Free Access
Volume 21, Number 3, July-September 2015
Page(s) 723 - 756
Published online 13 May 2015
  1. T. Aubin, Nonlinear Analysis on Manifolds. Monge-Ampère Equations, number 252. Grundlehren der Mathematischen Wissenschaften. Springer (1982). [Google Scholar]
  2. M. Badra and T. Takahashi, Stabilization of parabolic nonlinear systems with finite dimensional feedback or dynamical controllers: Application to the Navier–Stokes system. SIAM J. Control Optim. 49 (2011) 420–463. [CrossRef] [MathSciNet] [Google Scholar]
  3. V. Barbu, Stabilization of Navier–Stokes equations by oblique boundary feedback controllers. SIAM J. Control Optim. 50 (2012) 2288–2307. [CrossRef] [MathSciNet] [Google Scholar]
  4. V. Barbu, I. Lasiecka and R. Triggiani, Abstract settings for tangential boundary stabilization of Navier–Stokes equations by high- and low-gain feedback controllers. Nonlinear Anal. 64 (2006) 2704–2746. [CrossRef] [MathSciNet] [Google Scholar]
  5. V. Barbu, S.S. Rodrigues and A. Shirikyan, Internal exponential stabilization to a nonstationary solution for 3D Navier–Stokes equations. SIAM J. Control Optim. 49 (2011) 1454–1478. [CrossRef] [MathSciNet] [Google Scholar]
  6. V. Barbu and R. Triggiani, Internal stabilization of Navier–Stokes equations with finite-dimensional controllers. Indiana Univ. Math. J. 53 (2004) 1443–1494. [CrossRef] [MathSciNet] [Google Scholar]
  7. H. Cartan, Formes Différentielles. Collection Méthodes. Hermann Paris (1967). [Google Scholar]
  8. J.B. Conway, A Course in Functional Analysis, number 96. Grad. Texts Math. Springer, 2nd edition (1985). [Google Scholar]
  9. M.P. do Carmo, Differential Forms and Applications. Universitext, Springer (1994). [Google Scholar]
  10. J. Dodziuk, Sobolev spaces of differential forms and the Rham–Hodge isomorphism. J. Differ. Geom. 16 (1981) 63–73. [Google Scholar]
  11. N. Dunford and J.T. Schwartz, Linear Operators. Part I: General Theory. Number VII, 4th printing. Pure Appl. Math. Interscience Publishers. John Wiley & Sons (1967). [Google Scholar]
  12. 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]
  13. 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]
  14. A.V. Fursikov, M.D. Gunzburger and L.S. Hou, Trace theorems for three-dimensional, time-dependent solenoidal vector fields and their applications. Trans. Amer. Math. Soc. 354 (2002) 1079–1116. [CrossRef] [MathSciNet] [Google Scholar]
  15. A.V. Fursikov and O. Yu. Imanuvilov, Local exact boundary controllability of the Boussinesq equation. SIAM J. Control Optim. 36 (1998) 391–421. [CrossRef] [MathSciNet] [Google Scholar]
  16. A.V. Fursikov and O. Yu. Imanuvilov, Exact controllability of the Navier–Stokes and Boussinesq equations. Russian Math. Surveys 54 (1999) 565–618. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. González-Burgos, S. Guerrero and J.-P. Puel. Local exact controllability to the trajectories of the Boussinesq system via a fictitious control on the divergence equation. Commun. Pure Appl. Anal. 8 (2009) 311–333. [MathSciNet] [Google Scholar]
  18. P. Grisvard, Caractérisation de quelques espaces d’interpolation. Arch. Ration. Mech. Anal. 25 (1967) 40–63. [CrossRef] [MathSciNet] [Google Scholar]
  19. O. Yu. Imanuvilov, Remarks on exact controllability for the Navier–Stokes equations. ESAIM: COCV 6 (2001) 39–72. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  20. J. Jost, Riemannian Geometry and Geometric Analysis. Univesitext, Springer, 4th edition (2005). [Google Scholar]
  21. A. Kröner and S.S. Rodrigues, Remarks on the internal exponential stabilization to a nonstationary solution for 1D Burgers equations. RICAM-Report No. 2014-02 (submitted) (2014). Available at [Google Scholar]
  22. J.-L. Lions. Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod et Gauthier–Villars (1969). [Google Scholar]
  23. J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, vol. I, number 181. Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen. Springer-Verlag (1972). [Google Scholar]
  24. J. Nečas, Les Méthodes Directes en Théorie des Équations Elliptiques. Masson & Cie Éditeurs (1967). [Google Scholar]
  25. J.-P. Raymond and L. Thevenet, Boundary feedback stabilization of the two-dimensional Navier–Stokes equations with finite-dimensional controllers. Discrete Contin. Dyn. Syst. 27 (2010) 1159–1187. [CrossRef] [MathSciNet] [Google Scholar]
  26. S.S. Rodrigues, Methods of Geometric Control Theory in Problems of Mathematical Physics. Ph.D. thesis, Universidade de Aveiro, Portugal (2008). Available at [Google Scholar]
  27. S.S. Rodrigues, Local exact boundary controllability of 3D Navier–Stokes equations. Nonlinear Anal. 95 (2014) 175–190. [CrossRef] [MathSciNet] [Google Scholar]
  28. G. Schwarz, Hodge Decomposition – A Method for Solving Boundary Value Problems, Number 1607 in Lecture Notes in Mathematics. Springer (1995). [Google Scholar]
  29. A. Shirikyan, Control and mixing for 2D Navier–Stokes equations with space-time localised noise (2011). Available at [Google Scholar]
  30. K.T. Smith, Primer of Modern Analysis, Undergraduate Texts in Mathematics. Springer (1983). [Google Scholar]
  31. M.E. Taylor, Partial Differential Equations I – Basic Theory, number 115. Appl. Math. Sci. Springer (1997). (corrected 2nd printing). [Google Scholar]
  32. R. Temam, Navier–Stokes Equations and Nonlinear Functional Analysis, number 66. CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, 2nd edition (1995). [Google Scholar]
  33. R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, number 68. Appl. Math. Sci. Springer, 2nd edition (1997). [Google Scholar]
  34. R. Temam, Navier–Stokes Equations: Theory and Numerical Analysis. AMS Chelsea Publishing, reprint of the 1984 edition (2001). [Google Scholar]
  35. A. Trautman, Differential Geometry for Physicists, Stony Brook Lectures. Monogr. Textbooks Phys. Sci. Bibliopolis (1984). [Google Scholar]
  36. A.J. Weir, Lebesgue Integration and Measure. Cambridge University Press (1973). [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.