Navier-Stokes equations and turbulence / C. Foias [and three others].

Format:

Book

Author/Creator:

Foiaş, Ciprian, author.

Series:

Encyclopedia of mathematics and its applications ; v. 83.

Encyclopedia of mathematics and its applications ; volume 83

Language:

English

Subjects (All):

Turbulence.

Navier-Stokes equations.

Physical Description:

1 online resource (xiv, 347 pages) : digital, PDF file(s).

Edition:

First edition.

Other Title:

Navier-Stokes Equations & Turbulence

Place of Publication:

Cambridge : Cambridge University Press, 2001.

Language Note:

English

Summary:

This book aims to bridge the gap between practising mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The book is the result of many years of research by the authors to analyse turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier-Stokes equations what had been arrived at earlier by phenomenological arguments. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience. Each chapter is accompanied by appendices giving full details of the mathematical proofs and subtleties. This unique presentation should ensure a volume of interest to mathematicians, engineers and physicists.

Contents:

Introduction and Overview of Turbulence

Viscous Fluids. The Navier-Stokes Equations

Turbulence: Where the Interests of Engineers and Mathematicians Overlap

Elements of the Theories of Turbulence of Kolmogorov and Kraichnan

Function Spaces, Functional Inequalities, and Dimensional Analysis

Elements of the Mathematical Theory of the Navier-Stokes Equations

Energy and Enstrophy

Boundary Value Problems

Helmholtz-Leray Decomposition of Vector Fields

Weak Formulation of the Navier-Stokes Equations

Function Spaces

The Stokes Operator

Existence and Uniqueness of Solutions: The Main Results

Analyticity in Time

Gevrey Class Regularity and the Decay of the Fourier Coefficients

Function Spaces for the Whole-Space Case

The No-Slip Case with Moving Boundaries

Dissipation Rate of Flows

Nondimensional Estimates and the Grashof Number

Mathematical Complements

Proofs of Technical Results in Chapter II

Finite Dimensionality of Flows

Determining Modes

Determining Nodes

Attractors and Their Fractal Dimension

Approximate Inertial Manifolds

Proofs of Technical Results in Chapter III

Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors

Mathematical Framework, Definition of Stationary Statistical Solutions, and Banach Generalized Limits

Invariant Measures and Stationary Statistical Solutions in Dimension 2

Stationary Statistical Solutions in Dimension 3

Attractors and Stationary Statistical Solutions.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 331-342) and index.

ISBN:

9780511546754

1-107-11154-4

1-280-41654-8

9786610416547

0-511-17438-1

0-511-03936-0

0-511-15422-4

0-511-32829-X

0-511-54675-0

0-511-05242-1

OCLC:

56416088