Geodesic
Inverse problems for stationary Navier–Stokes systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 3, pp. 519-528
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An inverse problem for a nonlinear equation in a Hilbert space is considered in which the right-hand side that is a linear combination of given functionals is found from given values of these functionals on the solution. Sufficient conditions for the existence of a solution are established, and the solution set is shown to be homeomorphic to a finite-dimensional compact set. A boundary inverse problem for the three-dimensional thermal convection equations for a viscous incompressible fluid and an inverse magnetohydrodynamics problem are considered as applications. 
@article{ZVMMF_2014_54_3_a14,
     author = {A. Yu. Chebotarev},
     title = {Inverse problems for stationary {Navier{\textendash}Stokes} systems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {519--528},
     year = {2014},
     volume = {54},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_3_a14/}
}
TY  - JOUR
AU  - A. Yu. Chebotarev
TI  - Inverse problems for stationary Navier–Stokes systems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2014
SP  - 519
EP  - 528
VL  - 54
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_3_a14/
LA  - ru
ID  - ZVMMF_2014_54_3_a14
ER  - 
%0 Journal Article
%A A. Yu. Chebotarev
%T Inverse problems for stationary Navier–Stokes systems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2014
%P 519-528
%V 54
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_3_a14/
%G ru
%F ZVMMF_2014_54_3_a14
A. Yu. Chebotarev. Inverse problems for stationary Navier–Stokes systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 3, pp. 519-528. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_3_a14/

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

[2] Temam R., Uravneniya Nave–Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981 | MR | Zbl

[3] Temam R., Navier–Stokes equations and nonlinear functional analysis, SIAM, 1995 | MR

[4] Sermange M., Temam R., “Some mathematical questions related to the MHD equations”, Comm. on Pure and Appl. Math., 36 (1983), 635–664 | DOI | MR | Zbl

[5] Chebotarev A. Yu., “Konechnomernaya upravlyaemost dlya sistem tipa Nave–Stoksa”, Differen. ur-niya, 45:10 (2010), 1495–1503 | MR

[6] Prilepko A. I., Vasin I. A., “Razreshimost trekhmernoi obratnoi zadachi dlya nelineinykh uravnenii Nave–Stoksa”, Zh. vychisl. matem. i matem. fiz., 29:2 (1990), 1540–1552 | MR

[7] Prilepko A. I., Vasin I. A., “Postanovka i issledovanie nelineinoi obratnoi zadachi upravleniya dvizheniem vyazkoi neszhimaemoi zhidkosti”, Differents. ur-niya, 28:4 (1992), 697–705 | MR | Zbl

[8] Chebotarev A. Yu., “Obratnye zadachi dlya nelineinykh evolyutsionnykh uravnenii tipa Nave–Stoksa”, Differents. ur-niya, 31:3 (1995), 517–524 | MR | Zbl

[9] Chebotarev A. Yu., “Subdifferential inverse problems for stationary systems of Navier–Stokes type”, J. Inverse and Ill Posed Problems, 3:4 (1995), 268–279 | DOI | MR

[10] Chebotarev A. Yu., “Subdifferential inverse problems for evolution Navier–Stokes systems”, J. Inverse and Ill Posed Problems, 8:3 (2000), 275–287 | DOI | MR

[11] Choulli M., Imanuvilov O. Yu., Yamamoto M., Invese source problem for the Navier–Stokes equations, Preprint of UTMS, 2006-3

[12] Fan J., Nakamura G., “Well-posedness of an inverse problem of Navier–Stokes equations with the final overdetermination”, J. Inverse and Ill-Posed Problems, 17:6 (2009), 565–584 | DOI | MR | Zbl

[13] Fan J., Di Cristo M., Jiang Yu., Nakamura G., “Inverse viscosity problem for the Navier–Stokes equation”, J. Math. Anal. Appl., 365 (2010), 750–757 | DOI | MR | Zbl

[14] Chebotarev A. Yu., “Opredelenie pravoi chasti sistemy Nave-Stoksa i obratnye zadachi dlya uravnenii teplovoi konvektsii”, Zh. vychisl. matem. i matem. fiz., 51:12 (2011), 2279–2287 | MR | Zbl

[15] Chebotarev A. Yu., “Obratnaya zadacha dlya sistem Nave–Stoksa s konechnomernym pereopredeleniem”, Differents. ur-niya, 48:8 (2012), 1166–1173 | Zbl

[16] Zarubin A. G., “Zadacha o nestatsionarnoi svobodnoi konvektsii”, Zh. vychisl. matem. i matem. fiz., 8:6 (1968), 1378–1383 | MR | Zbl

[17] Chebotarev A. Yu., “Variatsionnye neravenstva dlya operatora tipa Nave–Stoksa i odnostoronnie zadachi dlya uravnenii vyazkoi teploprovodnoi zhidkosti”, Matem. zametki, 70:2 (2001), 296–307 | DOI | MR | Zbl

[18] Chebotarev A. Yu., “Stabilizatsiya storonnimi tokami ravnovesnykh MGD konfiguratsii”, Zh. vychisl. matem. i matem. fiz., 52:12 (2012), 2238–2246 | MR | Zbl