This book is the first attempt for a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics, along with other areas of science and technology. A synthetic view of the relation between infinite and finite dimensional systems is presented. Equations considered include reaction-diffusion, Navier-Stokes and other fluid mechanics equations, magnetohydrodynamics, thermohydraulics, pattern formation, Ginzburg-Landau and damped wave. The last chapter of the book introduces inertial manifolds, a subject of rapid development.

Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Applied Mathematical Sciences)

Science & Math

Roger Temam

Mathematics

Springer

This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional analysis and the theory of partial differential equations, all results in this book are given detailed mathematical proof.It is expected that the results and methods presented in this book will promote further investigation of mathematical models for processes in composite and perforated media, heat-transfer, energy transfer by radiation, processes of diffusion and filtration in porous media, and that they will stimulate research in other problems of mathematical physics and the theory of partial differential equations.

Navier-Stokes Equations (Studies in Mathematics and its Applications, Vol. 2)

North-Holland

This book was originally published in 1977 and has since been reprinted four times (the last reprint was in 1984). The current volume is reprinted and fully retypeset by the AMS. It is very close in content to the 1984 edition. The book presents a systematic treatment of results on the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluids. Considered are the linearized stationary case, the nonlinear stationary case, and the full nonlinear time-dependent case. The relevant mathematical tools are introduced at each stage. 
The new material in this book is Appendix III, reproducing a survey article written in 1998. This appendix contains a few aspects not addressed in the earlier editions, in particular a short derivation of the Navier-Stokes equations from the basic conservation principles in continuum mechanics, further historical perspectives, and indications on new developments in the area. The appendix also surveys some aspects of the related Euler equations and the compressible Navier-Stokes equations. Readers are advised to peruse this appendix before reading the core of the book. 
This book presents basic results on the theory of Navier-Stokes equations and, as such, continues to serve as a comprehensive reference source on the topic.

Navier-Stokes Equations: Theory and Numerical Analysis (AMS Chelsea Publishing)

American Mathematical Society

Navier–Stokes Equations (AMS Chelsea Publishing)

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Books by Roger Temam