Geodesic
On uniqueness of the solution of the chain of moment equations corresponding to the three-dimensional Navier–Stokes system
Sbornik. Mathematics, Tome 62 (1989) no. 2, pp. 465-490 
A. V. Fursikov. On uniqueness of the solution of the chain of moment equations corresponding to the three-dimensional Navier–Stokes system. Sbornik. Mathematics, Tome 62 (1989) no. 2, pp. 465-490. http://geodesic.mathdoc.fr/item/SM_1989_62_2_a8/
@article{SM_1989_62_2_a8,
     author = {A. V. Fursikov},
     title = {On~uniqueness of the~solution of the~chain of~moment equations corresponding to the three-dimensional {Navier{\textendash}Stokes} system},
     journal = {Sbornik. Mathematics},
     pages = {465--490},
     year = {1989},
     volume = {62},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_62_2_a8/}
}
TY  - JOUR
AU  - A. V. Fursikov
TI  - On uniqueness of the solution of the chain of moment equations corresponding to the three-dimensional Navier–Stokes system
JO  - Sbornik. Mathematics
PY  - 1989
SP  - 465
EP  - 490
VL  - 62
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1989_62_2_a8/
LA  - en
ID  - SM_1989_62_2_a8
ER  - 
%0 Journal Article
%A A. V. Fursikov
%T On uniqueness of the solution of the chain of moment equations corresponding to the three-dimensional Navier–Stokes system
%J Sbornik. Mathematics
%D 1989
%P 465-490
%V 62
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1989_62_2_a8/
%G en
%F SM_1989_62_2_a8

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

A theorem is proved on the uniqueness of the solution of the Cauchy problem for the chain of equations for the spatial moments corresponding to smooth solutions of the three-dimensional Navier–Stokes system in the case of any Reynolds numbers. By means of the uniqueness theorem it is proved that any solution of the chain of moment equations belonging to an appropriate function space forms a positive-definite system of moments for any time $t>0$ if its initial value was positive definite. Bibliography: 11 titles.

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

[2] Vishik M. I., Fursikov A. V., Matematicheskie zadachi statisticheskoi gidromekhaniki, Nauka, M., 1980 | MR

[3] Vishik M. I., Fursikov A. V., “Analiticheskie pervye integraly nelineinykh parabolicheskikh v smysle I. G. Petrovskogo sistem differentsialnykh uravnenii i ikh prilozheniya”, UMN, 29:2 (1974), 123–153 | MR | Zbl

[4] Vishik M. I., “Analiticheskie resheniya uravneniya Khopfa, sootvetstvuyuschego kvazilineinym parabolicheskim uravneniyam ili sisteme Nave–Stoksa”, Zadachi mekhaniki i matematicheskoi fiziki, Nauka, M., 1976, 69–97

[5] Fursikov A. V., “Razreshimost “v tselom” tsepochki uravnenii dlya prostranstvennykh momentov, sootvetstvuyuschikh gladkim resheniyam trekhmernoi sistemy Nave–Stokca”, Wiss. Z.T.N. Leuna-Merserburg, 27 (1985), 613–622 | MR | Zbl

[6] Fursikov A. V., “Svoistva reshenii nekotorykh ekstremalnykh zadach, svyazannykh s sistemoi Nave–Stoksa”, Matem. sb., 118(160) (1982), 323–349 | MR | Zbl

[7] Lions Zh.-L., Mazhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971 | Zbl

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

[9] Fursikov A. V., “Zadachi upravleniya i teoremy, kasayuschiesya odnoznachnoi razreshimosti smeshannoi kraevoi zadachi dlya trekhmernykh sistem Nave–Stoksa i Eilera”, Matem. sb., 115(157) (1981), 281–307 | MR

[10] Fursikov A. V., “Analiticheskie funktsionaly i odnoznachnaya razreshimost kvazilineinykh dissipativnykh sistem pri pochti vsekh nachalnykh usloviyakh”, Tr. MMO, 49 (1986), 3–55 | MR

[11] Douady A., “Le probleme des modelus pour les sous-espaces analytiques compacts d'un espace analytique donné”, Ann. Inst. Fourier, 16:1 (1966), 1–95 | MR | Zbl