AMS Chelsea Publishing 1984; 408 pp; hardcover Volume: 343 Reprint/Revision History: reprinted with corrections, 2001 ISBN10: 0821827375 ISBN13: 9780821827376 List Price: US$68 Member Price: US$61.20 Order Code: CHEL/343.H
 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 NavierStokes equations for viscous incompressible fluids. Considered are the linearized stationary case, the nonlinear stationary case, and the full nonlinear timedependent 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 NavierStokes 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 NavierStokes equations. Readers are advised to peruse this appendix before reading the core of the book. This book presents basic results on the theory of NavierStokes equations and, as such, continues to serve as a comprehensive reference source on the topic. Readership Graduate students and research mathematicians interested in fluid mechanics, linear and nonlinear PDEs, and numerical analysis. Reviews From a review of the first edition: "This book, in many ways remarkable, gives a detailed account of a number of results concerned with the theory and numerical analysis of the NavierStokes equations of viscous incompressible fluids."  Zentralblatt MATH Table of Contents  The steadystate Stokes equations
 Steadystate NavierStokes equations
 The evolution NavierStokes equation
 Appendix I: Properties of the curl operator and application to the steadystate NavierStokes equations
 Appendix II (by F. Thomasset): Implementation of nonconforming linear finite elements (Approximation APX5Twodimensional case)
 Appendix III: Some developments on NavierStokes equations in the second half of the 20th century
 Bibliography to Appendix III
 Comments
 Additional comments to the revised edition
 Bibliography
 Index
