The Navier-Stokes equations : an elementary functional analytic approach
Author(s)
Bibliographic Information
The Navier-Stokes equations : an elementary functional analytic approach
（Birkhäuser advanced texts : Basler Lehrbücher / edited by Herbert Amann, Hanspeter Kraft）
Birkhäuser, c2001
Available at / 28 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC21:532/SO282070547354
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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.
by "Nielsen BookData"