Free access
Issue
ESAIM: COCV
Volume 15, Number 4, October-December 2009
Page(s) 934 - 968
DOI http://dx.doi.org/10.1051/cocv:2008059
Published online 21 October 2008
  1. M. Badra, Feedback stabilization of 3-D Navier-Stokes equations based on an extended system, in Proceedings of the 22nd IFIP TC7 Conference (2005).
  2. M. Badra, Lyapunov function and local feedback boundary stabilization of the Navier-Stokes equations. SIAM J. Contr. Opt. (to appear).
  3. V. Barbu, Feedback stabilization of Navier-Stokes equations. ESAIM: COCV 9 (2003) 197–206 (electronic). [EDP Sciences]
  4. V. Barbu, I. Lasiecka and R. Triggiani, Tangential boundary stabilization of Navier-Stokes equations, Memoirs of the American Mathematical Society 181. AMS (2006).
  5. V. Barbu and R.L Triggiani, Internal stabilization of Navier-Stokes equations with finite-dimensional controllers. Indiana Univ. Math. J. 53 (2004) 1443–1494. [CrossRef] [MathSciNet]
  6. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and control of infinite-dimensional systems 1, Systems & Control: Foundations & Applications. Birkhäuser Boston Inc., Boston, MA, USA (1992).
  7. P. Constantin and C. Foias, Navier-Stokes equations, Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, USA (1988)
  8. J.-M. Coron and A.V. Fursikov, Global exact controllability of the 2D Navier-Stokes equations on a manifold without boundary. Russian J. Math. Phys. 4 (1996) 429–448. [MathSciNet]
  9. E. Fernández-Cara, S. Guerrero, O.Yu. Imanuvilov and J.-P. Puel, Local exact controllability of the Navier-Stokes system. J. Math. Pures Appl. 83 (2004) 1501–1542. [CrossRef] [MathSciNet]
  10. H. Fujita and H. Morimoto, On fractional powers of the Stokes operator. Proc. Japan Acad. 46 (1970) 1141–1143. [CrossRef] [MathSciNet]
  11. A.V. Fursikov, Stabilizability of two-dimensional Navier-Stokes equations with help of a boundary feedback control. J. Math. Fluid Mech. 3 (2001) 259–301. [CrossRef] [MathSciNet]
  12. A.V. Fursikov, Stabilization for the 3D Navier-Stokes system by feedback boundary control. Discrete Contin. Dyn. Syst. 10 (2004) 289–314. [CrossRef] [MathSciNet]
  13. G.P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations, Vol. I, Linearized steady problems, Springer Tracts in Natural Philosophy, Vol. 38. Springer-Verlag, New York (1994).
  14. G.P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations, Vol. II, Nonlinear steady problems, Springer Tracts in Natural Philosophy, Vol. 39. Springer-Verlag, New York (1994).
  15. P. Grisvard, Caractérisation de quelques espaces d'interpolation. Arch. Rational Mech. Anal. 25 (1967) 40–63. [CrossRef] [MathSciNet]
  16. P. Grisvard, Elliptic problems in nonsmooth domains, in Monographs and Studies in Mathematics, Vol. 24, Pitman (Advanced Publishing Program), Boston, MA, USA (1985).
  17. E. Hille and R.S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31. American Mathematical Society, Providence, RI, USA, revised edition (1957).
  18. I. Lasiecka and R. Triggiani, Control theory for partial differential equations: continuous and approximation theories. I. Abstract parabolic systems, in Encyclopedia of Mathematics and its Applications 74, Cambridge University Press, Cambridge (2000).
  19. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. I. Dunod, Paris (1968).
  20. A. Pazy, Semigroups of linear operators and applications to partial differential equations, in Applied Mathematical Sciences 44, Springer-Verlag, New York (1983).
  21. J.-P. Raymond, Feedback boundary stabilization of the two dimensional Navier-Stokes equations. SIAM J. Contr. Opt. 45 (2006) 790–828. [CrossRef] [MathSciNet]
  22. J.-P. Raymond, Feedback boundary stabilization of the three dimensional incompressible Navier-Stokes equations. J. Math. Pures Appl. 87 (2007) 627–669. [CrossRef] [MathSciNet]
  23. J.-P. Raymond, Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions. Ann. Inst. H. Poincaré, Anal. Non Linéaire 24 (2007) 921–951.
  24. M.E. Taylor, Partial differential equations. I. Basic theory, in Applied Mathematical Sciences 115, Springer-Verlag, New York (1996).
  25. R. Temam, Navier-Stokes equations. Theory and numerical analysis, Studies in Mathematics and its Applications, Vol. 2. North-Holland Publishing Co., Amsterdam, revised edition (1979). With an appendix by F. Thomasset.
  26. H. Triebel, Interpolation theory, function spaces, differential operators. Johann Ambrosius Barth, Heidelberg, second edition (1995).
  27. A. Yagi, Coïncidence entre des espaces d'interpolation et des domaines de puissances fractionnaires d'opérateurs. C. R. Acad. Sci. Paris Sér. I Math. 299 (1984) 173–176.