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

Johann Radon Institute for Computational and Applied Mathematics (RICAM), ÖAW, Altenbergerstraße 69, 4040 Linz, Austria
sergio.rodrigues@oeaw.ac.at

Received: 24 October 2013
Revised: 11 July 2014

Abstract

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.