Local exact controllability of micropolar fluids

This paper is devoted to prove the local exact controllability to the trajectories of micropolar fluids with distributed controls supported in small sets. First, we deduce new Carleman inequalities for associated linearized systems which leads to null controllability at any time T > 0. Then, we deduce a local result concerning the exact controllability to the trajectories of the whole nonlinear system. The arguments are presented separately in the two-dimensional and three-dimensional cases, since the required techniques are different.