Geodesic
On correlation of two solution classes of Navier–Stokes equation
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 3, pp. 56-66 
V. B. Levenshtam. On correlation of two solution classes of Navier–Stokes equation. Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 3, pp. 56-66. http://geodesic.mathdoc.fr/item/VMJ_2010_12_3_a5/
@article{VMJ_2010_12_3_a5,
     author = {V. B. Levenshtam},
     title = {On correlation of two solution classes of {Navier{\textendash}Stokes} equation},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {56--66},
     year = {2010},
     volume = {12},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2010_12_3_a5/}
}
TY  - JOUR
AU  - V. B. Levenshtam
TI  - On correlation of two solution classes of Navier–Stokes equation
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2010
SP  - 56
EP  - 66
VL  - 12
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMJ_2010_12_3_a5/
LA  - ru
ID  - VMJ_2010_12_3_a5
ER  - 
%0 Journal Article
%A V. B. Levenshtam
%T On correlation of two solution classes of Navier–Stokes equation
%J Vladikavkazskij matematičeskij žurnal
%D 2010
%P 56-66
%V 12
%N 3
%U http://geodesic.mathdoc.fr/item/VMJ_2010_12_3_a5/
%G ru
%F VMJ_2010_12_3_a5

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

We consider an initial boundary value problem for Navier–Stokes equation with mass power polinomial depend on unknown (velocity). We introduce for it the definitions of solution and generalized solution and we derive the conditions, under with a generalized solution is a solution.

[1] Simonenko I. B., “Obosnovanie metoda usredneniya dlya zadachi konvektsii v pole bystro ostsilliruyuschikh sil i dlya drugikh parabolicheskikh uravnenii”, Mat. sb., 87(129):2 (1972), 236–253 | MR | Zbl

[2] Ladyzhenskaya O. A., Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970, 288 pp. | MR

[3] Levenshtam V. B., “Metod usredneniya v zadache konvektsii pri vysokochastotnykh naklonnykh vibratsiyakh”, Sib. mat. zhurn., 37:5 (1996), 1103–1116 | MR | Zbl

[4] Krasnoselskii M. A., Zabreiko P. P., Pustylnik E. I., Sobolevskii P. E., Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, M., 1966, 499 pp. | MR | Zbl

[5] Yudovich V. I., Metod linearizatsii v gidrodinamicheskoi teorii ustoichivosti, Izd-vo RGU, Rostov-na-Donu, 1984, 192 pp. | Zbl

[6] Simonenko I. B., Metod usredneniya v teorii nelineinykh uravnenii parabolicheskogo tipa s prilozheniem k zadacham gidrodinamicheskoi ustoichivosti, Izd-vo RGU, Rostov-na-Donu, 1989, 112 pp. | Zbl

[7] Levenshtam V. B., “Odno svoistvo proektora $\Pi$ gidrodinamiki”, Kompleksnyi analiz, differentsialnye i integralnye uravneniya, Elista, 1990, 89–96