Stabilization of Navier-Stokes flows.
The purpose of the paper is to analyse the stabilization of Navier-Stokes flows. One of its main results is that the equilibrium solutions of Navier-Stokes equations are exponentially stabilizable by finite-dimensional feedback controllers with support in the interior of the domain or on the boundary. The author also discusses the stochastic stabilization and robustness of stabilizable feedbacks. This analysis provides a pattern for the design of efficient stabilizable feedback controllers in problems of practical interest. The book is organized as follows. After some preliminaries, a few stabilization techniques for nonlinear parabolic-like equations in Hilbert spaces are presented. In Chapter 3 the feedback stabilization of stationary solutions of Navier-Stokes equations are discussed. The next two chapters deal with the stochastic stabilization of Navier-Stokes equations and with the robust stabilization of Navier-Stokes equations via the \(H^\infty\)-control theory, respectively.
scientific article; zbMATH DE number 5793096