Stabilization of Navier-Stokes flows.
type: Item
instance of: scholarly article
title: Stabilization of Navier-Stokes flows.
zbMATH Open document ID: 1213.76001
DOI: 10.1007/978-0-85729-043-4
author: Viorel Barbu
published in: Communications and Control Engineering
publication date: 2010-09-29T00:00:00Z
review text: 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.
reviewed by: Ruxandra Stavre
Mathematics Subject Classification ID: 76-02
Mathematics Subject Classification ID: 76D55
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 5793096
zbMATH Keywords: internal stabilization
zbMATH Keywords: boundary stabilization
zbMATH Keywords: stochastic stabilization
zbMATH Keywords: robust stabilizable feedback
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-0-85729-043-4
OpenAlex ID: W4295102232
description: scientific article; zbMATH DE number 5793096