Stabilization of Navier–Stokes Flows

1. Front Matter

   Pages I-XI

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2. Preliminaries

   • Viorel Barbu

   Pages 1-24

3. Stabilization of Abstract Parabolic Systems

   • Viorel Barbu

   Pages 25-85

4. Stabilization of Navier–Stokes Flows

   • Viorel Barbu

   Pages 87-175

5. Stabilization by Noise of Navier–Stokes Equations

   • Viorel Barbu

   Pages 177-236

6. Robust Stabilization of the Navier–Stokes Equation via the H ^∞-Control Theory

   • Viorel Barbu

   Pages 237-270

7. Back Matter

   Pages 271-276

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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 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.

• Controller
• Feedback
• Navier-Stokes
• Stabilization
• Stochastic
• fluid- and aerodynamics
• partial differential equations

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)

• Fac. Mathematics, Al. I. Cuza University, Iasi, Romania

  Viorel Barbu

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.

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