accordance with this criterium we verify the IR relevance for certain classes of composite operators. All these operators turn out to be actually IR irrelevant for arbitrary values of the RG expansion parameter $\varepsilon$. This confirms the absence of the crossover and the possibility of extrapolation of the RG results (obtained for asymptotically small values of $\varepsilon$) to the physical range $\varepsilon>2$.

[1] Monin A. S., Yaglom A. M., Statisticheskaya gidromekhanika, T. 2, Nauka, M., 1967

[2] McComb W. D., The Physics of Fluid Turbulence, Clarendon, Oxford, 1990 | MR

[3] Zinn-Justin J., Quantum Field Theory and Critical Phenomena, Clarendon, Oxford, 1989 | MR

[4] De Dominicis C., Martin P. C., Phys. Rev., A29:1 (1979), 419–422 | DOI

[5] Yakhot V., Orszag S., J. Sci. Comp., 1:1 (1986), 3 | DOI | MR | Zbl

[6] McComb W. D., Phys. Rev., A46:8 (1992), 4797–4812 | DOI

[7] Ladyzhenskaya O. A., Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970 | MR

[8] Kuni F. M., Storonkin B. A., TMF, 14:2 (1973), 220–234 | MR

[9] Klimontovich Yu. L., Statisticheskaya fizika, Nauka, M., 1982 | MR

[10] Adzhemyan L. Ts., Vasilev A. N., Pismak Yu. M., TMF, 57:2 (1983), 268–281 | MR | Zbl

[11] Adzhemyan L. Ts., Antonov N. V., Vasilev A. N., ZhETF, 95:4 (1989), 1272–1288

[12] Adzhemyan L. Ts., Vasilev A. N., Gnatich M., TMF, 74:2 (1988), 180–191 | MR

[13] Antonov N. V., Vestnik SPbU. Ser. fiz. , khim., 1992, no. 4 (25), 6–11

[14] Adzhemyan L. Ts., Antonov N. V., Kim T. L., TMF, 100:3 (1994), 382–401 | MR | Zbl

[15] Vasilev A. N., Funktsionalnye metody v kvantovoi teorii polya i statistike, Izd-vo LGU, L., 1976

[16] Adzhemyan L. Ts., Vasilev A. N., Gnatich M., Pismak Yu. M., TMF, 78:3 (1989), 368–383 | MR

[17] Honkonen J., Nalimov M. Yu., Helsinki University Preprint HU-TFT-93-54, Helsinki, 1993