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Springer Monographs in Mathematics An Introduction to the Mathematical Theory of the Navier-Stokes Equations

An Introduction to the Mathematical Theory of the Navier-Stokes Equations

Steady-State Problems

Authors: Galdi, Giovanni P.

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About this book

The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of boundary-value problems related to the Navier-Stokes equations. These properties  include existence, uniqueness and regularity of solutions in bounded as well as unbounded domains. Whenever the domain is unbounded, the asymptotic behavior of solutions  is also investigated.

This book is the new edition of the original two volume book, under the same title, published in 1994.

In this new edition, the two volumes have merged into one and two more chapters on steady generalized oseen flow in exterior domains and steady Navier–Stokes flow in three-dimensional exterior domains have been added. Most of the proofs given in the previous edition were also updated.

An introductory first chapter describes all relevant questions treated in the book and lists and motivates a number of significant and still open questions. It is written in an expository style so as to be accessible also to  non-specialists. Each chapter is preceded by a substantial, preliminary discussion of the problems treated, along with their motivation and the strategy used to solve them. Also, each chapter ends with a section dedicated to alternative approaches and procedures, as well as historical notes.

The book contains more than 400 stimulating exercises, at different levels of difficulty, that will help the junior researcher and the graduate student to gradually become accustomed with the subject. Finally, the book is endowed with a vast bibliography that includes more than 500 items. Each item brings a reference to the section of the book where it is cited.

 

The book will be useful to researchers and graduate students in mathematics in particular mathematical fluid mechanics and differential equations.

 

Review of First Edition, First Volume:

“The emphasis of this book is on an introduction to the mathematical theory of the stationary Navier-Stokes equations. It is written in the style of a textbook and is essentially self-contained. The problems are presented clearly and in an accessible manner. Every chapter begins with a good introductory discussion of the problems considered, and ends with interesting notes on different approaches developed in the literature. Further, stimulating exercises are proposed. (Mathematical Reviews, 1995)

Reviews

From the reviews of the second edition:

“The book yields a comprehensive, detailed and self-contained study of the basic mathematical properties of different boundary-value problems related to the Navier-Stokes equations. These properties include existence, uniqueness and regularity of solutions. … The book contains more than 400 carefully choosen exercises at different levels of difficulty that will help the young researcher. The comprehensive bibliography contains more than 500 items. Galdi’s monograph can strongly be recommended to every mathematician (and theoretical physicist) interested in mathematical fluid mechanics or in PDEs.” (Jürgen Socolowsky, Zentralblatt MATH, Vol. 1245, 2012)


Table of contents (13 chapters)

Table of contents (13 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-0-387-09620-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA in USD
  • ISBN 978-0-387-09619-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA in USD
  • ISBN 978-1-4939-5017-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to the Mathematical Theory of the Navier-Stokes Equations
Book Subtitle
Steady-State Problems
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-387-09620-9
DOI
10.1007/978-0-387-09620-9
Hardcover ISBN
978-0-387-09619-3
Softcover ISBN
978-1-4939-5017-1
Series ISSN
1439-7382
Edition Number
2
Number of Pages
XIV, 1018
Number of Illustrations
4 b/w illustrations
Additional Information
Originally published as volume 38 in series: Springer Tracts in Natural Philosophy
Topics