Navier-Stokes Equations and Turbulence

C. Foias; O. Manley; R. Rosa; R. Temam

doi:10.1017/CBO9780511546754

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 analyse 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.

Review of the hardback:'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.'

Source: SIAM Review

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Navier-Stokes Equations and Turbulence

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-xiii

Acknowledgments
pp xiv-xiv

Chapter I - Introduction and Overview of Turbulence
pp 1-24

Chapter II - Elements of the Mathematical Theory of the Navier–Stokes Equations
pp 25-114

Chapter III - Finite Dimensionality of Flows
pp 115-168

Chapter IV - Stationary Statistical Solutions of the Navier–Stokes Equations, Time Averages, and Attractors
pp 169-254

Chapter V - Time-Dependent Statistical Solutions of the Navier–Stokes Equations and Fully Developed Turbulence
pp 255-330

References
pp 331-342

Index
pp 343-347

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