Sur la contrôlabilité des fluides parfaits incompressibles
Thèses d'Orsay, no. 577 (2000) , 132 p.
@phdthesis{BJHTUP11_2000__0577__P0_0,
     author = {Glass, Olivier},
     title = {Sur la contr\^olabilit\'e des fluides parfaits incompressibles},
     series = {Th\`eses d'Orsay},
     publisher = {Universit\'e de Paris-Sud Centre d'Orsay},
     number = {577},
     year = {2000},
     language = {fr},
     url = {http://www.numdam.org/item/BJHTUP11_2000__0577__P0_0/}
}
TY  - BOOK
AU  - Glass, Olivier
TI  - Sur la contrôlabilité des fluides parfaits incompressibles
T3  - Thèses d'Orsay
PY  - 2000
IS  - 577
PB  - Université de Paris-Sud Centre d'Orsay
UR  - http://www.numdam.org/item/BJHTUP11_2000__0577__P0_0/
LA  - fr
ID  - BJHTUP11_2000__0577__P0_0
ER  - 
%0 Book
%A Glass, Olivier
%T Sur la contrôlabilité des fluides parfaits incompressibles
%S Thèses d'Orsay
%D 2000
%N 577
%I Université de Paris-Sud Centre d'Orsay
%U http://www.numdam.org/item/BJHTUP11_2000__0577__P0_0/
%G fr
%F BJHTUP11_2000__0577__P0_0
Glass, Olivier. Sur la contrôlabilité des fluides parfaits incompressibles. Thèses d'Orsay, no. 577 (2000), 132 p. http://numdam.org/item/BJHTUP11_2000__0577__P0_0/

[1] L. V. Ahlfors, Complex analysis : An introduction of the theory of analytic functions of one complex variable, Second edition, McGraw-Hill Book Co., New York-Toronto-London, 1966. | MR

[2] C. Bardos & U. Frisch, Finite-time regularity for bounded and unbounded ideal incompressible fluids using Holder estimates, in Proceedings of the conference held at the university of Paris-Sud Orsay, France, June 12-13, 1975, Springer-Verlag, Lectures Notes in Mathematics 565, pp. 1-13 | MR | Zbl

[3] J.-M. Coron, Global Asymptotic Stabilization for controllable systems without drift, Math. Control Signal Systems, 5, 1992, pp. 295-312. | MR | Zbl

[4] J.-M. Coron, Return method : Application to controllability, Séminaire Equations aux Dérivées Partielles, 1992-1993, Ecole polytechnique, Centre de Mathématiques, exposé XIV. | MR | Zbl | Numdam

[5] J.-M. Coron, Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels, C. R. Acad. Sci. Paris, Sér. I Math. 317 (1993), no. 3, pp. 271-276. | MR | Zbl

[6] J.-M. Coron, On the controllability of 2-D incompressible perfect fluids, J. Math. Pures Appl., 75, 1996, pp. 155-188. | MR | Zbl

[7] 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, pp. 35-75. (http://www.emath.fr/cocv/) | MR | Zbl | Numdam

[8] J.-M. Coron, On null asymptotic stabilisation of the 2-D Euler equation of incompressible fluids on simply connected domains, Prépublication d'Orsay, no. 59 (1998).

[9] J.-M. Coron, Sur la stabilisation des fluides parfaits incompressibles bidimensionnels, Séminaire sur les Equations aux Dérivées Partielles, 1998-1999, École polytechnique, Centre de Mathématiques, Exposé VII. | MR | Zbl | Numdam

[10] J.-M. Coron & A.V. Fursikov, Global exact controllability of the 2D Navier-Stokes equations on a manifold without boundary. Russian J. Math. Phys. 4 (1996), no. 4, pp. 429-448. | MR | Zbl

[11] C. Fabre, Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems. ESAIM : Control Optimisation and Calculus of Variations 1 (1996), pp. 267-302. (http://www.emath.fr/cocv/) | MR | Zbl | Numdam

[12] C. Fabre, J.-P. Puel & E. Zuazua, Approximate controllability for semilinear heat equation, Proc. Royal Soc. Edinbourgh, 125 A (1995), pp. 31-61. | MR | Zbl | DOI

[13] E. Fernàndez-Cara & J. Real, On a conjecture due to J.-L. Lions. Nonlinear Anal. 21 (1993), no. 11, pp. 835-847. | MR | Zbl | DOI

[14] A.V. Fursikov, On boundary zero controllability of the three-dimensional Navier-Stokes equations. Theory of the Navier-Stokes equations, pp. 31-45, Ser. Adv. Math. Appl. Sci., 47 (1998). | MR | Zbl | DOI

[15] A.V. Fursikov & O.Yu. Imanuvilov, Local exact boundary controllability of the Navier-Stokes system. Optimization methods in partial differential equations, pp. 115-129, Contemp. Math., 209 (1997). | MR | Zbl

[16] A.V. Fursikov & O.Yu. Imanuvilov, Local exact controllability of the Navier-Stokes equations. C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), no. 3, pp. 275-280. | MR | Zbl

[17] A.V. Fursikov & O.Yu. Imanuvilov, On exact boundary zero-controllability of two-dimensional Navier-Stokes equations. Mathematical problems for Navier-Stokes equations. Acta Appl. Math. 37 (1994), no. 1-2, pp. 67-76. | MR | Zbl

[18] O. Glass, Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles en dimension 3, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), no. 9, pp. 987-992. | MR | Zbl

[19] O. Glass, Contrôlabilité de l'équation d'Euler tridimensionnelle pour les fluides parfaits incompressibles, Séminaire sur les Equations aux Dérivées Partielles, 1997-1998, École Polytechnique, Centre de Mathématiques, Exposé XV. | MR | Zbl

[20] P. Hermann & H. Kersten, Über die stetige Abhängigkeit der Lösung des Neumann-Problems für die Prae-Maxwellschen Gleichungen von ihren Randdaten. Arch. Math. (Basel) 36 (1981), no. 1, pp. 79-82. | MR | Zbl

[21] G. Hernandez, Contrôle actif des instabilités hydrodynamiques des écoulements subsoniques compressibles, Thèse de doctorat de l'Institut National Polytechnique de Toulouse, 1996.

[22] O. Yu. Imanuvilov, On exact controllability for Navier-Stokes equations, ESAIM : Control Optimisation and Calculus of Variations 3 (1998), pp. 97-131. (http://www.emath.fr/cocv/) | MR | Zbl | Numdam

[23] T. Kato, On classical solutions of the two-dimensional nonstationary Euler equation, Arch. Rational Mech. Anal., 25, 1967, pp. 188-200 | MR | Zbl | DOI

[24] A. V. Kazhikov, Note on the formulation of the problem of flow through a bounded region using equations of perfect fluid, PMM USSR, 44, 1981, pp. 672-674. | Zbl | MR

[25] J.-L. Lions, Are there connections between turbulence and controllability ?, 9th INRIA International Conference, Antibes, June 12-15, 1990.

[26] J.-L. Lions, Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles, Paris, Gauthier-Villars, 1968. | MR | Zbl

[27] J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués, Tomes 1 et 2, Recherches en Mathématiques Appliquées 8 et 9, Masson, Paris, 1988. | MR | Zbl

[28] J.-L. Lions & E. Zuazua, Contrôlabilité exacte des approximations de Galerkin des équations de Navier-Stokes. C. R. Acad. Sci. Paris Sér. I Math. 324 (1997), no. 9, pp. 1015-1021. | MR | Zbl

[29] J.-L. Lions & E. Zuazua, Approximate controllability of a hydro-elastic coupled system. ESAIM : Control Optimisation and Calculus of Variations 1 (1996), pp. 1-15. (http://www.emath.fr/cocv/) | MR | Zbl | Numdam

[30] R. Nirenberg & R. O. Wells Jr., Approximation theorems on differentiable submanifolds of a complex manifold, Trans. Amer. Math. Soc. 142 (1969), pp. 15-35. | MR | Zbl | DOI

[31] A. Osses & J.-P. Puel, Approximate controllability for a linear model of fluid structure interaction, ESAIM : Control Optimisation and Calculus of Variations 4 (1999), pp. 497-514. (http://www.emath.fr/cocv/) | MR | Zbl | Numdam

[32] C. Pommerenke, Boundary behaviour of conformai maps, Grundlehren der mathematischen wissenschaften 299, Spinger Verlag, Berlin, 1992. | MR | Zbl

[33] R. Temam, Navier-Stokes equations. Theory and numerical analysis. Third Edition. Studies in Mathematics and its Applications, Vol. 2. North-Holland Publishing Co., Amsterdam-New York-Oxford, 1984. | MR | Zbl

[34] W. Wolibner, Un théorème sur l'existence du mouvement plan d'un fluide parfait, homogène, incompressible, pendant un temps infiniment long, Math. Z. 37, 1933, pp. 698-726. | MR | Zbl | JFM

[35] E. Zuazua, Exact controllability for semilineax wave equatios in one space dimension, Ann. Inst. Henri Poincaré, Nonlinear Analysis, 10 (1993), pp. 109-129. | MR | Zbl | Numdam | DOI