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 ⊂ R d , d ≥ 2 , with support in a finite set of points ξ k ∈ O , j = 1 , … , M . More precisely, M d ≥ N , where N is the number of unstable eigenvalues of the Stokes–Oseen operator. The controller is expressed in terms of eigenfunctions φ j ∗ , 1 ≤ j ≤ N , of the dual Stokes–Oseen operator.