Navier-Stokes Equations and Turbulence

by C. Foias, O. Manley, R. Rosa, R. Temam

Overview

This book presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. It 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 that had been arrived at earlier by phenomenological arguments. Appendices give full details of the mathematical proofs and subtleties.

Product Details

ISBN-13:	9780521360326
Publisher:	Cambridge University Press
Publication date:	08/27/2001
Series:	Encyclopedia of Mathematics and its Applications , #83
Pages:	364
Product dimensions:	6.14(w) x 9.21(h) x 0.83(d)

Table of Contents

Preface; Acknowledgements; 1. Introduction and overview of turbulence; 2. Elements of the mathematical theory of the Navier–Stokes equations; 3. Finite dimensionality of flows; 4. Stationary statistical solutions of the Navier–Stokes equations, time averages and attractors; 5. Time-dependent statistical solutions of the Navier–Stokes equations and fully developed turbulence; References; Index.

Editorial Reviews

"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

"Such a book by experts who are the originators and major contributors to the area of connections between the Navier-Stokes equations and the conventional theory of turbulence is highly welcomed. The authors have done a great service to the community. The book belongs on the bookshelf of anyone who is seriously interested in the question of what the Navier-Stokes equations can tell us about turbulence from an analytic point of view." Matematical Reviews

"...this is a book that can be read with pleasure by college seniors, graduate students, or professors familiar with the subject." Physics Today

"The book is written in a clear, comprehensive style with full proofs and contains numerous mathematical technicalities. The topics are developed with almost self-contained chapters, making the difficult matter easily understandable. It can be recommended to physicists and geophysicists who seriously seem an understanding of the mathematical aspects of turbulence theory." Pure and Applied Geophysics

From the Publisher