On exact controllability for the Navier-Stokes equations
ESAIM: Control, Optimisation and Calculus of Variations (1998)
- Volume: 3, page 97-131
- ISSN: 1292-8119
Access Full Article
topHow to cite
topImanuvilov, O. Yu.. "On exact controllability for the Navier-Stokes equations." ESAIM: Control, Optimisation and Calculus of Variations 3 (1998): 97-131. <http://eudml.org/doc/90536>.
@article{Imanuvilov1998,
author = {Imanuvilov, O. Yu.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {locally distributed control},
language = {eng},
pages = {97-131},
publisher = {EDP Sciences},
title = {On exact controllability for the Navier-Stokes equations},
url = {http://eudml.org/doc/90536},
volume = {3},
year = {1998},
}
TY - JOUR
AU - Imanuvilov, O. Yu.
TI - On exact controllability for the Navier-Stokes equations
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1998
PB - EDP Sciences
VL - 3
SP - 97
EP - 131
LA - eng
KW - locally distributed control
UR - http://eudml.org/doc/90536
ER -
References
top- [1] V.M. Alekseev, V.M. Tikhomirov, S.V. Fomin: Optimaal Control, Consultants Bureau, New York, 1987. Zbl0689.49001MR924574
- [2] D. Chae, O.Yu. Imanuvilov, S.M. Kim: Exact controllability for semilinear parabolic equations with Neumann boundary conditions, J. of Dynamical and Control Syst. 2, 1996, n° 4, 449-483. Zbl0946.93007MR1420354
- [3] J.-M. Coron: On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier-slip boundary conditions, ESAIM: Control, Optimisation and Calculus of Variations, 1, 1996, 35-75. Zbl0872.93040MR1393067
- [4] J.-M. Coron: On the controllability of 2-D incompressible perfect fluids. J. Math. Pures et Appl., 75, 1996, 155-188. Zbl0848.76013MR1380673
- [5] J.-M. Coron: Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels, C. R. Acad. Sci. Paris, 317, Série I, 1993, 271-276. Zbl0781.76013MR1233425
- [6] J.-M. Coron, A.V. Fursikov: Global exact controllability of the 2-D Navier-Stokes equations on manifold without boundary, Russian Journal of Math. Physics 4, 1996, n° 3, 1-20. Zbl0938.93030MR1470445
- [7] C. Fabre: Résultats d'unicité pour les équations de Stokes et applications au contrôle, C. R. Acad. Sci. Paris, 322, Série I, 19961191-1196. Zbl0861.35073
- [8] C. Fabre, G. Lebeau: Prolongement unique des solutions de l'équation de Stokes, Com. P.D.E., 21, 1996, n° 3 - 4, 573-596. Zbl0849.35098MR1387461
- [9] A.V. Fursikov: Lagrange principle for problems of optimal control of ill-posed or singular distributed systems, J. Maths Pures Appl., 71, 1992, n° 2, 139-195. Zbl0829.49001MR1170249
- [10] A.V. Fursikov: Exact boundary zero controllability of three dimensional Navier-Stokes equations, J. of Dynamical and Control Syst., 1, 1995, n° 3, 325-350. Zbl0951.93005MR1354539
- [11] A.V. Fursikov: The Cauchy problem for a second-order elliptic equation in a conditionally well-posed formulation, Trans. Moscow Math. Soc., 1990, 139-176. Zbl0716.35023MR1056468
- [12] A.V. Fursikov, O.Yu. Imanuvilov: On controllability of certain systems simulating a fluid flow, in Flow Control, IMA vol. Math. Appl., Ed. by M.D. Gunzburger, Springer-Verberg, New York, 68, 1995, 148-184. Zbl0922.93006MR1348646
- [13] A.V. Fursikov, O.Yu. Imanuvilov: On exact boundary zero-controllability of two-dimensional Navier-Stokes equations, Acta Applicandæ Mathematicæ, 37, 1994, 67-76. Zbl0809.93006MR1308746
- [14] A.V. Fursikov, O.Yu. Imanuvilov: Local exact controllability of two dimensional Navier-Stokes system with control on the part of the boundary, Sbornik Mathematics, 187, 1996, n° 9, 1355-1390. Zbl0869.35074MR1422385
- [15] A.V. Fursikov, O.Yu. Imanuvilov: Local exact boundary controllability of the Boussinesq equation, SIAM J. Cont. Opt., 36, Issue 2, 1998. Zbl0907.76020MR1616510
- [16] A.V. Fursikov, O.Yu. Imanuvilov: Local exact controllability of the Navier-Stokes Equations, C. R. Acad. Sci. Paris, 323, Série I, 1996, 275-280. Zbl0873.76020MR1404773
- [17] A.V. Fursikov, O. Yu. Imanuvilov, Controllability of evolution equations, Lecture notes series 34 SNU, Seoul 1996. Zbl0862.49004MR1406566
- [18] A.V. Fursikov, O.Yu. Imanuvilov: On approximate controllability of the Stokes system, Annales de la Faculté des Sciences de Toulouse, 11, 1993, 205-232. Zbl0925.93416MR1253389
- [19] L. Hörmander: Linear Partial Differential Operators, Springer-Verlag, Berlin, 1963. Zbl0108.09301MR404822
- [20] O.Yu. Imanuvilov: Boundary controllability of parabolic equations, Sbornik Mathematics, 186, 1995, n° 6, 879-900. Zbl0845.35040MR1349016
- [21] O.Yu. Imanuvilov: Local exact controllability for the 2-D Navier-Stokes equations with the Navier slip boundary conditions, Lecture Notes in Physics, 491, 1997, 148-168. Zbl0897.35063MR1601027
- [22] A.N. Kolmogorov, S.V. Fomin: Introductory Real Analysis, Dover Publications, INC, New York, 1996. Zbl0213.07305MR377445
- [23] O.A. Ladyzenskaja, N.N. Ural'ceva: Linear and Quasilinear Equations of Elliptic Type, Academic Press, New York, 1968. MR244627
- [24] J.-L. Lions: Contrôle des Systèmes Distribués Singuliers, Gauthier-Villars, Paris, 1983. Zbl0514.93001MR712486
- [25] J.-L. Lions: Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag 1971. Zbl0203.09001MR271512
- [26] J.-L. Lions: Are there connections bet ween turbulence and controllability?9e Conférence internationale de l'INRIA, Antibes. 12-15 juin 1990.
- [27] R. Temam: Navier-Stokes Equations, North-Holland Publishing Company, Amsterdam, 1979. Zbl0426.35003MR603444
Citations in EuDML Documents
top- Viorel Barbu, Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise
- Viorel Barbu, Feedback stabilization of Navier–Stokes equations
- Jean-Pierre Puel, Inégalités de Carleman globales pour les problèmes elliptiques non homogènes
- Viorel Barbu, Feedback stabilization of Navier–Stokes equations
- Armen Shirikyan, Exact controllability in projections for three-dimensional Navier–Stokes equations
- Hussain A. El-Saify, G. M. Bahaa, Optimal control for coupled systems governed by Petrowsky type equations with control-constrained and infinite number of variables
- Oleg Yu. Imanuvilov, Remarks on exact controllability for the Navier-Stokes equations
- Oleg Yu. Imanuvilov, Remarks on exact controllability for the Navier-Stokes equations
- Thierry Horsin, Local exact lagrangian controllability of the Burgers viscous equation
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.