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

Abstract

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.