The Navier-Stokes equations : an elementary functional analytic approach

Author(s)

Bibliographic Information

The Navier-Stokes equations : an elementary functional analytic approach

Hermann Sohr

(Birkhäuser advanced texts : Basler Lehrbücher / edited by Herbert Amann, Hanspeter Kraft)

Birkhäuser, c2001

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Note

Includes bibliographocal references (p. [355]-363) and index

Description and Table of Contents

Description

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.

Table of Contents

Preliminary Results.- The Stationary Navier-Stokes Equations.- The Linearized Nonstationary Theory.- The Full Nonlinear Navier-Stokes Equations.

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Details

  • NCID
    BA5363271X
  • ISBN
    • 9783764365455
  • LCCN
    2001043020
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Basel
  • Pages/Volumes
    x, 367 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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