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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. ## About book:

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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.

Part I presents the Navier-Stokes equations of viscous incompressible fluids and the main boundary-value problems usually associated with these equations. The case of the flow in a bounded domain with periodic or zero boundary conditions is studied and the functional setting of the equation as well as various results on existence, uniqueness, and regularity of time-dependent solutions are given. Part II studies the behavior of solutions of the Navier-Stokes equation when t approaches infinity and attempts to explain turbulence. Part III treats questions related to numerical approximation. In the Appendix, which is new to the second edition, concepts of inertial manifolds are described, definitions and some typical results are recalled, and the existence of inertial systems for two-dimensional Navier-Stokes equations is shown.

- Series:
**CBMS-NSF Regional Conference Series in Applied Mathematics** - Author:
**Roger Temam** - Year:
**1987** - Publisher:
**Society for Industrial Mathematics** - Language:
**English** - ISBN:
**9780898713404,0898713404**

- DPI:
**300** - File size:
**1 283 086** - Format:
**djvu**

Security code:

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 ...

This volume contains the Proceedings of the Third International Conference on Navier-Stokes Equations and Related Nonlinear Problems. The conference was held in Funchal (Madeira, Portugal), on May 21-27, 1994. In addition to the editor, the organizers wer...

This book presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. It is the result of many years of research by the authors to analyze turbulence using Sobolev spaces and functio...

This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are...

This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are...

The Navier-Stokes equations were firmly established in the 19th Century as the system of nonlinear partial differential equations which describe the motion of most commonly occurring fluids in air and water, and since that time exact solutions have been s...

This is the fourth of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self-contained and accessible to the nonspecialist....

The main concern in all scientific work must be the human being himsel[ This, one should never forget among all those diagrams and equations. Albert Einstein This volume is part of a comprehensive presentation of nonlinear functional analysis, the basic c...

The book presents a systematic and unified study of geometric nonlinear functional analysis. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to geometric measure ...

This study contains the definitions of several ring constructions used in various applications. The concept of a groupoid-graded ring includes many of these constructions as special cases and makes it possible to unify the exposition. Research results on ...

This eagerly anticipated new book from Tony Lawson contends that economics can profit from a more explicit concern with ontology (enquiry into the nature of existence) than has been its custom. By admitting that economics is not exactly a picture of healt...

Protagoras was an important Greek thinker of the fifth century BC, the most famous of the so called Sophists, though most of what we know of him and his thought comes to us mainly through the dialogues of his strenuous opponent Plato. In this book, Ugo Zi...

Exploring the relationship between discourses of cultural hybridity and projects for social equality, The Caribbean Postcolonial reveals a far greater diversity of political and aesthetic practices of cultural hybridity than has been generally recognized ...

The first instance of detailed scholarly engagement with the cultural legacy of John Brown, this collection seeks to examine the lasting impact of Brown and his armed slave rebellion of 1859....

Cultural imperialism and acculturation find close counterparts in many of the policies and attitudes of Napoleonic administrators in their Italian provinces, explored here from the rich archival sources of the Parisian and Italian archives, long neglecte...

This is a study of the evolving relationship between the British colonial state and the copper mining industry in Northern Rhodesia, from the early stages of development to decolonization, encompassing depression, wartime mobilization and fundamental chan...

Criminal records are essential to the smooth running of the criminal justice system, but are overlooked and taken for granted. Terry Thomas considers their uses within the criminal justice system and beyond--especially the growth of their use for pre-empl...