Stabilization of Navier–Stokes Flows (eBook)

Viorel Barbu (Autor)

eBook Download: PDF

2010 | 2011
XII, 276 Seiten
Springer London (Verlag)
978-0-85729-043-4 (ISBN)

Infos

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.

Inhalt

Preface 6
Contents 8
Symbols and Notation 11
Preliminaries 12
Banach Spaces and Linear Operators 12
Sobolev Spaces and Elliptic Boundary Value Problems 14
The Semigroups of Class C0 23
The Nonlinear Cauchy Problem 25
Strong Solutions to Navier-Stokes Equations 28
Stabilization of Abstract Parabolic Systems 36
Nonlinear Parabolic-like Systems 36
Internal Stabilization of Linearized System 41
Boundary Stabilization of Linearized System 53
Stabilization by Noise of the Linearized Systems 56
Internal Stabilization of Nonlinear Parabolic-like Systems 63
Stabilization of Time-periodic Flows 77
Comments to Chap. 2 96
Stabilization of Navier-Stokes Flows 97
The Navier-Stokes Equations of Incompressible Fluid Flows 97
The Spectral Properties of the Stokes-Oseen Operator 101
Internal Stabilization via Spectral Decomposition 103
The Tangential Boundary Stabilization of Navier-Stokes Equations 129
Normal Stabilization of a Plane-periodic Channel Flow 152
Internal Stabilization of Time-periodic Flows 166
The Numerical Implementation of Stabilizing Feedback 169
Unique Continuation and Generic Properties of Eigenfunctions 173
Comments on Chap. 3 184
Stabilization by Noise of Navier-Stokes Equations 186
Internal Stabilization by Noise 186
Stabilization of the Stokes-Oseen Equation by Impulse Feedback Noise Controllers 210
The Tangential Boundary Stabilization by Noise 220
Stochastic Stabilization of Periodic Channel Flows by Noise Wall Normal Controllers 226
Stochastic Processes 239
Comments on Chap. 4 245
Robust Stabilization of the Navier-Stokes Equation via the Hinfty-Control Theory 246
The State-space Formulation of the Hinfty-Control Problem 246
The Hinfty-Control Problem for the Stokes-Oseen System 257
The Hinfty-Control Problem for the Navier-Stokes Equations 261
The Hinfty-Control Problem for Boundary Control Problem 276
Comments on Chap. 5 279
References 280
Index 284

Produkt-Details

• Erscheint lt. Verlag: 19.11.2010
• Reihe/Serie: Communications and Control Engineering
• Reihe/Serie: Communications and Control Engineering
• Zusatzinfo: XII, 276 p.
• Verlagsort: London
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Naturwissenschaften ► Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Controller • Feedback • fluid- and aerodynamics • Navier-Stokes • Partial differential equations • Stabilization • stochastic
• ISBN-10: 0-85729-043-6 / 0857290436
• ISBN-13: 978-0-85729-043-4 / 9780857290434