# The Navier-Stokes Equations

## An Elementary Functional Analytic Approach

Textbook

Part of the Birkhäuser Advanced Texts Basler Lehrbücher book series (BAT)

1. Front Matter
Pages i-x
2. Hermann Sohr
Pages 1-42
3. Hermann Sohr
Pages 43-106
4. Hermann Sohr
Pages 107-184
5. Hermann Sohr
Pages 185-260
6. Hermann Sohr
Pages 261-353
7. Back Matter
Pages 355-367

### Introduction

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 0 of the Euclidean space ]Rn, 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 first 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 O. 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 significant from the physical point of view. For mathematical generality, we will develop the lin­ earized theory for all n 2 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverse aspects available are spread out in the literature. However, the literature 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.

### Keywords

Functional analysis approximation equation function functional analysis Functionals Mathematica Navier-Stokes equation Navier-Stokes equations nonlinear system pressure proof solution theorem

### Bibliographic information

• Book Title The Navier-Stokes Equations
• Book Subtitle An Elementary Functional Analytic Approach
• Authors Hermann Sohr
• Series Title Birkhäuser Advanced Texts Basler Lehrbücher
• DOI https://doi.org/10.1007/978-3-0348-8255-2
• Copyright Information Birkhäuser Verlag 2001
• Publisher Name Birkhäuser, Basel
• eBook Packages
• Softcover ISBN 978-3-0348-9493-7
• eBook ISBN 978-3-0348-8255-2
• Series ISSN 1019-6242
• Series E-ISSN 2296-4894
• Edition Number 1
• Number of Pages X, 367
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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