<p>This work was initiated in the summer of 1985 while all of the authors were at the Center of Nonlinear Studies of the Los Alamos National Laboratory; it was then continued and polished while the authors were at Indiana Univer sity, at the University of Paris-Sud (Orsay), and again at Los Alamos in 1986 and 1987. Our aim was to present a direct geometric approach in the theory of inertial manifolds (global analogs of the unstable-center manifolds) for dissipative partial differential equations. This approach, based on Cauchy integral mani folds for which the solutions of the partial differential equations are the generating characteristic curves, has the advantage that it provides a sound basis for numerical Galerkin schemes obtained by approximating the inertial manifold. The work is self-contained and the prerequisites are at the level of a graduate student. The theoretical part of the work is developed in Chapters 2-14, while in Chapters 15-19 we apply the theory to several remarkable partial differ ential equations.</p>

Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations (Applied Mathematical Sciences, 70)

Crafts, Hobbies & Home

Foias, C.

Temam, R.

Constantin, P.

Nicolaenko, B.

Gardening & Landscape Design

Springer

<p>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 functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier-Stokes equations that had been arrived at earlier by phenomenological arguments. Appendices give full details of the mathematical proofs and subtleties.</p>

Navier-Stokes Equations and Turbulence (Encyclopedia of Mathematics and its Applications, Series Number 83)

Reference

Manley, O.

Rosa, R.

Encyclopedias & Subject Guides

Cambridge University Press

Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations (Applied Mathematical Sciences)

The material treated in this book is limited to infinite-dimensional dissipative dynamical systems; a few finite-dimensional systems are presented to serve as reference examples or model problems. Most of the the systems considered are derived from evolutionary partial differential equations associated with boundary-value problems.

Infinite-Dimensional Dynamical Systems in Mechanics and Physics

Springer, Verlag

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