EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 15 / No 4 (October-December 2009) ESAIM: COCV, 15 4 (2009) 934-968 References
Free Access
Issue
ESAIM: COCV
Volume 15, Number 4, October-December 2009
Page(s) 934 - 968
DOI https://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). [Google Scholar]
  2. M. Badra, Lyapunov function and local feedback boundary stabilization of the Navier-Stokes equations. SIAM J. Contr. Opt. (to appear). [Google Scholar]
  3. V. Barbu, Feedback stabilization of Navier-Stokes equations. ESAIM: COCV 9 (2003) 197–206 (electronic). [EDP Sciences] [Google Scholar]
  4. V. Barbu, I. Lasiecka and R. Triggiani, Tangential boundary stabilization of Navier-Stokes equations, Memoirs of the American Mathematical Society 181. AMS (2006). [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  7. P. Constantin and C. Foias, Navier-Stokes equations, Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, USA (1988) [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  10. H. Fujita and H. Morimoto, On fractional powers of the Stokes operator. Proc. Japan Acad. 46 (1970) 1141–1143. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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). [Google Scholar]
  15. P. Grisvard, Caractérisation de quelques espaces d'interpolation. Arch. Rational Mech. Anal. 25 (1967) 40–63. [Google Scholar]
  16. P. Grisvard, Elliptic problems in nonsmooth domains, in Monographs and Studies in Mathematics, Vol. 24, Pitman (Advanced Publishing Program), Boston, MA, USA (1985). [Google Scholar]
  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). [Google Scholar]
  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). [Google Scholar]
  19. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. I. Dunod, Paris (1968). [Google Scholar]
  20. A. Pazy, Semigroups of linear operators and applications to partial differential equations, in Applied Mathematical Sciences 44, Springer-Verlag, New York (1983). [Google Scholar]
  21. J.-P. Raymond, Feedback boundary stabilization of the two dimensional Navier-Stokes equations. SIAM J. Contr. Opt. 45 (2006) 790–828. [Google Scholar]
  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] [Google Scholar]
  23. J.-P. Raymond, Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions. Ann. Inst. H. Poincaré, Anal. Non Linéaire 24 (2007) 921–951. [Google Scholar]
  24. M.E. Taylor, Partial differential equations. I. Basic theory, in Applied Mathematical Sciences 115, Springer-Verlag, New York (1996). [Google Scholar]
  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. [Google Scholar]
  26. H. Triebel, Interpolation theory, function spaces, differential operators. Johann Ambrosius Barth, Heidelberg, second edition (1995). [Google Scholar]
  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. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.