On exact controllability for the Navier-Stokes equations

O. Yu. Imanuvilov

ESAIM: Control, Optimisation and Calculus of Variations (1998)

  • Volume: 3, page 97-131
  • ISSN: 1292-8119

How to cite

top

Imanuvilov, 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. [1] V.M. Alekseev, V.M. Tikhomirov, S.V. Fomin: Optimaal Control, Consultants Bureau, New York, 1987. Zbl0689.49001MR924574
  2. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [17] A.V. Fursikov, O. Yu. Imanuvilov, Controllability of evolution equations, Lecture notes series 34 SNU, Seoul 1996. Zbl0862.49004MR1406566
  18. [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. [19] L. Hörmander: Linear Partial Differential Operators, Springer-Verlag, Berlin, 1963. Zbl0108.09301MR404822
  20. [20] O.Yu. Imanuvilov: Boundary controllability of parabolic equations, Sbornik Mathematics, 186, 1995, n° 6, 879-900. Zbl0845.35040MR1349016
  21. [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. [22] A.N. Kolmogorov, S.V. Fomin: Introductory Real Analysis, Dover Publications, INC, New York, 1996. Zbl0213.07305MR377445
  23. [23] O.A. Ladyzenskaja, N.N. Ural'ceva: Linear and Quasilinear Equations of Elliptic Type, Academic Press, New York, 1968. MR244627
  24. [24] J.-L. Lions: Contrôle des Systèmes Distribués Singuliers, Gauthier-Villars, Paris, 1983. Zbl0514.93001MR712486
  25. [25] J.-L. Lions: Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag 1971. Zbl0203.09001MR271512
  26. [26] J.-L. Lions: Are there connections bet ween turbulence and controllability?9e Conférence internationale de l'INRIA, Antibes. 12-15 juin 1990. 
  27. [27] R. Temam: Navier-Stokes Equations, North-Holland Publishing Company, Amsterdam, 1979. Zbl0426.35003MR603444

Citations in EuDML Documents

top
  1. Viorel Barbu, Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise
  2. Viorel Barbu, Feedback stabilization of Navier–Stokes equations
  3. Viorel Barbu, Feedback stabilization of Navier–Stokes equations
  4. Jean-Pierre Puel, Inégalités de Carleman globales pour les problèmes elliptiques non homogènes
  5. Armen Shirikyan, Exact controllability in projections for three-dimensional Navier–Stokes equations
  6. Hussain A. El-Saify, G. M. Bahaa, Optimal control for n × n coupled systems governed by Petrowsky type equations with control-constrained and infinite number of variables
  7. Oleg Yu. Imanuvilov, Remarks on exact controllability for the Navier-Stokes equations
  8. Oleg Yu. Imanuvilov, Remarks on exact controllability for the Navier-Stokes equations
  9. Thierry Horsin, Local exact lagrangian controllability of the Burgers viscous equation

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.