Boundary observability inequalities for the 3D Oseen–Stokes system and applications

Controllability properties for the Navier–Stokes system are closely related to observability properties for the adjoint Oseen–Stokes system; boundary observability inequalities are derived, for that adjoint system, that will be appropriate to deal with suitable constrained controls, like finite-dimensional controls supported in a given subset of the boundary. As an illustration, new boundary controllability results for the Oseen–Stokes system are derived. Finally, some further plausible consequences of the derived inequalities, concerning the Navier–Stokes system, are discussed.