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
Hidden Bibliographic Details
Other authors / contributors:Foiaş, Ciprian.
ISBN:0521360323
Notes:Includes bibliographical references and index.
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505 0 0 |g Ch. I.  |t Introduction and Overview of Turbulence --  |g 1.  |t Viscous Fluids. The Navier-Stokes Equations --  |g 2.  |t Turbulence: Where the Interests of Engineers and Mathematicians Overlap --  |g 3.  |t Elements of the Theories of Turbulence of Kolmogorov and Kraichnan --  |g 4.  |t Function Spaces, Functional Inequalities, and Dimensional Analysis --  |g Ch. II.  |t Elements of the Mathematical Theory of the Navier-Stokes Equations --  |g 1.  |t Energy and Enstrophy --  |g 2.  |t Boundary Value Problems --  |g 3.  |t Helmholtz-Leray Decomposition of Vector Fields --  |g 4.  |t Weak Formulation of the Navier-Stokes Equations --  |g 5.  |t Function Spaces --  |g 6.  |t The Stokes Operator --  |g 7.  |t Existence and Uniqueness of Solutions: The Main Results --  |g 8.  |t Analyticity in Time --  |g 9.  |t Gevrey Class Regularity and the Decay of the Fourier Coefficients --  |g 10.  |t Function Spaces for the Whole-Space Case --  |g 11.  |t The No-Slip Case with Moving Boundaries --  |g 12.  |t Dissipation Rate of Flows --  |g 13.  |t Nondimensional Estimates and the Grashof Number --  |g Ch. III.  |t Finite Dimensionality of Flows --  |g 1.  |t Determining Modes --  |g 2.  |t Determining Nodes --  |g 3.  |t Attractors and Their Fractal Dimension --  |g 4.  |t Approximate Inertial Manifolds --  |g Ch. IV.  |t Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors --  |g 1.  |t Mathematical Framework, Definition of Stationary Statistical Solutions, and Banach Generalized Limits --  |g 2.  |t Invariant Measures and Stationary Statistical Solutions in Dimension 2 --  |g 3.  |t Stationary Statistical Solutions in Dimension 3 --  |g 4.  |t Attractors and Stationary Statistical Solutions --  |g 5.  |t Average Transfer of Energy and the Cascades in Turbulent Flows.  |g App. C.  |t A Mathematical Complement: The Accretivity Property in Dimension 3 --  |g Ch. V.  |t Time-Dependent Statistical Solutions of the Navier-Stokes Equations and Fully Developed Turbulence --  |g 1.  |t Time-Dependent Statistical Solutions of Bounded Domains --  |g 2.  |t Homogeneous Statistical Solutions --  |g 3.  |t Reynolds Equation for the Average Flow --  |g 4.  |t Self-Similar Homogeneous Statistical Solutions --  |g 5.  |t Relation with and Application to the Conventional Theory of Turbulence --  |g 6.  |t Some Concluding Remarks. 
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