Navier-Stokes equations and turbulence /

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 t...

Full description

Bibliographic Details
Other Authors:	Foiaş, Ciprian, Foiaş, Ciprian
Format:	Book
Language:	English
Published:	Cambridge ; New York : Cambridge University Press, 2001 Cambridge, U.K. ; New York : 2001 Cambridge, UK ; New York : c2001 New York : 2001
Series:	Encyclopedia of mathematics and its applications ; v. 83 Encyclopedia of mathematics and its applications ; v. 83 Encyclopedia of mathematics and its applications ; v. 83 Encyclopedia of mathematics and its applications v. 83
Subjects:	Navier-Stokes equations Turbulence

Table of Contents:

Ch. I Introduction and Overview of Turbulence
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
Ch. II. Elements of the Mathematical Theory of the Navier-Stokes Equations
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
Ch. III. Finite Dimensionality of Flows
1. Determining Modes
2. Determining Nodes
3. Attractors and Their Fractal Dimension
4. Approximate Inertial Manifolds
Ch. IV. Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors
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. App. C. A Mathematical Complement: The Accretivity Property in Dimension 3
Ch. V. Time-Dependent Statistical Solutions of the Navier-Stokes Equations and Fully Developed Turbulence
1. Time-Dependent Statistical Solutions of 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.
Ch. I Introduction and Overview of Turbulence
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
Ch. II. Elements of the Mathematical Theory of the Navier-Stokes Equations
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
Ch. III. Finite Dimensionality of Flows
1. Determining Modes
2. Determining Nodes
3. Attractors and Their Fractal Dimension
4. Approximate Inertial Manifolds
Ch. IV. Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors
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. App. C. A Mathematical Complement: The Accretivity Property in Dimension 3
Ch. V. Time-Dependent Statistical Solutions of the Navier-Stokes Equations and Fully Developed Turbulence
1. Time-Dependent Statistical Solutions of Bounded Domains
2. Homogeneous Statistical Solutions
Ch. I Introduction and Overview of Turbulence. 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
Ch. II. Elements of the Mathematical Theory of the Navier-Stokes Equations. 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
Ch. III. Finite Dimensionality of Flows.
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
Ch. I Introduction and Overview of Turbulence
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.
Ch. II Elements of the Mathematical Theory of the Navier-Stokes Equations
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.
Ch. III Finite Dimensionality of Flows
1. Determining Modes
2. Determining Nodes
3. Attractors and Their Fractal Dimension
4. Approximate Inertial Manifolds.
Ch. IV Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors
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.
Ch. V Time-Dependent Statistical Solutions of the Navier-Stokes Equations and Fully Developed Turbulence
1. Time-Dependent Statistical Solutions of 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.
App. C A Mathematical Complement: The Accretivity Property in Dimension 3
1 Determining Modes. 2. Determining Nodes. 3. Attractors and Their Fractal Dimension. 4. Approximate Inertial Manifolds
Ch. IV. Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors. 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. App. C. A Mathematical Complement: The Accretivity Property in Dimension 3
Ch. V. Time-Dependent Statistical Solutions of the Navier-Stokes Equations and Fully Developed Turbulence. 1. Time-Dependent Statistical Solutions of Bounded Domains. 2. Homogeneous Statistical Solutions. 3. Reynolds Equation for the Average Flow. 4. Self-Similar 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.
5 Relation with and Application to the Conventional Theory of Turbulence. 6. Some Concluding Remarks.

Navier-Stokes equations and turbulence /

Similar Items