Free access
Volume 16, Number 3, July-September 2010
Page(s) 677 - 694
Published online 02 July 2009
  1. A. Agrachev and A. Sarychev, Navier–Stokes equations controllability by means of low modes forcing. J. Math. Fluid Mech. 7 (2005) 108–152. [CrossRef] [MathSciNet]
  2. A. Agrachev and A. Sarychev, Controllability of 2D Euler and Navier–Stokes equations by degenerate forcing. Comm. Math. Phys. 265 (2006) 673–697. [CrossRef] [MathSciNet]
  3. J.T. Beale, T. Kato and A. Majda, Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Comm. Math. Phys. 94 (1984) 61–66. [CrossRef] [MathSciNet]
  4. P. Constantin and C. Foias, Navier–Stokes Equations. University of Chicago Press, Chicago, USA (1988).
  5. J.-M. Coron, On the controllability of 2-D incompressible perfect fluids. J. Math. Pures Appl. 75 (1996) 155–188. [MathSciNet]
  6. D.E. Edmunds and H. Triebel, Function Spaces, Entropy Numbers, Differential Operators. Cambridge University Press, Cambridge, UK (1996).
  7. 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]
  8. A.V. Fursikov and O.Yu. Imanuvilov, Exact controllability of the Navier–Stokes and Boussinesq equations. Russian Math. Surveys 54 (1999) 93–146. [CrossRef] [MathSciNet]
  9. O. Glass, Exact boundary controllability of 3-D Euler equation. ESAIM: COCV 5 (2000) 1–44. [CrossRef] [EDP Sciences]
  10. G. Lorentz, Approximation of Functions. Chelsea Publishing Co., New York, USA (1986).
  11. S.S. Rodrigues, Navier–Stokes equation on the rectangle: controllability by means of low mode forcing. J. Dyn. Control Syst. 12 (2006) 517–562. [CrossRef] [MathSciNet]
  12. A. Shirikyan, Approximate controllability of three-dimensional Navier–Stokes equations. Comm. Math. Phys. 266 (2006) 123–151. [CrossRef] [MathSciNet]
  13. A. Shirikyan, Exact controllability in projections for three-dimensional Navier–Stokes equations. Ann. Inst. H. Poincaré, Anal. Non Linéaire 24 (2007) 521–537.
  14. A. Shirikyan, Euler equations are not exactly controllable by a finite-dimensional external force. Physica D 237 (2008) 1317–1323. [CrossRef] [MathSciNet]
  15. M.E. Taylor, Partial Differential Equations, III. Springer-Verlag, New York (1996).
  16. R. Temam, Local existence of Formula solution of the Euler equation of incompressible perfect fluids. Lect. Notes Math. 565 (1976) 184–194. [CrossRef]