Stabilization of Navier–Stokes Flows

  • Viorel Barbu

Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Viorel Barbu
    Pages 1-24
  3. Viorel Barbu
    Pages 87-175
  4. Back Matter
    Pages 271-276

About this book

Introduction

Stabilization of Navier–Stokes Flows presents recent notable progress in the mathematical theory of stabilization of Newtonian fluid flows. Finite-dimensional feedback controllers are used to stabilize exponentially the equilibrium solutions of Navier–Stokes equations, reducing or eliminating turbulence. Stochastic stabilization and robustness of stabilizable feedback are also discussed. The text treats the questions:

• What is the structure of the stabilizing feedback controller?

• How can it be designed using a minimal set of eigenfunctions of the Stokes–Oseen operator?

The analysis developed here provides a rigorous pattern for the design of efficient stabilizable feedback controllers to meet the needs of practical problems and the conceptual controllers actually detailed will render the reader’s task of application easier still. Stabilization of Navier–Stokes Flows avoids the tedious and technical details often present in mathematical treatments of control and Navier–Stokes equations and will appeal to a sizeable audience of researchers and graduate students interested in the mathematics of flow and turbulence control and in Navier-Stokes equations in particular. The chief points of linear functional analysis, linear algebra, probability theory and general variational theory of elliptic, parabolic and Navier–Stokes equations are reviewed in an introductory chapter and at the end of chapters 3 and 4.

Keywords

Controller Feedback Navier-Stokes Stabilization Stochastic

Authors and affiliations

  • Viorel Barbu
    • 1
  1. 1.Fac. MathematicsAl. I. Cuza UniversityIasiRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-85729-043-4
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Engineering
  • Print ISBN 978-0-85729-042-7
  • Online ISBN 978-0-85729-043-4
  • Series Print ISSN 0178-5354
  • About this book