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Local Null Controllability of the N-Dimensional Navier–Stokes System with N − 1 Scalar Controls in an Arbitrary Control Domain

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Abstract

In this paper we deal with the local null controllability of the N-dimensional Navier–Stokes system with internal controls having one vanishing component. The novelty of this work is that no condition is imposed on the control domain.

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References

  1. Alekseev, V.M., Tikhomirov, V.M., Fomin, S.V. : Optimal Control. Translated from the Russian by V. M. Volosov, Contemporary Soviet Mathematics. Consultants Bureau, New York (1987)

  2. Coron J.-M., Guerrero S.: Null controllability of the N-dimensional Stokes system with N-1 scalar controls. J. Differ. Equ. 246, 2908–2921 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Fernández-Cara E., Guerrero S., Imanuvilov O.Yu., Puel J.-P.: Local exact controllability of the Navier–Stokes system. J. Math. Pures Appl. 83, 1501–1542 (2004)

    MathSciNet  MATH  Google Scholar 

  4. Fernández-Cara E., Guerrero S., Imanuvilov O.Yu., Puel J.-P.: Some controllability results for the N-dimensional Navier–Stokes system and Boussinesq systems with N-1 scalar controls. SIAM J. Control Optim. 45, 146–173 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fursikov, A., Imanuvilov, O.Yu.: Controllability of Evolution Equations. Lecture Notes #34, Seoul National University, Korea (1996)

  6. Imanuvilov O.Yu.: Remarks on exact controllability for the Navier–Stokes equations. ESAIM Control Optim. Calc. Var. 6, 39–72 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Imanuvilov O.Yu., Puel J.-P., Yamamoto M.: Carleman estimates for parabolic equations with nonhomogeneous boundary conditions. Chin. Ann. Math. 30(4), 333–378 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ladyzenskaya, O.A.: The mathematical theory of viscous incompressible flow, revised English edition, translated from the Russian by Richard A. Silverlman, Gordon and Breach Science Publishers, New York, London (1963)

  9. Temam R.: Navier–Stokes Equations, Theory ans Numerical Analysis, Stud. Math. Appl., vol. 2. North-Holland, Amsterdam (1977)

    Google Scholar 

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Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Boîte Courrier 187, 75252, Paris Cedex 05, France

    N. Carreño & S. Guerrero

Authors
  1. N. Carreño
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  2. S. Guerrero
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Correspondence to N. Carreño.

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Communicated by O. Pironneau

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Carreño, N., Guerrero, S. 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, 139–153 (2013). https://doi.org/10.1007/s00021-012-0093-2

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  • DOI: https://doi.org/10.1007/s00021-012-0093-2

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