Geodesic
Uniqueness classes for a non-stationary system of Stokes equations in unbounded domains
Sbornik. Mathematics, Tome 187 (1996) no. 3, pp. 315-333 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A problem for a non-stationary system of Stokes equations in unbounded domains with adhesion condition at boundary is considered. For domains with non-compact boundaries uniqueness classes for this problem are selected depending on the geometry of the domain. They are formulated in terms of bounds on the ‘growth’ of the velocity as $|x|\to \infty$. 
@article{SM_1996_187_3_a0,
     author = {N. M. Asadullin and F. Kh. Mukminov},
     title = {Uniqueness classes for a~non-stationary system of {Stokes} equations in unbounded domains},
     journal = {Sbornik. Mathematics},
     pages = {315--333},
     year = {1996},
     volume = {187},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_3_a0/}
}
TY  - JOUR
AU  - N. M. Asadullin
AU  - F. Kh. Mukminov
TI  - Uniqueness classes for a non-stationary system of Stokes equations in unbounded domains
JO  - Sbornik. Mathematics
PY  - 1996
SP  - 315
EP  - 333
VL  - 187
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1996_187_3_a0/
LA  - en
ID  - SM_1996_187_3_a0
ER  - 
%0 Journal Article
%A N. M. Asadullin
%A F. Kh. Mukminov
%T Uniqueness classes for a non-stationary system of Stokes equations in unbounded domains
%J Sbornik. Mathematics
%D 1996
%P 315-333
%V 187
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1996_187_3_a0/
%G en
%F SM_1996_187_3_a0
N. M. Asadullin; F. Kh. Mukminov. Uniqueness classes for a non-stationary system of Stokes equations in unbounded domains. Sbornik. Mathematics, Tome 187 (1996) no. 3, pp. 315-333. http://geodesic.mathdoc.fr/item/SM_1996_187_3_a0/

[1] Bogovskii M. E., “Reshenie nekotorykh zadach vektornogo analiza, svyazannykh s operatorami $\operatorname{Div}$ i $\operatorname{grad}$”, Trudy seminara S. L. Soboleva, no. 1, Nauka, Novosibirsk, 1980, 5–40 | MR

[2] Guschin A. K., “O ravnomernoi stabilizatsii reshenii vtoroi smeshannoi zadachi dlya parabolicheskogo uravneniya”, Matem. sb., 119 (1982), 451–508 | MR

[3] Heywood J. G., “On uniqueness questions in the theory of viscous flow”, Acta Math., 138 (1976), 61–102 | DOI | MR

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

[5] Ladyzhenskaya O. A, Solonnikov V. A., “O nachalno-kraevoi zadache dlya linearizovannoi sistemy uravnenii Nave–Stoksa v oblastyakh s nekompaktnymi granitsami”, Tr. MIAN, 159, Nauka, M., 1983, 37–40 | MR | Zbl

[6] Mukminov F. Kh., “O ravnomernoi stabilizatsii reshenii vneshnei zadachi dlya uravnenii Nave–Stoksa”, Matem. sb., 185:3 (1994), 41–68 | MR | Zbl

[7] Oleinik O. A., Iosifyan G. A., “Analog printsipa Sen-Venana i edinstvennost reshenii kraevykh zadach v neogranichennykh oblastyakh dlya parabolicheskikh uravnenii”, UMN, 31 (1976), 142–166 | MR | Zbl

[8] Tacklind S., “Sur les classes quasianalytiques des solutions des equations aux derivees partielles du type parabolique”, Nova Acta Reg. Soc. Sci. Upsaliensis. Ser. 4, 10:3 (1936)

[9] Borchers W., Sohr H., “The equations $\operatorname{Div}\mathbf u=f$ and $\operatorname{rot}\mathbf v=g$ with homogeneous Dirichlet boundary condition”, Hokkaido Math. J., 19 (1990), 67–87 | MR | Zbl