Geodesic
Optimal Boundary Control of Steady-State Flow of a Viscous Inhomogeneous Incompressible Fluid
Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 666-678.

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We study the problem of optimal boundary control of two-dimensional steady-state flow of a viscous inhomogeneous incompressible fluid. The role of control is played by the values of the velocity on a part of the boundary of the domain considered. On the remaining part of the boundary, the vector of flow velocity and the fluid density are given. We seek the fluid density as a scalar function (determined by the initial data) of the stream function, study the solvability of the problem, and obtain necessary optimality conditions. 
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     author = {A. A. Illarionov},
     title = {Optimal {Boundary} {Control} of {Steady-State} {Flow} of a {Viscous} {Inhomogeneous} {Incompressible} {Fluid}},
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A. A. Illarionov. Optimal Boundary Control of Steady-State Flow of a Viscous Inhomogeneous Incompressible Fluid. Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 666-678. http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a2/

[1] Frolov N. N., “O razreshimosti kraevoi zadachi dvizheniya neodnorodnoi zhidkosti”, Matem. zametki, 53:6 (1993), 130–140 | MR | Zbl

[2] Frolov N. N., “Kraevaya zadacha, opisyvayuschaya dvizhenie neodnorodnoi zhidkosti”, Sib. matem. zh., 37:2 (1996), 433–451 | MR | Zbl

[3] Chebotarev A. Yu., “Statsionarnye variatsionnye neravenstva v modeli neodnorodnoi zhidkosti”, Sib. matem. zh., 38:5 (1997), 1185–1193 | MR

[4] Fursikov A. V., “Svoistva reshenii nekotorykh ekstremalnykh zadach, svyazannykh s sistemoi Nave–Stoksa”, Matem. sb., 118 (180):3 (7) (1982), 323–349 | MR | Zbl

[5] Fursikov A. V., “Zadachi upravleniya i teoremy, kasayuschiesya odnoznachnoi razreshimosti smeshannoi kraevoi zadachi dlya trekhmernykh uravnenii Nave–Stoksa”, Matem. sb., 115:2 (1981), 281–306 | MR | Zbl

[6] Lions Zh.-L., Upravlenie singulyarnymi raspredelennymi sistemami., Nauka, M., 1987

[7] Gunzburger M. D., Hou L., Svobodny T. P., “Boundary velocity control of incompressible flow with application to viscous drag reduction”, SIAM J. Contr. Optim., 30:1 (1992), 167–182 | DOI | MR

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

[9] Trenogin V. A., Funktsionalnyi analiz, Nauka, M., 1980 | Zbl

[10] Conca C., Murat F., Pironneau O., “The Stokes and Navier–Stokes equation with boundary conditions involving the pressure”, Japan J. Math., 20:2 (1994), 279–318 | MR | Zbl