Barbu Stabilization of Navier-Stokes Flows

1. Auflage 2010
ISBN: 978-0-85729-043-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 276 Seiten

Reihe: Communications and Control Engineering

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.

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.

Autoren/Hrsg.

Barbu, Viorel

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Symbols and Notation;11
4;Preliminaries;12
4.1;Banach Spaces and Linear Operators;12
4.2;Sobolev Spaces and Elliptic Boundary Value Problems;14
4.3;The Semigroups of Class C0;23
4.4;The Nonlinear Cauchy Problem;25
4.5;Strong Solutions to Navier-Stokes Equations;28
5;Stabilization of Abstract Parabolic Systems;36
5.1;Nonlinear Parabolic-like Systems;36
5.2;Internal Stabilization of Linearized System;41
5.3;Boundary Stabilization of Linearized System;53
5.4;Stabilization by Noise of the Linearized Systems;56
5.5;Internal Stabilization of Nonlinear Parabolic-like Systems;63
5.6;Stabilization of Time-periodic Flows;77
5.7;Comments to Chap. 2;96
6;Stabilization of Navier-Stokes Flows;97
6.1;The Navier-Stokes Equations of Incompressible Fluid Flows;97
6.2;The Spectral Properties of the Stokes-Oseen Operator;101
6.3;Internal Stabilization via Spectral Decomposition;103
6.4;The Tangential Boundary Stabilization of Navier-Stokes Equations;129
6.5;Normal Stabilization of a Plane-periodic Channel Flow;152
6.6;Internal Stabilization of Time-periodic Flows;166
6.7;The Numerical Implementation of Stabilizing Feedback;169
6.8;Unique Continuation and Generic Properties of Eigenfunctions;173
6.9;Comments on Chap. 3;184
7;Stabilization by Noise of Navier-Stokes Equations;186
7.1;Internal Stabilization by Noise;186
7.2;Stabilization of the Stokes-Oseen Equation by Impulse Feedback Noise Controllers;210
7.3;The Tangential Boundary Stabilization by Noise;220
7.4;Stochastic Stabilization of Periodic Channel Flows by Noise Wall Normal Controllers;226
7.5;Stochastic Processes;239
7.6;Comments on Chap. 4;245
8;Robust Stabilization of the Navier-Stokes Equation via the Hinfty-Control Theory;246
8.1;The State-space Formulation of the Hinfty-Control Problem;246
8.2;The Hinfty-Control Problem for the Stokes-Oseen System;257
8.3;The Hinfty-Control Problem for the Navier-Stokes Equations;261
8.4;The Hinfty-Control Problem for Boundary Control Problem;276
8.5;Comments on Chap. 5;279
9;References;280
10;Index;284