Navier-Stokes equations and nonlinear functional analysis / Roger Temam.

Format:

Book

Author/Creator:

Temam, Roger.

Contributor:

Society for Industrial and Applied Mathematics.

Series:

CBMS-NSF regional conference series in applied mathematics ; 66.

CBMS-NSF regional conference series in applied mathematics ; 66

Language:

English

Subjects (All):

Fluid dynamics.

Navier-Stokes equations--Numerical solutions.

Navier-Stokes equations.

Nonlinear functional analysis.

Physical Description:

1 electronic text (xiv, 141 p.) : ill., digital file.

Edition:

2nd ed.

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1995.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

This second edition, like the first, attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations in the following areas: existence, uniqueness, and regularity of solutions in space dimensions two and three; large time behavior of solutions and attractors; and numerical analysis of the Navier-Stokes equations. Since publication of the first edition of these lectures in 1983, there has been extensive research in the area of inertial manifolds for Navier-Stokes equations. These developments are addressed in a new section devoted entirely to inertial manifolds. Inertial manifolds were first introduced under this name in 1985 and, since then, have been systematically studied for partial differential equations of the Navier-Stokes type. Inertial manifolds are a global version of central manifolds. When they exist they encompass the complete dynamics of a system, reducing the dynamics of an infinite system to that of a smooth, finite-dimensional one called the inertial system. Although the theory of inertial manifolds for Navier-Stokes equations is not complete at this time, there is already a very interesting and significant set of results which deserves to be known, in the hope that it will stimulate further research in this area. These results are reported in this edition.

Contents:

Preface to the Second Edition

Introduction

Part I: Questions related to the existence, uniqueness and regularity of solutions. Chapter 1: Representation of a flow: The Navier-Stokes equations

Chapter 2: Functional setting of the equations

Chapter 3: Existence and uniqueness theorems (mostly classical results)

Chapter 4: New a priori estimates and applications

Chapter 5: Regularity and fractional dimension

Chapter 6: Successive regularity and compatibility conditions at t=0 (bounded case)

Chapter 7: Analyticity in time

Chapter 8: Lagrangian representation of the flow

Part II: Questions related to stationary solutions and functional invariant sets (attractors). Chapter 9: The Couette-Taylor experiment

Chapter 10: Stationary solutions of the Navier-Stokes equations

Chapter 11: The squeezing property

Chapter 12: Hausdorff dimension of an attractor

Part III: Questions related to the numerical approximation. Chapter 13: Finite time approximation

Chapter 14: Long time approximation of the Navier-Stokes equations

Appendix: Inertial manifolds and Navier-Stokes equations

Comments and bibliography

Update for the Second Edition

References.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. 131-141).

Title from title screen, viewed 04/05/2011.

ISBN:

1-68015-789-2

1-61197-005-9

Publisher Number:

CB66 SIAM