Boundary Observability Inequalities for the Oseen--Stokes System

Sérgio Rodrigues^*

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 we use one of them to derive a new boundary controllability result for the Oseen--Stokes system. Finally, we discuss some further plausible consequences of the derived inequalities, concerning the boundary feedback stabilization of the Navier--Stokes system.

Mathematics Subject Classification: 35Q35 93B07

Keywords: Navier--Stokes system; boundary observability inequalities

Minisymposion: On Optimal Feedback Control for Partial Differential Equations: Theory and Numerical Methods