Geodesic
On the solvability of the second boundary value problem for the Stokes system
Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 3, pp. 26-39

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

We consider the second boundary value problem for the Stokes system in the half-space. We prove the theorem on the existence of a solution in Sobolev spaces.
Keywords: elliptic system, boundary value problem, Stokes system, Sobolev space. 
L. N. Bondar. On the solvability of the second boundary value problem for the Stokes system. Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 3, pp. 26-39. http://geodesic.mathdoc.fr/item/SJIM_2014_17_3_a2/
@article{SJIM_2014_17_3_a2,
     author = {L. N. Bondar},
     title = {On the solvability of the second boundary value problem for the {Stokes} system},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {26--39},
     year = {2014},
     volume = {17},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2014_17_3_a2/}
}
TY  - JOUR
AU  - L. N. Bondar
TI  - On the solvability of the second boundary value problem for the Stokes system
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2014
SP  - 26
EP  - 39
VL  - 17
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SJIM_2014_17_3_a2/
LA  - ru
ID  - SJIM_2014_17_3_a2
ER  - 
%0 Journal Article
%A L. N. Bondar
%T On the solvability of the second boundary value problem for the Stokes system
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2014
%P 26-39
%V 17
%N 3
%U http://geodesic.mathdoc.fr/item/SJIM_2014_17_3_a2/
%G ru
%F SJIM_2014_17_3_a2

[1] Solonnikov V. A., “Otsenki resheniya odnoi nachalno-kraevoi zadachi dlya lineinoi nestatsionarnoi sistemy uravnenii Nave–Stoksa”, Zap. nauch. sem. LOMI, 59, 1976, 178–254 | MR | Zbl

[2] Demidenko G. V., “O neobkhodimykh usloviyakh korrektnosti zadachi Koshi dlya linearizovannoi sistemy Nave–Stoksa”, Sib. mat. zhurn., 29:3 (1988), 186–189 | MR | Zbl

[3] Aleksandrovskii I. L., “Uslovie razreshimosti pervoi kraevoi zadachi dlya linearizovannoi sistemy Nave–Stoksa”, Sib. mat. zhurn., 39:6 (1998), 1211–1224 | MR | Zbl

[4] Demidenko G. V., “O korrektnoi razreshimosti kraevykh zadachv poluprostranstve dlya kvaziellipticheskikh uravnenii”, Sib. mat. zhurn., 29:4 (1988), 54–67 | MR | Zbl

[5] Demidenko G. V., “Integralnye operatory, opredelyaemye kvaziellipticheskimi uravneniyami. II”, Sib. mat. zhurn., 35:1 (1994), 41–65 | MR | Zbl

[6] Demidenko G. V., “On solvability of boundary value problems for quasi-elliptic systems in $R^n_+$”, J. Anal. Appl., 4:1 (2006), 1–11 | DOI | MR | Zbl

[7] Uspenskii S. V., “O predstavlenii funktsii, opredelyaemykh odnim klassom gipoellipticheskikh operatorov”, Tr. Mat. in-ta im. V. A. Steklova AN SSSR, 117, 1972, 292–299 | MR | Zbl

[8] Demidenko G. V., Uspenskii S. V., Uravneniya i sistemy, ne razreshennye otnositelno starshei proizvodnoi, Nauch. kniga, Novosibirsk, 1998 | MR | Zbl

[9] Lizorkin P. I., “Obobschennoe liuvillevskoe differentsirovanie i metod multiplikatorov v teorii vlozhenii klassov differentsiruemykh funktsii”, Tr. Mat. in-ta im. V. A. Steklova AN SSSR, 105, 1969, 89–167 | MR | Zbl

[10] Demidenko G. V., “O kvaziellipticheskikh operatorakh v $R_n$”, Sib. mat. zhurn., 39:5 (1998), 1028–1037 | MR | Zbl

[11] Demidenko G. V., “Izomorfnye svoistva odnogo klassa differentsialnykh operatorov i ikh prilozheniya”, Sib. mat. zhurn., 42:5 (2001), 1036–1056 | MR | Zbl

[12] Demidenko G. V., “Kvaziellipticheskie operatory i uravneniya sobolevskogo tipa. II”, Sib. mat. zhurn., 50:5 (2009), 1060–1069 | MR | Zbl