GLOBAL CARLEMAN INEQUALITIES FOR STOKES AND PENALIZED STOKES EQUATIONS

In this note we use the result of [22] to prove a global Carleman inequality related to the null controllability of penalized Stokes kind systems. The constants of the obtained Carleman inequality are uniform in terms of the penalization parameter epsilon. It then provides a null control with a uniformly (in epsilon) bounded L-2 norm. With a limiting argument we also deduce a new Carleman inequality for Stokes type system. Thus, we apply theses results to obtain the null controllability of Oseen and Navier-Stokes system in the penalized and in the non penalized cases.