Some Controllability Results forthe N-Dimensional Navier--Stokes and Boussinesq systems with N-1 scalar controls

Enrique Fernández-Cara, Sergio Guerrero, Oleg Yu. Imanuvilov, Jean-Pierre Puel
2006 SIAM Journal of Control and Optimization  
In this paper we deal with some controllability problems for systems of the Navier-Stokes and Boussinesq kind with distributed controls supported in small sets. Our main aim is to control N -dimensional systems (N + 1 scalar unknowns in the case of the Navier-Stokes equations) with N − 1 scalar control functions. In a first step, we present some global Carleman estimates for suitable adjoint problems of linearized Navier-Stokes and Boussinesq systems. In this way, we obtain null controllability
more » ... ull controllability properties for these systems. Then, we deduce results concerning the local exact controllability to the trajectories. We also present (global) null controllability results for some (truncated) approximations of the Navier-Stokes equations.
doi:10.1137/04061965x fatcat:f6xzzp44bvbxvgabssv7euh3wi