Exact boundary controllability of Galerkin's approximations of Navier-Stokes equations

Jacques-Louis Lions; Enrique Zuazua

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)

  • Volume: 26, Issue: 4, page 605-621
  • ISSN: 0391-173X

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Lions, Jacques-Louis, and Zuazua, Enrique. "Exact boundary controllability of Galerkin's approximations of Navier-Stokes equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 26.4 (1998): 605-621. <http://eudml.org/doc/84340>.

@article{Lions1998,
author = {Lions, Jacques-Louis, Zuazua, Enrique},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {605-621},
publisher = {Scuola normale superiore},
title = {Exact boundary controllability of Galerkin's approximations of Navier-Stokes equations},
url = {http://eudml.org/doc/84340},
volume = {26},
year = {1998},
}

TY - JOUR
AU - Lions, Jacques-Louis
AU - Zuazua, Enrique
TI - Exact boundary controllability of Galerkin's approximations of Navier-Stokes equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1998
PB - Scuola normale superiore
VL - 26
IS - 4
SP - 605
EP - 621
LA - eng
UR - http://eudml.org/doc/84340
ER -

References

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  1. [C1] J.M. Coron, On the controllability of 2D incompressible perfect fluids, J. Math. Pures Appl.75 (1996), 155-188. Zbl0848.76013MR1380673
  2. [C2] J.M. Coron, On the controllability of the 2D incompressible Navier-Stokes equations with the Navier slip boundary condition, ESAIM:COCV1 (1996), 35-75 (http://www.emath.fr/cocv/). Zbl0872.93040MR1393067
  3. [CF] J.M. Coron - A. Fursikov, Global exact controllability of the 2D Navier-Stokes equations on a manifold without boundary, Russian J. Math. Phys.4 (4) (1996), 1-19. Zbl0938.93030MR1470445
  4. [FI] A. Fursikov - O. Yu. Imanuvilov, "Controllability of evolution equations ", Lecture Notes Series 34, Research Institute of Mathematics, Global Analysis Research Center, Seoul National University, Korea, 1996. Zbl0862.49004MR1406566
  5. [L1] J.-L. Lions," Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires"; Dunod, Paris, 1969. Zbl0189.40603MR259693
  6. [L2] J.-L. Lions, Are there connections between turbulence and controllability?, In: "Analyse et optimisation des systèmes", Lecture Notes in Control and Information Sciences vol.144, Springer-Verlag, Berlin- Heidelberg -New York, 1990. 
  7. [L3] J.L. Lions, On the approximate controllability with global state constraints, In: "Computational Science for the 21st Century", M. O. Bristeau et al. eds., Wiley, 1977, pp. 718-727. Zbl0914.93012
  8. [LM] J.-L. Lions - E. Magenes, "Problèmes aux Limites Non Homogènes et applications", Dunod, Paris, 1968. Zbl0165.10801
  9. [LZ1] J.-L. Lions - E. Zuazua,, A generic uniqueness result for the Stokes system and its control theoretical consequences, In: "Partial Differential Equations and Applications ", P. Marcellini et al. (eds.), Marcel Dekker Inc. LNPAS177, 1996, p. 221-235. Zbl0852.35112MR1371594
  10. [LZ2] J.-L. Lions - E. Zuazua, Contrôlabilité exacte des approximations de Galerkin des équations de Navier-Stokes, C. R. Acad. Sci. Paris Sér. I.Math.234 (1997), 1015-1021. Zbl0894.93020MR1451243
  11. [LZ3] J.-L. Lions - E. Zuazua, On the cost of controlling unstable systems: The case of boundary controls, J. Anal. Math., to appear. Zbl0892.93036MR1616414
  12. [R] R.T. Rockafellar, "Convex Analysis", Princeton University Press, Princeton, N. J., 1969. Zbl0193.18401MR1451876

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