In this paper, we study the local exact controllability to special trajectories of the micropolar fluid systems in dimension and . We show that controllability is possible acting only on one velocity.
Accepté le :
DOI : 10.1051/cocv/2016010
Mots clés : Controllability, micropolar fluid
@article{COCV_2017__23_2_637_0, author = {Guerrero, Sergio and Cornilleau, Pierre}, title = {On the local exact controllability of micropolar fluids with few controls}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {637--662}, publisher = {EDP-Sciences}, volume = {23}, number = {2}, year = {2017}, doi = {10.1051/cocv/2016010}, mrnumber = {3608097}, zbl = {1358.93034}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2016010/} }
TY - JOUR AU - Guerrero, Sergio AU - Cornilleau, Pierre TI - On the local exact controllability of micropolar fluids with few controls JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 637 EP - 662 VL - 23 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2016010/ DO - 10.1051/cocv/2016010 LA - en ID - COCV_2017__23_2_637_0 ER -
%0 Journal Article %A Guerrero, Sergio %A Cornilleau, Pierre %T On the local exact controllability of micropolar fluids with few controls %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 637-662 %V 23 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2016010/ %R 10.1051/cocv/2016010 %G en %F COCV_2017__23_2_637_0
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
Insensitizing controls having one vanishing component for the Navier-Stokes system. J. Math. Pures Appl. 101 (2014) 27–53. | DOI | MR | Zbl
and ,Null controllability of the N-dimensional Stokes system with N-1 scalar controls. J. Differ. Equ. 246 (2009) 2908–2921. | DOI | MR | Zbl
and ,Local exact controllability of micropolar fluids. J. Math. Fluid Mech. 9 (2007) 419–453. | DOI | MR | Zbl
and ,Null controllability of the heat equation with boundary Fourier conditions: the linear case. ESAIM: COCV 12 (2006) 442–465. | Numdam | MR | Zbl
, , and ,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
Remarks on exact controllability for the Navier–Stokes equations. ESAIM: COCV 6 (2001) 39–72. | Numdam | MR | Zbl
,Carleman estimates for parabolic equations with nonhomogeneous conditions. Chin. Ann. Math. B 30 (2009) 333–378. | DOI | MR | Zbl
, and ,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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