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Navier-Stokes Equations and Turbulence

By: C. Foias, R. Rosa, R. Temam, O. Manley

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Hardcover | 24 October 2001

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Hardcover
364 Pages

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23.5 x 16.5 x 3.0

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This book aims to bridge the gap between practising mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The book is the result of many years of research by the authors to analyze turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier-Stokes equations what had been arrived at earlier by phenomenological arguments. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience. Each chapter is accompanied by appendices giving full details of the mathematical proofs and subtleties. This unique presentation should ensure a volume of interest to mathematicians, engineers, and physicists.

Industry Reviews

From the hardback review: 'The authors are distinguished researchers who have made fundamental contributions to mathematical fluid dynamics over their careers. The aim of the volume is, in the authors' own words, 'to let physicists and engineers know about existing mathematical tools from which they might benefit [and] ... to help mathematicians learn what physical turbulence is about so they can focus their research on problems of interest of physics. ...' The monograph is a substantial step toward bringing together physicists' and engineers' theoretical treatments of turbulence with mathematicisns' rigorous analysis of the Navier-Strokes equations and their solutions. In this regard the book is the first of its type. This book is far from elementary, but the authors' efforts to make it accessible on several levels make it a valuable and unique resource for researchers interested in both turbulence theory and mathematical analysis. I hope, as do the authors, that this work will help to establish new and constructive lines of communication between these two communities.' SIAM Review

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You Can Find This Book In

Non-Fiction Science Physics Classical Mathematics Fluid Mechanics Science in General Maths for Scientists Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Fluids Hydraulics & Pneumatics

Mathematics Applied Mathematics Medicine Medicine in General

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Paperback

Published: 12th June 2008

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Preface	p. ix
Acknowledgments	p. xiv
Introduction and Overview of Turbulence	p. 1
Introduction	p. 1
Viscous Fluids. The Navier-Stokes Equations	p. 1
Turbulence: Where the Interests of Engineers and Mathematicians Overlap	p. 5
Elements of the Theories of Turbulence of Kolmogorov and Kraichnan	p. 9
Function Spaces, Functional Inequalities, and Dimensional Analysis	p. 14
Elements of the Mathematical Theory of the Navier-Stokes Equations	p. 25
Introduction	p. 25
Energy and Enstrophy	p. 27
Boundary Value Problems	p. 29
Helmholtz-Leray Decomposition of Vector Fields	p. 36
Weak Formulation of the Navier-Stokes Equations	p. 39
Function Spaces	p. 41
The Stokes Operator	p. 49
Existence and Uniqueness of Solutions: The Main Results	p. 55
Analyticity in Time	p. 62
Gevrey Class Regularity and the Decay of the Fourier Coefficients	p. 67
Function Spaces for the Whole-Space Case	p. 75
The No-Slip Case with Moving Boundaries	p. 77
Dissipation Rate of Flows	p. 80
Nondimensional Estimates and the Grashof Number	p. 87
Mathematical Complements	p. 90
Proofs of Technical Results in Chapter II	p. 102
Finite Dimensionality of Flows	p. 115
Introduction	p. 115
Determining Modes	p. 123
Determining Nodes	p. 131
Attractors and Their Fractal Dimension	p. 137
Approximate Inertial Manifolds	p. 150
Proofs of Technical Results in Chapter III	p. 156
Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors	p. 169
Introduction	p. 169
Mathematical Framework, Definition of Stationary Statistical Solutions, and Banach Generalized Limits	p. 172
Invariant Measures and Stationary Statistical Solutions in Dimension 2	p. 183
Stationary Statistical Solutions in Dimension 3	p. 189
Attractors and Stationary Statistical Solutions	p. 194
Average Transfer of Energy and the Cascades in Turbulent Flows	p. 198
New Concepts and Results Used in Chapter IV	p. 218
Proofs of Technical Results in Chapter IV	p. 227
A Mathematical Complement: The Accretivity Property in Dimension 3	p. 244
Time-Dependent Statistical Solutions of the Navier-Stokes Equations and Fully Developed Turbulence	p. 255
Introduction	p. 255
Time-Dependent Statistical Solutions on Bounded Domains	p. 262
Homogeneous Statistical Solutions	p. 271
Reynolds Equation for the Average Flow	p. 280
Self-Similar Homogeneous Statistical Solutions	p. 283
Relation with and Application to the Conventional Theory of Turbulence	p. 295
Some Concluding Remarks	p. 310
Proofs of Technical Results in Chapter V	p. 312
References	p. 331
Index	p. 343
Table of Contents provided by Syndetics. All Rights Reserved.

Navier-Stokes Equations and Turbulence

At a Glance

Hardcover

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Paperback

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