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The Navier-Stokes Equations

An Elementary Functional Analytic Approach

  • Book
  • © 2001

Overview

Authors:
  1. Hermann Sohr

    1. , Department of Mathematics, University Paderborn, Paderborn, Germany

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  • 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?
  • Includes supplementary material: sn.pub/extras

Part of the book series: Modern Birkhäuser Classics (MBC)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Hermann Sohr
    Pages 1-42

  3. Preliminary Results

    • Hermann Sohr
    Pages 43-106

  4. The Stationary Navier-Stokes Equations

    • Hermann Sohr
    Pages 107-184

  5. The Linearized Nonstationary Theory

    • Hermann Sohr
    Pages 185-260

  6. The Full Nonlinear Navier-Stokes Equations

    • Hermann Sohr
    Pages 261-353

  7. Back Matter

    Pages 355-367
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Keywords

About this book

The primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers’ convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However,theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.

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)

Authors and Affiliations

  • , Department of Mathematics, University Paderborn, Paderborn, Germany

    Hermann Sohr

About the author

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

Bibliographic Information

  • Book Title: The Navier-Stokes Equations

  • Book Subtitle: An Elementary Functional Analytic Approach

  • Authors: Hermann Sohr

  • Series Title: Modern Birkhäuser Classics

  • DOI: https://doi.org/10.1007/978-3-0348-0551-3

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel 2001

  • Hardcover ISBN: 978-3-7643-6545-5Published: 01 September 2001

  • Softcover ISBN: 978-3-0348-0550-6Published: 14 December 2012

  • eBook ISBN: 978-3-0348-0551-3Published: 13 December 2012

  • Series ISSN: 2197-1803

  • Series E-ISSN: 2197-1811

  • Edition Number: 1

  • Number of Pages: X, 367

  • Additional Information: Originally published in the Birkhäuser Advanced Texts Basler Lehrbücher series

  • Topics: Partial Differential Equations, Mathematical Physics, Functional Analysis

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