Communications and Control Engineering

Stabilization of Navier–Stokes Flows

Authors: Barbu, Viorel

  • Provides applied mathematicians with methods for control of fluids as examples of more general partial-differential equation control problems Gives the control researcher a more sophisticated method of treating flow-control problems than traditional passivity-based approaches Provides conceptual designs for controllers to start readers on the path to their own practical flow control systems

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About this book

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.

About the authors

Professor Barbu is a professor with the University Al.I.Cuza (Romania) and member of Romanian Academy. He had visiting professorship positions with several universities in the USA and Europe including the following: Purdue University, Cincinnati University, Virginia University, Ohio University, Bonn University, University of Bologna. He has published a dozen monographs and 170 research papers in the following fields: nonlinear PDEs, control theory of parameter distributed systems and of Navier–Stokes equations, Stochatic PDEs, integral equations.

Reviews

From the book reviews:

“The book is well written and nice to read. Each chapter is followed by numerous references. Many of the results presented in the book come from papers by the author and co-authors. This book is an excellent introduction to the subject and is recommended to researchers wanting to learn about stabilization problems for parabolic equations.” (Jean-Pierre Raymond, Mathematical Reviews, March, 2015)

Table of contents (5 chapters)

  • Preliminaries

    Barbu, Viorel

    Pages 1-24

  • Stabilization of Abstract Parabolic Systems

    Barbu, Viorel

    Pages 25-85

  • Stabilization of Navier–Stokes Flows

    Barbu, Viorel

    Pages 87-175

  • Stabilization by Noise of Navier–Stokes Equations

    Barbu, Viorel

    Pages 177-236

  • Robust Stabilization of the Navier–Stokes Equation via the H ∞-Control Theory

    Barbu, Viorel

    Pages 237-270

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-0-85729-043-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-0-85729-042-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-1-4471-2610-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Stabilization of Navier–Stokes Flows
Authors
Series Title
Communications and Control Engineering
Copyright
2011
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-0-85729-043-4
DOI
10.1007/978-0-85729-043-4
Hardcover ISBN
978-0-85729-042-7
Softcover ISBN
978-1-4471-2610-2
Series ISSN
0178-5354
Edition Number
1
Number of Pages
XII, 276
Topics