Stabilization of NavierStokes Flows [Paperback]

Stabilization of NavierStokes 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 NavierStokes 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 readers task of application easier still.Stabilization of NavierStokes Flows avoids the tedious and technical details often present in mathematical treatments of control and NavierStokes 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.

This volume presents recent and notable progress in the mathematical theory of stabilization of Newtonian fluid flows. It avoids the tedious technical details often seen in mathematical treatments of the subject and will thus appeal to a wide range of readers.

Preliminaries.- Stabilization of Abstract Parabolic Systems.- Stabilization of NavierStokes Flows.- Stabilization by Noise of NavierStokes Equations.- Robust Stabilization of the NavierStokes Equation via the H-infinity Control Theory.

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)Professor Barbu is a professor with the Universilóä