Local Null Controllability of the N-Dimensional Ladyzhenskaya-Smagorinsky with N-1 Scalar Controls

  • Dany Nina Huaman
  • Juan LímacoEmail author
  • Miguel R. Nuñez Chávez
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 17)


This paper deals with the null controllability of a differential turbulence model of the Ladyzhenskaya-Smagorinsky kind. In the equations, we find local and nonlocal nonlinearities: the usual transport terms and a turbulent viscosity that depends on the global in space energy dissipated by the mean flow. We prove that the N-systems are locally null-controllable with N-1 scalar controls in an arbitrary control domain.


Ladyzhenskaya-Smagorinsky Boussinesq Null controllability Carleman inequalities 


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Dany Nina Huaman
    • 1
  • Juan Límaco
    • 1
    Email author
  • Miguel R. Nuñez Chávez
    • 1
  1. 1.Instituto de Matemática e EstatísticaUFFNiterói, RJBrazil

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