The internal stabilization of the Stokes–Oseen equation by feedback point controllers

One designs a stabilizable feedback controller for the Stokes–Oseen equation in an open domain O⊂RdO⊂Rd, d≥2d≥2, with support in a finite set of points ξk∈Oξk∈O, j=1,…,Mj=1,…,M. More precisely, Md≥NMd≥N, where NN is the number of unstable eigenvalues of the Stokes–Oseen operator. The controller is expressed in terms of eigenfunctions φj∗,1≤j≤N, of the dual Stokes–Oseen operator.