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Softcover ISBN:  9781470477868 
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AMS Member Price:  $120.60 $91.35 
Softcover ISBN:  9781470477868 
Product Code:  CHEL/343.H.S 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470429942 
Product Code:  CHEL/343.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Softcover ISBN:  9781470477868 
eBook ISBN:  9781470429942 
Product Code:  CHEL/343.H.S.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 

Book DetailsAMS Chelsea PublishingVolume: 343; 1984; 408 ppMSC: Primary 76; Secondary 65; 35
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.
ReadershipGraduate students and research mathematicians interested in fluid mechanics, linear and nonlinear PDEs, and numerical analysis.

Table of Contents

Chapters

Chapter 1. The steadystate Stokes equations

Chapter 2. Steadystate Navier–Stokes equations

Chapter 3. The evolution Navier–Stokes equation

Appendix I. Properties of the curl operator and application to the steadystate Navier–Stokes equations

Appendix II. Implementation of nonconforming linear finite elements (Approximation APX5—Twodimensional case)

Appendix III. Some developments on Navier–Stokes equations in the second half of the 20th century

Bibliography to Appendix III


Additional Material

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


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

Chapters

Chapter 1. The steadystate Stokes equations

Chapter 2. Steadystate Navier–Stokes equations

Chapter 3. The evolution Navier–Stokes equation

Appendix I. Properties of the curl operator and application to the steadystate Navier–Stokes equations

Appendix II. Implementation of nonconforming linear finite elements (Approximation APX5—Twodimensional case)

Appendix III. Some developments on Navier–Stokes equations in the second half of the 20th century

Bibliography to Appendix III

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