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All issues Volume 20 / No 4 (October-December 2014) ESAIM: COCV, 20 4 (2014) 1181-1202 References
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Issue
ESAIM: COCV
Volume 20, Number 4, October-December 2014
Page(s) 1181 - 1202
DOI https://doi.org/10.1051/cocv/2014011
Published online 08 August 2014
  1. V.M. Alekseev, V.M. Tikhomirov and S.V. Fomin, Optimal control. Contemporary Soviet Mathematics. Translated from the Russian by V.M. Volosov. Consultants Bureau, New York (1987). [Google Scholar]
  2. F.D. Araruna, E. Fernández-Cara and D.A. Souza, On the control of the Burgers-alpha model. Adv. Differ. Eq. 18 (2013) 935–954. [Google Scholar]
  3. N. Carreño and S. Guerrero, Local null controllability of the N-dimensional Navier−Stokes system with N − 1 scalar controls in an arbitrary control domain. J. Math. Fluid Mech. 15 (2013) 139–153. [CrossRef] [MathSciNet] [Google Scholar]
  4. A. Cheskidov, D.D. Holm, E. Olson and E.S. Titi, On a Leray-α model of turbulence. Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci. 461 (2005) 629–649. [CrossRef] [Google Scholar]
  5. P. Constantin and C. Foias, Navier−Stokes equations, Chicago Lect. Math. University of Chicago Press, Chicago, IL (1988). [Google Scholar]
  6. J.-M. Coron, On the controllability of the 2-D incompressible Navier−Stokes equations with the Navier slip boundary conditions. ESAIM: COCV 1 (1995/96) 35–75. [Google Scholar]
  7. 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]
  8. J.-M. Coron and S. Guerrero, Null controllability of the N-dimensional Stokes system with N − 1 scalar controls. J. Differ. Eq. 246 (2009) 2908–2921. [Google Scholar]
  9. J.-M. Coron and P. Lissy, Local null controllability of the three-dimensional navier−stokes system with a distributed control having two vanishing components. Preprint (2012). [Google Scholar]
  10. R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Tome 1, Collection du Commissariat à l’Énergie Atomique: Série Scientifique. [Collection of the Atomic Energy Commission: Science Series]. Masson, Paris (1984). [Google Scholar]
  11. S. Ervedoza, O. Glass, S. Guerrero and J.-P. Puel, Local exact controllability for the one-dimensional compressible Navier−Stokes equation. Arch. Ration. Mech. Anal. 206 (2012) 189–238. [CrossRef] [MathSciNet] [Google Scholar]
  12. E. Fernández-Cara and S. Guerrero, Null controllability of the Burgers system with distributed controls. Systems Control Lett. 56 (2007) 366–372. [CrossRef] [MathSciNet] [Google Scholar]
  13. E. Fernández-Cara, S. Guerrero, O.Y. 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]
  14. E. Fernández-Cara, S. Guerrero, O.Y. Imanuvilov and J.-P. Puel, Some controllability results for the N-dimensional Navier−Stokes and Boussinesq systems with N − 1 scalar controls. SIAM J. Control Optim. 45 (2006) 146–173. [CrossRef] [MathSciNet] [Google Scholar]
  15. H. Fujita and T. Kato, On the Navier−Stokes initial value problem. I. Arch. Rational Mech. Anal. 16 (1964) 269–315. [CrossRef] [MathSciNet] [Google Scholar]
  16. H. Fujita and H. Morimoto, On fractional powers of the Stokes operator. Proc. Japan Acad. 46 (1970) 1141–1143. [CrossRef] [MathSciNet] [Google Scholar]
  17. A.V. Fursikov and O.Y. Imanuvilov, Exact controllability of the Navier−Stokes and Boussinesq equations. Uspekhi Mat. Nauk 54 (1999) 93–146. [Google Scholar]
  18. A.V. Fursikov and O.Y. Imanuvilov, Controllability of evolution equations, vol. 34 of Lect. Notes Ser. Seoul National University Research Institute of Mathematics Global Analysis Research Center, Seoul (1996). [Google Scholar]
  19. J.D. Gibbon and D.D. Holm, Estimates for the LANS-α, Leray-α and Bardina models in terms of a Navier−Stokes Reynolds number. Indiana Univ. Math. J. 57 (2008) 2761–2773. [CrossRef] [MathSciNet] [Google Scholar]
  20. O. Glass and S. Guerrero, On the uniform controllability of the Burgers equation. SIAM J. Control Optim. 46 (2007) 1211–1238. [Google Scholar]
  21. 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]
  22. S. Guerrero, Local exact controllability to the trajectories of the Boussinesq system. Ann. Inst. Henri Poincaré Anal. Non Linéaire 23 (2006) 29–61. [CrossRef] [Google Scholar]
  23. S. Guerrero and O.Y. Imanuvilov, Remarks on global controllability for the Burgers equation with two control forces. Annal. Inst. Henri Poincaré Anal. Non Linéaire 24 (2007) 897–906. [CrossRef] [Google Scholar]
  24. S. Guerrero, O.Y. Imanuvilov and J.-P. Puel, A result concerning the global approximate controllability of the Navier−Stokes system in dimension 3. J. Math. Pures Appl. 98 (2012) 689–709. [CrossRef] [Google Scholar]
  25. O.Y. Imanuvilov, Remarks on exact controllability for the Navier−Stokes equations. ESAIM: COCV 6 (2001) 39–72. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  26. J. Leray, Sur le mouvement d’un liquide visqueux emplissant l’espace. Acta Math. 63 (1934) 193–248. [Google Scholar]
  27. J.-L. Lions, Remarques sur la controlâbilite approchée, in Spanish-French Conference on Distributed-Systems Control, Spanish. Univ. Málaga, Málaga (1990) 77–87. [Google Scholar]
  28. J. Simon, Compact sets in the space Lp(0,T;B). Annal. Mat. Pura Appl. 146 (1987) 65–96. [Google Scholar]
  29. L. Tartar, An introduction to Sobolev spaces and interpolation spaces, vol. 3 of Lect. Notes of the Unione Matematica Italiana. Springer, Berlin (2007). [Google Scholar]
  30. R. Temam, Navier−Stokes equations. Theory and numerical analysis. Vol. 2 of Studies Math. Appl. North-Holland Publishing Co., Amsterdam (1977). [Google Scholar]

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