Geodesic
Solvability of the Stationary Optimal Control Problem for Motion Equations of Second Grade Fluids
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 554-560

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

We investigate the optimal Dirichlet boundary control problem for stationary motion equations of second grade fluids. We consider boundary control of the flow on a bounded domain in $\mathbb{R}^n$, $n=2,3$. We show the existence of a weak solution minimizing a given cost functional.
Keywords: hydrodynamics, non-Newtonian fluids, second grade fluids, optimal control, Dirichlet boundary control. 
E. S. Baranovskii. Solvability of the Stationary Optimal Control Problem for Motion Equations of Second Grade Fluids. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 554-560. http://geodesic.mathdoc.fr/item/SEMR_2012_9_a30/
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[1] R. S. Rivlin, J. L. Ericksen, “Stress deformation relations for isotropic materials”, J. Rational Mech. Anal., 4 (1955), 322–425 | MR

[2] D. Cioranescu, E. H. Ouazar, “Existence and uniqueness for fluids of second grade”, Research Notes in Mathematics, 109, 1984, 308–340 | MR

[3] V. Coscia, G. P. Galdi, “Existence, uniqueness, and stability of regular steady motions of a second grade fluid”, Int. J. Non-Linear Mech., 29 (1994), 493–506 | DOI | MR | Zbl

[4] C. le Roux, “Existence and uniqueness of the flow of second-grade fluids with slip boundary conditions”, Arch. Rational Mech. Anal., 148 (1999), 309–356 | DOI | MR | Zbl

[5] R. V. Goldshtein, V. A. Gorodtsov, Mekhanika sploshnykh sred, v. I, Nauka. Fizmatlit, Moskva, 2000

[6] J. E. Dunn, R. L. Fosdick, “Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade”, Arch. Rational Mech. Anal., 56 (1974), 191–252 | DOI | MR | Zbl

[7] R. A. Adams, J. J. F. Fournier, Sobolev spaces, 2 ed., Elsevier, 2003 | MR

[8] A. V. Fursikov, Optimalnoe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Nauchnaya kniga, Novosibirsk, 1999