BOUNDARY CONTROLLABILITY OF A STATIONARY STOKES SYSTEM WITH LINEAR CONVECTION OBSERVED ON AN INTERIOR CURVE

We study the approximate controllability of a. stationary Stokes syste m with linearized convection in a bounded domain of R-N. The control a cts on a part of the boundary and the velocity field is observed on an interior curve (N= 2) or surface (N=3). We establish the L-2-approxim ate controllability under certain compatibility conditions and suitabl e geometrical assumptions on the curve or surface. We build controls o f minimal L-2-norm by duality. To compute the control, we propose a nu merical method, based on duality techniques, consisting in the minimiz ation of a nonquadratic functional coupled to a Stakes system. It is t ested in several situations leading to interesting numerical results.