Modern Birkhäuser Classics

The Navier-Stokes Equations

An Elementary Functional Analytic Approach

Authors: Sohr, Hermann

  • Elementary and selfcontained approach to the mathematical theory of the viscous incompressible Navier-Stokes equations  
  • Requires familiarity with the basic functional analytic tools in Hilbert and Banach spaces only  
  • Fills a gap by providing a systematic treatment of the subject​ 
see more benefits

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-0348-0551-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-0348-0550-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

The primary objective of this monograph is to develop an elementary and self-contained approach to the mathematical theory of a viscous, incompressible fluid in a domain of the Euclidean space, described by the equations of Navier-Stokes.

Moreover, the theory is presented for completely general domains, in particular, for arbitrary unbounded, nonsmooth domains. Therefore, restriction was necessary to space dimensions two and three, which are also the most significant from a physical point of view. For mathematical generality, however, the linearized theory is expounded for general dimensions higher than one.

Although the functional analytic approach developed here is, in principle, known to specialists, the present book fills a gap in the literature providing a systematic treatment of a subject that has been documented until now only in fragments. The book is mainly directed to students familiar with basic tools in Hilbert and Banach spaces. However, for the readers’ convenience, some fundamental properties of, for example, Sobolev spaces, distributions and operators are collected in the first two chapters.

- - -

The book is written in a well arranged way, easy to survey and with utilization of the newest results. For its study, it is necessary to know only the basic functional analytic tools in Hilbert and Banach spaces. It is determined for an extensive circle of readers, from students up to experts in science and also for specialists in the field.
(Zentralblatt MATH)   

The author’s purpose in this book is to develop an “elementary and self-contained approach” to the mathematical theory of the viscous incompressible Navier-Stokes equations from basic functional analytic tools. Another objective is to develop the results in reasonably full generality, in particular to allow for arbitrary nonsmooth, possibly unbounded, spatial domains.
(Mathematical Reviews)  

About the authors

Hermann Sohr is professor of mathematics, especially mathematical fluid mechanics, at the University Paderborn, Germany.

Reviews

From the reviews:

“The book is well written and not unnecessarily wordy. There is an up-to-date bibliography and a nice index. … a mathematician who wishes to know what the important issues concerning eq. (1) are and what has been achieved, would find this an excellent source. Equally, a mathematically-minded student, with a good grounding in analysis and who has decided to work in this area, or the teacher who wants to teach a course on this material would find this a valuable text.” (P. N. Shankar,Current Science, Vol. 85 (2), July, 2003)

Table of contents (5 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-0348-0551-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-0348-0550-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
The Navier-Stokes Equations
Book Subtitle
An Elementary Functional Analytic Approach
Authors
Series Title
Modern Birkhäuser Classics
Copyright
2001
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0551-3
DOI
10.1007/978-3-0348-0551-3
Softcover ISBN
978-3-0348-0550-6
Series ISSN
2197-1803
Edition Number
1
Number of Pages
X, 367
Additional Information
Originally published in the Birkhäuser Advanced Texts Basler Lehrbücher series
Topics