Format:
1 Online-Ressource (xiv, 347 pages)
,
digital, PDF file(s).
ISBN:
9780511546754
Series Statement:
Encyclopedia of mathematics and its applications volume 83
Content:
This book aims to bridge the gap between practising mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The book is the result of many years of research by the authors to analyse 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 what had been arrived at earlier by phenomenological arguments. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience. Each chapter is accompanied by appendices giving full details of the mathematical proofs and subtleties. This unique presentation should ensure a volume of interest to mathematicians, engineers and physicists.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
,
Introduction and Overview of Turbulence -- Viscous Fluids. The Navier-Stokes Equations -- Turbulence: Where the Interests of Engineers and Mathematicians Overlap -- Elements of the Theories of Turbulence of Kolmogorov and Kraichnan -- Function Spaces, Functional Inequalities, and Dimensional Analysis -- Elements of the Mathematical Theory of the Navier-Stokes Equations -- Energy and Enstrophy -- Boundary Value Problems -- Helmholtz-Leray Decomposition of Vector Fields -- Weak Formulation of the Navier-Stokes Equations -- Function Spaces -- The Stokes Operator -- Existence and Uniqueness of Solutions: The Main Results -- Analyticity in Time -- Gevrey Class Regularity and the Decay of the Fourier Coefficients -- Function Spaces for the Whole-Space Case -- The No-Slip Case with Moving Boundaries -- Dissipation Rate of Flows -- Nondimensional Estimates and the Grashof Number -- Mathematical Complements -- Proofs of Technical Results in Chapter II -- Finite Dimensionality of Flows -- Determining Modes -- Determining Nodes -- Attractors and Their Fractal Dimension -- Approximate Inertial Manifolds -- Proofs of Technical Results in Chapter III -- Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors -- Mathematical Framework, Definition of Stationary Statistical Solutions, and Banach Generalized Limits -- Invariant Measures and Stationary Statistical Solutions in Dimension 2 -- Stationary Statistical Solutions in Dimension 3 -- Attractors and Stationary Statistical Solutions.
Additional Edition:
ISBN 9780521064606
Additional Edition:
ISBN 9780521360326
Additional Edition:
ISBN 9780521360326
Additional Edition:
ISBN 9780521064606
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9780521360326
Language:
English
DOI:
10.1017/CBO9780511546754
