@article{SEDP_1998-1999____A7_0, author = {Coron, Jean-Michel}, title = {Sur la stabilisation des fluides parfaits incompressibles bidimensionnels}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:7}, pages = {1--15}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {1998-1999}, zbl = {1086.93511}, mrnumber = {1721325}, language = {fr}, url = {http://www.numdam.org/item/SEDP_1998-1999____A7_0/} }
TY - JOUR AU - Coron, Jean-Michel TI - Sur la stabilisation des fluides parfaits incompressibles bidimensionnels JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:7 PY - 1998-1999 SP - 1 EP - 15 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_1998-1999____A7_0/ LA - fr ID - SEDP_1998-1999____A7_0 ER -
%0 Journal Article %A Coron, Jean-Michel %T Sur la stabilisation des fluides parfaits incompressibles bidimensionnels %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:7 %D 1998-1999 %P 1-15 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/item/SEDP_1998-1999____A7_0/ %G fr %F SEDP_1998-1999____A7_0
Coron, Jean-Michel. Sur la stabilisation des fluides parfaits incompressibles bidimensionnels. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 7, 15 p. http://www.numdam.org/item/SEDP_1998-1999____A7_0/
[1] R.W. Brockett, Asymptotic stability and feedback stabilization, dans : Differential Geometric Control Theory, R.W. Brockett, R.S. Millman et H.J. Sussmann éds, Progress in Math., 27 (1983) p. 181-191, Birkhäuser, Basel-Boston. | MR | Zbl
[2] W.L. Chow, Uber systeme von linearen partiellen differentialgleichung ester ordnung, Math. Ann. 117 (1940-41) p. 227-232.
[3] F.H. Clarke, Yu. S. Ledyaev, R.J. Stern, Asymptotic stability and smooth Lyapunov functions, J. Diffferential Equations, 149 (1998) p. 69-114. | MR | Zbl
[4] J.-M. Coron, Global asymptotic stabilization for controllable systems without drift, Math. Control Signals Systems, 5 (1992) p. 295-312. | MR | Zbl
[5] J.-M. Coron, Stabilization in finite time of locally controllable systems by means of continuous time-varying feedback laws, SIAM J. Control and Optimization, 33 (1995) p. 804-833. | MR | Zbl
[6] J-M. Coron, Contrôlabilité exacte frontière de l’équation d’Euler des fluides parfaits incompressibles bidimensionnels,C. R. Acad. Sci. Paris, t. 317, Série I, (1993) p. 271-276. | Zbl
[7] J-M. Coron, Return method : Application to controllability, Séminaire Équations aux Dérivées Partielles, 1992-1993, École polytechnique, Centre de Mathématiques, exposé 14. | Numdam | MR | Zbl
[8] J-M. Coron, On the controllability of the 2-D incompressible perfect fluids, J. Math. Pures et Appliquées, 75 (1996) p. 155-188. | MR | Zbl
[9] J-M. Coron, On the null asymptotic stabilization of the 2-D incompressible Euler equation in a simply connected domain, prépublication, Université Paris-Sud, 59 (1998), accepté pour publication dans SIAM J. Control and Optimization. | Zbl
[10] O. Glass, Contrôlabilité exacte frontière de l’équation d’Euler des fluides parfaits incompressibles en dimension 3, C.R. Acad. Sci. Paris, t. 325, Série I, (1997) p. 987-992. | Zbl
[11] O. Glass, Contrôlabilité de l’équation d’Euler tridimensionnelle pour les fluides parfaits incompressibles, Séminaire Équations aux Dérivées Partielles, 1997-1998, École polytechnique, Centre de Mathématiques, exposé 15. | Numdam | Zbl
[12] O. Glass, Exact boundary controllability of 3-D Euler equation, prépublication, Décembre 1998. | Numdam | Zbl
[13] V. Komornik, Rapid boundary stabilization of linear distributed systems, SIAM J. Control Optim., 35 (1997) p. 1591-1613. | MR | Zbl
[14] Zbl
, The operator translation along the trajectories of differential equations, Trans. Math. Monographs, 19 (1968). |[15] Geometric methods in nonlinear analysis, Springer-Verlag, Berlin, 1983.
et ,[16] J. Kurzweil, On the inversion of Lyapunov’s second theorem on stability of motion, Ann. Math. Soc. Trans. Ser.2, 24 (1956) p. 19-77. | Zbl
[17] I. Lasiecka and R. Triggiani, Differential and Algebraic Ricatti Equations with Applications to Boundary/Point Control Problems : Continuous and Approximation Theory, Lecture Notes in Control and Information Sciences, vol. 164, Springer-Verlag, Berlin, Heidelberg, New York, 1991. | Zbl
[18] J.-L. Lions, Exact controllability, stabilizability, and perturbations for distributed systems, SIAM Rev., 30 (1988) p. 1-68. | MR | Zbl
[19] J.-L. Lions, Are there connections between turbulence and controllability ?, 9th INRIA International Conference, Antibes, June 12-15, 1990.
[20] A. Majda, Vorticity and the mathematical theory of incompressible fluid flow, Comm. Pure Appl. Math., 39, special issue, (1986) p. 187-220. | MR | Zbl
[21] P.K. Rashevski, About connecting two points of complete nonholonomic space by admissible curve, Uch Zapiski ped. inst. Libknexta, 2 (1938) p. 83-94.
[22] C. Samson, Velocity and torque feedback control of a nonholonomic cart, dans : Advanced Robot Control, Proceedings de « International workshop on nonlinear and adaptative control : Issues in robotics », Grenoble, France, novembre 21-23, 1990, éd. : C. Canudas de Wit, Lecture Notes in Control and Information Sciences, vol. 162, p. 125-151, Springer-Verlag, Berlin Heidelberg New York, 1991. | MR | Zbl
[23] M. Slemrod, A note on complete controllability and stabilizability for linear control systems in Hilbert space, SIAM J. Control, 12 (1974) p. 500-508. | MR | Zbl
[24] E.D. Sontag et H. Sussmann, Remarks on continuous feedbacks, IEEE CDC, Albuquerque, 2 (1980) p. 916-921.
[25] H.J. Sussmann, Subanalytic sets and feedback control, J. Differential Equations, 31 (1979) p. 31-52. | MR | Zbl