Geodesic
Optimal control of cylinder rotation in a~viscous fluid
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 1, pp. 95-105.

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The paper deals with the axisymmetric problem of optimal boundary control of a mechanical system consisting of two coaxial cylinders and an incompressible viscous fluid filling the area between them. The control parameter is the angular velocity of the outer cylinder. It is required to stop the inner cylinder at a prescribed time with minimal energy cost. The unique solvability of the problem is proved and the optimality system is derived.
Mots-clés : viscous fluid
Keywords: rigid body, optimal control. 
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V. N. Starovoitov. Optimal control of cylinder rotation in a~viscous fluid. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 1, pp. 95-105. http://geodesic.mathdoc.fr/item/SJIM_2013_16_1_a9/

[1] Fursikov A. V., Optimalnoe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Nauch. kniga, Novosibirsk, 1999 | Zbl

[2] Imanuvilov O., Takahashi T., “Exact controllability of a fluid-rigid body system”, J. Math. Pure Appl., 87:4 (2007), 408–437 | MR | Zbl

[3] Hoffmann K.-H., Starovoitov V. N., “On a motion of a solid body in a viscous incompressible fluid. Two-dimensional case”, Adv. Math. Sci. Appl., 9:2 (1999), 633–648 | MR | Zbl

[4] Starovoitov V. N., Neregulyarnye zadachi gidrodinamiki, Dis. $\dots$ d. fiz.-mat. nauk, Novosibirsk, 2000, 225 pp.

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

[6] Lions Zh.-L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972 | MR | Zbl

[7] Takahashi T., “Analisys of strong solutions for the equations modeling the motion of a rigidfluid system in a bounded domain”, Adv. Differential Equations, 8 (2003), 1499–1532 | MR | Zbl

[8] Starovoitov V. N., “Zadacha o dreife tverdogo tela v vyazkoi zhidkosti”, Vestn. NGU. Ser. Matematika, mekhanika i informatika, 6:2 (2006), 89–103 | MR

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