@article{COCV_1996__1__35_0,
author = {Coron, Jean-Michel},
title = {On the controllability of the {2-D} incompressible {Navier-Stokes} equations with the {Navier} slip boundary conditions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {35--75},
year = {1996},
publisher = {SMAI (Soci\'et\'e de math\'ematiques appliqu\'ees et industrielles)},
address = {Paris},
volume = {1},
mrnumber = {1393067},
zbl = {0872.93040},
language = {en},
url = {https://www.numdam.org/item/COCV_1996__1__35_0/}
}
TY - JOUR AU - Coron, Jean-Michel TI - On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 1996 SP - 35 EP - 75 VL - 1 PB - SMAI (Société de mathématiques appliquées et industrielles) PP - Paris UR - https://www.numdam.org/item/COCV_1996__1__35_0/ LA - en ID - COCV_1996__1__35_0 ER -
%0 Journal Article %A Coron, Jean-Michel %T On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions %J ESAIM: Control, Optimisation and Calculus of Variations %D 1996 %P 35-75 %V 1 %I SMAI (Société de mathématiques appliquées et industrielles) %C Paris %U https://www.numdam.org/item/COCV_1996__1__35_0/ %G en %F COCV_1996__1__35_0
Coron, Jean-Michel. On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 1 (1996), pp. 35-75. https://www.numdam.org/item/COCV_1996__1__35_0/
[1] : Sobolev spaces, Academic Press, San Diego, London, 1978. | Zbl | MR
[2] , , and : Fluid dynamic limits of kinetic equations I: formal derivations, J. Statistical Physics, 63, 1991, 323-344. | MR
[3] : Derivation of slip boundary conditions for the Navier-Stokes System from the Boltzmann equation, J. Statistical Physics, 54, 1989, 829-857. | Zbl | MR
[4] : Global asymptotic stabilization for controllable systems without drift, Math. Control Signals Systems, 5, 1992, 295-312. | Zbl | MR
[5] : Stabilization of controllable systems, preprint, 1993, to appear in Nonholonomic geometry, A. Bellaïche and J.-J. Risler ed., Progress in Math., Birkhäuser. | Zbl | MR
[6] : Relations entre commandabilité et stabilisations non linéaires, in Nonlinear partial differential equations and their applications, Collège de France seminars, Paris 1989-1991, Vol.11, H. Brezis and J.-L. Lions eds., Pitman Res. Notes Math. Ser., London, 299, 1994, 68-86. | Zbl | MR
[7] : Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels, C. R. Acad. Sci. Paris, 317, 1993, 271-276. | Zbl | MR
[8] : On the controllability of 2-D incompressible perfect fluids, J. Math. Pures et Appliquées, 75, 1996, 155-188. | Zbl | MR
[9] : Uniqueness result for Stokes equations and their consequences in linear and nonlinear control problems, in Contrôlabilité approchée des solutions de quelques équations d'évolution, Habilitation à diriger des recherches, Université Pierre et Marie Curie, January 1996. | MR
[10] and : A result concerning approximate controllability for the Navier-Stokes Equations, SIAM J. Control, to appear.
[11] and : On a conjecture due to J.-L. Lions, Nonlinear Analysis, Theory, Methods et Appl., 21, 1993, 835-847. | Zbl | MR
[12] : Exact boundary zero controllability of three-dimensional Navier-Stokes equations, J. Dynamical Control et Systems, 1, 1995, 325-350. | Zbl | MR
[13] and : On controllability of certain Systems simulating a fluid flow, in Flow Control, IMA vol. in Math. and its Appl. , M.D. Gunzburger ed., Springer Verlag, New York, 68, 1995, 149-184. | Zbl | MR
[14] and : On exact boundary zero controllability of the two-dimensional Navier-Stokes equation, Acta Appl. Math., 36, 1994, 1-10. | Zbl | MR
[15] and : Local exact controllability of the Navier-Stokes equations, RIM-GARC preprint series 95-92, Seoul National University, February 1996. | MR
[16] and : On the vanishing viscosity limit for acoustic phenomena in a bounded region, Arch. Rat. Mechanics and Analysis, 75, 1981, 257-268. | Zbl | MR
[17] and : Mathematical models of turbulence, Academic Press, 1972. | Zbl
[18] : Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod et Gauthier-Villars, Paris, 1969. | Zbl | MR
[19] : Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles, Gauthier-Villars, Paris, 1968. | Zbl | MR
[20] : Are there connections between turbulence and controllability?, 9th IN-RIA International Conference, Antibes, June 12-25, 1990.
[21] : Exact controllability for distributed Systems. Some trends and some problems, in: Applied and Industrial Mathematics, R. Spigler ed., Kluwer Academic Publishers, Dordrecht, Boston, London, 1991, 59-84. | Zbl | MR
[22] and : Problèmes aux limites non homogènes et applications, vol. 1, Dunod, Paris, 1968. | Zbl | MR
[23] : Some theorems of existence for solutions of the Navier-Stokes equations with slip boundary condition in half-space, Ricerche di Matematica, 40, 1991, 81-135. | Zbl | MR
[24] : Sur les lois du mouvement des fluides, Mem. Acad. R. Sci. Inst. France, 6, 1823, 389-440.
[25] : On the effect of internal friction of fluids on the motion of pendulums, Trans. Cambridge Philos. Soc., 9, 1851, 8-106.






