Stabilization of Navier-Stokes Flows

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 reader's 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.

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 Includes supplementary material: sn.pub/extras

Auteur
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 NavierStokes equations, Stochatic PDEs, integral equations.

Contenu
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.