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PRINTED BOOKS

Title Navier-Stokes equations and turbulence / C. Foias ... [and others].

Published Cambridge : Cambridge University Press, 2001.

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Location Call No. Status
 UniM Bund  532.0527 NAVI {Bund89 20200519}  v.83 2001    AVAILABLE
Physical description xiv, 347 pages : illustrations ; 25 cm.
Series Encyclopedia of mathematics and its applications ; v. 83.
Encyclopedia of mathematics and its applications ; v. 83.
Bibliography Includes bibliographical references and index.
Contents Chapter I Introduction and Overview of Turbulence 1 -- 1. Viscous Fluids. The Navier-Stokes Equations 1 -- 2. Turbulence: Where the Interests of Engineers and Mathematicians Overlap 5 -- 3. Elements of the Theories of Turbulence of Kolmogorov and Kraichnan 9 -- 4. Function Spaces, Functional Inequalities, and Dimensional Analysis 14 -- Chapter II Elements of the Mathematical Theory of the Navier-Stokes Equations 25 -- 1. Energy and Enstrophy 27 -- 2. Boundary Value Problems 29 -- 3. Helmholtz-Leray Decomposition of Vector Fields 36 -- 4. Weak Formulation of the Navier-Stokes Equations 39 -- 5. Function Spaces 41 -- 6. Stokes Operator 49 -- 7. Existence and Uniqueness of Solutions: The Main Results 55 -- 8. Analyticity in Time 62 -- 9. Gevrey Class Regularity and the Decay of the Fourier Coefficients 67 -- 10. Function Spaces for the Whole-Space Case 75 -- 11. No-Slip Case with Moving Boundaries 77 -- 12. Dissipation Rate of Flows 80 -- 13. Nondimensional Estimates and the Grashof Number 87 -- Appendix A. Mathematical Complements 90 -- Appendix B. Proofs of Technical Results in Chapter II 102 -- Chapter III Finite Dimensionality of Flows 115 -- 1. Determining Modes 123 -- 2. Determining Nodes 131 -- 3. Attractors and Their Fractal Dimension 137 -- 4. Approximate Inertial Manifolds 150 -- Appendix A. Proofs of Technical Results in Chapter III 156 -- Chapter IV Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors 169 -- 1. Mathematical Framework, Definition of Stationary Statistical Solutions, and Banach Generalized Limits 172 -- 2. Invariant Measures and Stationary Statistical Solutions in Dimension 2 183 -- 3. Stationary Statistical Solutions in Dimension 3 189 -- 4. Attractors and Stationary Statistical Solutions 194 -- 5. Average Transfer of Energy and the Cascades in Turbulent Flows 198 -- Appendix A. New Concepts and Results Used in Chapter IV 218 -- Appendix B. Proofs of Technical Results in Chapter IV 227 -- Appendix C. A Mathematical Complement: The Accretivity Property in Dimension 3 244 -- Chapter V Time-Dependent Statistical Solutions of the Navier-Stokes Equations and Fully Developed Turbulence 255 -- 1. Time-Dependent Statistical Solutions on Bounded Domains 262 -- 2. Homogeneous Statistical Solutions 271 -- 3. Reynolds Equation for the Average Flow 280 -- 4. Self-Similar Homogeneous Statistical Solutions 283 -- 5. Relation with and Application to the Conventional Theory of Turbulence 295 -- Appendix A. Proofs of Technical Results in Chapter V 312.
Summary This book presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians.
Other author FoiaƟ, Ciprian.
Subject Turbulence.
Navier-Stokes equations.
ISBN 0521360323 No price