Description 
1 online resource (xiv, 141 pages) : illustrations 
Series 
CBMSNSF regional conference series in applied mathematics ; 66 

CBMSNSF regional conference series in applied mathematics ; 66

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 NavierStokes 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 CouetteTaylor experiment  Chapter 10: Stationary solutions of the NavierStokes 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 NavierStokes equations  Appendix: Inertial manifolds and NavierStokes equations  Comments and bibliography  Update for the Second Edition  References 
Summary 
This second edition, like the first, attempts to arrive as simply as possible at some central problems in the NavierStokes 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 NavierStokes equations. Since publication of the first edition of these lectures in 1983, there has been extensive research in the area of inertial manifolds for NavierStokes 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 NavierStokes 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, finitedimensional one called the inertial system. Although the theory of inertial manifolds for NavierStokes 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 
Analysis 
Dynamical systems 

Inertial manifolds 

NavierStokes equations 

Nonlinear functional analysis 

Turbulence 
Bibliography 
Includes bibliographical references (pages 131141) 
Subject 
Fluid dynamics.


NavierStokes equations  Numerical solutions.


Nonlinear functional analysis.

Form 
Electronic book

Author 
Society for Industrial and Applied Mathematics.

ISBN 
1611970059 (electronic bk.) 

1680157892 (electronic bk.) 

9781611970050 (electronic bk.) 

9781680157895 (electronic bk.) 

(paperback) 

(paperback) 
