Abstract

This chapter presents an improved boundary feedback controller for the two- and three-dimensional Navier–Stokes equations, in a bounded domain Ω, for prescribed drag and lift coefficients. In order to determine the feedback control law, we consider an extended system coupling the equations governing the Navier–Stokes problem with an equation satisfied by the control on the bluff body, which is a part of the domain boundary. By using the Faedo–Galerkin method and a priori estimation techniques, a boundary control is built. This control law ensures the controllability of the discrete system. Then, a compactness result then allows us to pass to the limit in the non-linear system satisfied by the approximated solutions.

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