Navier-Stokes equations and turbulence /

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Bibliographic Details
Imprint:New York : Cambridge University Press, 2001.
Description:xiv, 347 p. ; 25 cm.
Language:English
Series:Encyclopedia of mathematics and its applications ; v. 83
Subject:Turbulence.
Navier-Stokes equations.
Navier-Stokes equations.
Turbulence.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/4513550
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Other authors / contributors:FoiasĖ§, Ciprian.
ISBN:0521360323
Notes:Includes bibliographical references and index.
Table of Contents:
  • Preface
  • Acknowledgments
  • Chapter I. Introduction and Overview of Turbulence
  • Introduction
  • 1.. Viscous Fluids. The Navier-Stokes Equations
  • 2.. Turbulence: Where the Interests of Engineers and Mathematicians Overlap
  • 3.. Elements of the Theories of Turbulence of Kolmogorov and Kraichnan
  • 4.. Function Spaces, Functional Inequalities, and Dimensional Analysis
  • Chapter II. Elements of the Mathematical Theory of the Navier-Stokes Equations
  • Introduction
  • 1.. Energy and Enstrophy
  • 2.. Boundary Value Problems
  • 3.. Helmholtz-Leray Decomposition of Vector Fields
  • 4.. Weak Formulation of the Navier-Stokes Equations
  • 5.. Function Spaces
  • 6.. The Stokes Operator
  • 7.. Existence and Uniqueness of Solutions: The Main Results
  • 8.. Analyticity in Time
  • 9.. Gevrey Class Regularity and the Decay of the Fourier Coefficients
  • 10.. Function Spaces for the Whole-Space Case
  • 11.. The No-Slip Case with Moving Boundaries
  • 12.. Dissipation Rate of Flows
  • 13.. Nondimensional Estimates and the Grashof Number
  • Appendix A.. Mathematical Complements
  • Appendix B.. Proofs of Technical Results in Chapter II
  • Chapter III. Finite Dimensionality of Flows
  • Introduction
  • 1.. Determining Modes
  • 2.. Determining Nodes
  • 3.. Attractors and Their Fractal Dimension
  • 4.. Approximate Inertial Manifolds
  • Appendix A.. Proofs of Technical Results in Chapter III
  • Chapter IV. Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors
  • Introduction
  • 1.. Mathematical Framework, Definition of Stationary Statistical Solutions, and Banach Generalized Limits
  • 2.. Invariant Measures and Stationary Statistical Solutions in Dimension 2
  • 3.. Stationary Statistical Solutions in Dimension 3
  • 4.. Attractors and Stationary Statistical Solutions
  • 5.. Average Transfer of Energy and the Cascades in Turbulent Flows
  • Appendix A.. New Concepts and Results Used in Chapter IV
  • Appendix B.. Proofs of Technical Results in Chapter IV
  • Appendix C.. A Mathematical Complement: The Accretivity Property in Dimension 3
  • Chapter V. Time-Dependent Statistical Solutions of the Navier-Stokes Equations and Fully Developed Turbulence
  • Introduction
  • 1.. Time-Dependent Statistical Solutions on Bounded Domains
  • 2.. Homogeneous Statistical Solutions
  • 3.. Reynolds Equation for the Average Flow
  • 4.. Self-Similar Homogeneous Statistical Solutions
  • 5.. Relation with and Application to the Conventional Theory of Turbulence
  • 6.. Some Concluding Remarks
  • Appendix A.. Proofs of Technical Results in Chapter V
  • References
  • Index