**AMS Chelsea Publishing**

Volume: 343;
1984;
408 pp;
Hardcover

MSC: Primary 76;
Secondary 65; 35

Print ISBN: 978-0-8218-2737-6

Product Code: CHEL/343.H

List Price: $68.00

Individual Member Price: $61.20

**Electronic ISBN: 978-1-4704-2994-2
Product Code: CHEL/343.H.E**

List Price: $68.00

Individual Member Price: $61.20

# Navier–Stokes Equations: Theory and Numerical Analysis

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*Roger Temam*

This book was originally published in 1977 and has since been
reprinted four times (the last reprint was in 1984). The current
volume is reprinted and fully retypeset by the AMS. It is very close
in content to the 1984 edition. The book presents a systematic
treatment of results on the theory and numerical analysis of the
Navier-Stokes equations for viscous incompressible fluids. Considered
are the linearized stationary case, the nonlinear stationary case,
and the full nonlinear time-dependent case. The relevant mathematical
tools are introduced at each stage.

The new material in this book is Appendix III, reproducing a survey article
written in 1998. This appendix contains a few aspects not addressed in the
earlier editions, in particular a short derivation of the Navier-Stokes
equations from the basic conservation principles in continuum mechanics,
further historical perspectives, and indications on new developments in the
area. The appendix also surveys some aspects of the related Euler equations
and the compressible Navier-Stokes equations. Readers are advised to peruse
this appendix before reading the core of the book.

This book presents basic results on the theory of Navier-Stokes
equations and, as such, continues to serve as a comprehensive
reference source on the topic.

#### Table of Contents

# Table of Contents

## Navier-Stokes Equations: Theory and Numerical Analysis

- Cover Cover11
- Title page iii4
- Dedication v6
- Contents vii8
- Preface to the AMS-Chelsea edition ix10
- Preface to the third (revised) edition xi12
- Foreword xiii14
- The steady-state Stokes equations 116
- Steady-state Navier–Stokes equations 105120
- The evolution Navier–Stokes equation 167182
- Appendix I: Properties of the curl operator and application to the steady-state Navier–Stokes equations 311326
- Appendix II: Implementation of non-conforming linear finite elements (Approximation APX5—Two-dimensional case) 321336
- Appendix III: Some developments on Navier–Stokes equations in the second half of the 20th century 337352
- Bibliography to Appendix III 363378
- Comments 381396
- Additional comments to the revised edition 387402
- Bibliography 389404
- Index 407422
- Back Cover Back Cover1426

#### Readership

Graduate students and research mathematicians interested in fluid mechanics, linear and nonlinear PDEs, and numerical analysis.

#### Reviews

This book, in many ways remarkable, gives a detailed account of a number of results concerned with the theory and numerical analysis of the Navier-Stokes equations of viscous incompressible fluids.

-- Zentralblatt MATH