On the local exact controllability of micropolar fluids with few controls
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 637-662.

In this paper, we study the local exact controllability to special trajectories of the micropolar fluid systems in dimension d=2 and d=3. We show that controllability is possible acting only on one velocity.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016010
Classification : 93B05, 35K20
Mots clés : Controllability, micropolar fluid
Guerrero, Sergio 1 ; Cornilleau, Pierre 2

1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 75252 Paris cedex 05, France.
2 Teacher at Lycée Louis-le-Grand, 123, rue Saint-Jacques, 75005 Paris, France.
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Guerrero, Sergio; Cornilleau, Pierre. On the local exact controllability of micropolar fluids with few controls. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 637-662. doi : 10.1051/cocv/2016010. http://www.numdam.org/articles/10.1051/cocv/2016010/

V.-M. Alekseev, V.-M. Tikhomirov and S.-V. Fomin, Optimal Control, Contemporary Soviet Mathematics. Consultants Bureau, New York (1987). | MR | Zbl

N. Carreño and M. Gueye, Insensitizing controls having one vanishing component for the Navier-Stokes system. J. Math. Pures Appl. 101 (2014) 27–53. | DOI | MR | Zbl

J.-M. Coron and S. Guerrero, Null controllability of the N-dimensional Stokes system with N-1 scalar controls. J. Differ. Equ. 246 (2009) 2908–2921. | DOI | MR | Zbl

E. Fernández-Cara and S. Guerrero, Local exact controllability of micropolar fluids. J. Math. Fluid Mech. 9 (2007) 419–453. | DOI | MR | Zbl

E. Fernández-Cara, M. González-Burgos, S. Guerrero and J.-P. Puel, Null controllability of the heat equation with boundary Fourier conditions: the linear case. ESAIM: COCV 12 (2006) 442–465. | Numdam | MR | Zbl

A.V. Fursikov and O.Y. Imanuvilov, Controllability of evolution equations. Vol. 34 of Lect. Notes Ser. Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul (1996). | MR | Zbl

O.Yu. Imanuvilov, Remarks on exact controllability for the Navier–Stokes equations. ESAIM: COCV 6 (2001) 39–72. | Numdam | MR | Zbl

O.Y. Imanuvilov, J.-P. Puel and M. Yamamoto, Carleman estimates for parabolic equations with nonhomogeneous conditions. Chin. Ann. Math. B 30 (2009) 333–378. | DOI | MR | Zbl

O.A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, revised English edition, translated from the Russian by Richard A. Silverman. Gordon and Breach Science Publishers, New York-London (1963). | MR | Zbl

J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Vol. 2 of Travaux et Recherches Mathématiques, No. 18. Dunod, Paris (1968). | MR | Zbl

G. Lukaszewicz, Micropolar fluids, theory and applications. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser (1999). | MR | Zbl

R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis. Vol. 2 of Stud. Math. Appl. North-Holland, Amsterdam-New York-Oxford (1977). | MR | Zbl

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