In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.

The articles in this volume are based on recent research on the phenomenon of turbulence in fluid flows collected by the Institute for Mathematics and its Applications. This volume looks into the dynamical properties of the solutions of the Navier-Stokes equations, the equations of motion of incompressible, viscous fluid flows, in order to better understand this phenomenon. Although it is a basic issue of science, it has implications over a wide spectrum of modern technological applications. The articles offer a variety of approaches to the Navier-Stokes problems and related issues. This book should be of interest to both applied mathematicians and engineers.

This book provides a survey of the frontiers of research in the numerical modeling and mathematical analysis used in the study of the atmosphere and oceans. The details of the current practices in global atmospheric and ocean models, the assimilation of observational data into such models and the numerical techniques used in theoretical analysis of the atmosphere and ocean are among the topics covered.
Truly interdisciplinary: scientific interactions between specialties of atmospheric and ocean sciences and applied and computational mathematics
Uses the approach of computational mathematicians, applied and numerical analysts and the tools appropriate for unsolved problems in the atmospheric and oceanic sciences
Contributions uniquely address central problems and provide a survey of the frontier of research

This title 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 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 before reading the core of the book.

This book describes the implementation of multilevel methods for the numerical simulation of turbulent flows. The general ideas for the algorithms presented stem from dynamical systems theory and are based on the decomposition of the unknown function into two or more arrays corresponding to different scales in the Fourier space. Before describing in detail the numerical algorithm, survey chapters on the mathematical theory of the Navier-Stokes equations and on the physics of the conventional theory of turbulence are included. The multilevel methods are applied here to the simulation of homogeneous isotropic turbulent flows as well as turbulent channel flows. The implementation issues are discussed in detail and numerical simulations of the flows cited above are presented and analyzed. The methods have been applied in the context of the direct numerical simulation and are therefore compared to such simulations.

In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.

The articles in this volume are based on recent research on the phenomenon of turbulence in fluid flows collected by the Institute for Mathematics and its Applications. This volume looks into the dynamical properties of the solutions of the Navier-Stokes equations, the equations of motion of incompressible, viscous fluid flows, in order to better understand this phenomenon. Although it is a basic issue of science, it has implications over a wide spectrum of modern technological applications. The articles offer a variety of approaches to the Navier-Stokes problems and related issues. This book should be of interest to both applied mathematicians and engineers.

Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schr??dinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.

Ecrit dans un style qui convient aux mathA(c)maticiens et A leur formation, cette introduction A la mA(c)canique des milieux continus et A la modA(c)lisation mathA(c)matique reste nA(c)anmoins proche de la physique. En particulier, les Auteurs font une distinction claire entre ce qui est admis et ce qui est prouvA(c). Outre les fondements de la mA(c)canique des milieux continus, cet ouvrage contient des introductions plus ou moins dA(c)taillA(c)es A diverses disciplines connexes: magnA(c)tohydrodynamique, combustion, dynamique des fluides gA(c)ophysiques, ... Les Auteurs ont voulu A(c)viter une approche trop abstraite des problA]mes traitA(c)s et garder un langage mathA(c)matique A(c)lA(c)mentaire (les prA(c)-requis sont l'algA]bre linA(c)aire et le calcul diffA(c)rentiel et intA(c)gral connus de tout A(c)tudiant de licence ou de classes prA(c)paratoires et de tout ingA(c)nieur). Ce livre sera utile A un public trA]s large, depuis les ingA(c)nieurs modA(c)lisateurs jusqu'aux A(c)tudiants des deux premiers cycles de l'UniversitA(c), des Classes prA(c)paratoires.