On exact controllability for the navier-stokes equations

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 3, Issue , 1998, Pages 97-131

  Imanuvilov, O Yu ^a  

^a Korea Institute for Advanced Study   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84996141310     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:1998104     Document Type: Article

References (26)

1. V.M. Alekseev, V.M. Tikhomirov, S.V. Fomin: Optimal Control, Consultants Bureau, New York, 1987.
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, no 4, 449-483.
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.
4. J.-M. Coron: On the controllability of 2-D incompressible perfect fluids. J. Math. Pures et Appl., 75, 1996, 155-188.
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.
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, no 3, 1-20.
7. C. Fabre: Résultats d’unicité pour les équations de Stokes et applications au contrôle, C. R. Acad. Sci. Paris, 322, Série I, 1996 1191-1196.
8. C. Fabre, G. Lebeau: Prolongement unique des solutions de l’équation de Stokes, Com. P.D.E., 21, 1996, no 3-4, 573-596.
9. A.V. Fursikov: Lagrange principle for problems of optimal control of ill-posed or singular distributed systems, J. Maths Pures Appl., 71, 1992, no 2, 139-195.
10. A.V. Fursikov: Exact boundary zero controllability of three dimensional Navier-Stokes equations, J. of Dynamical and Control Syst., 1, 1995, no 3, 325-350.
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.
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.
13. A.V. Fursikov, O.Yu. Imanuvilov: On exact boundary zero-controllability of twodimensional Navier-Stokes equations, Acta Applicandæ Mathematicæ, 37, 1994, 6776.
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, no 9, 1355-1390.
15. A.V. Fursikov, O.Yu. Imanuvilov: Local exact boundary controllability of the Boussi-nesq equation, SIAM J. C’ont. Opt., 36, Issue 2, 1998.
16. A.V. Fursikov, O.Yu. Imanuvilov: Local exact controllability of the Navier-Stokes Equations, C. P. Acad. Sei. Paris, 323, Série I, 1996, 275-280.
17. A.V. Fursikov, O. Yu. Imanuvilov: Controllability of evolution equations, Lecture notes series 34 SNU, Seoul 1996.
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.
19. L. Hörmander: Linear Partial Differential Operators, Springer-Verlag, Berlin, 1963. O.Yu. Imanuvilov: Boundary controllability of parabolic equations, Sbornik Mathematics, 186, 1995, no 6, 879-900.
20. 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.
21. A.N. Kolmogorov, S.V. Fomin: Introductory Real Analysis, Dover Publications, INC, New York, 1996.
22. O.A. Ladyzenskaja, N.N. Ural’ceva: Linear and Quasilinear Equations of Elliptic Type, Academic Press, New York, 1968.
23. J.-L. Lions: Contrôle des Systèmes Distribués Singuliers, Gauthier-Villars, Paris, 1983.
24. J.-L. Lions: Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag 1971.
25. J.-L. Lions: Are there connections between turbulence and controllability? pe Conférence internationale de l’INRIA, Antibes. 12-15 juin 1990.
26. R. Temam: Navier-Stokes Equations, North-Holland Publishing Company, Amsterdam, 1979.