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Foundations of fluid dynamics

Author: Giovanni Gallavotti
Publisher: Berlin ; New York : Springer, ©2002.
Series: Texts and monographs in physics.
Edition/Format:   Print book : EnglishView all editions and formats
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This monograph on fluid mechanics is not only a superb and unique textbook but also an impressive piece of research. It is the only textbook that fully covers turbulence, all the way from the works  Read more...

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Document Type: Book
All Authors / Contributors: Giovanni Gallavotti
ISBN: 3540414150 9783540414155
OCLC Number: 47044953
Description: xviii, 513 pages : illustrations ; 25 cm.
Contents: 1. Continua and Generalities About Their Equations. 1.1. Continua. 1.2. Equations of Motion of a Fluid in General. Ideal and Incompressible Cases. Incompressible Euler, Navier-Stokes and Navier-Stokes-Fourier Equations. 1.3. The Rescaling Method and Estimates of the Approximations. 1.4. Elements of Hydrostatics. 1.5. The Convection Problem. Rayleigh's Equations. 1.6. Kinematics: Incompressible Fields, Vector Potentials, Decompositions of a General Field. 1.7. Vorticity Conservation in the Euler Equation. Clebsch Potentials and Hamiltonian Form of Euler Equations. Bidimensional Fluids --
2. Empirical Algorithms. 2.1. Incompressible Euler and Navier-Stokes Fluid Dynamics. First Empirical Solutions Algorithms. Auxiliary Friction and Heat Equation Comparison Methods. 2.2. Another Class of Empirical Algorithms. Spectral Method. Stokes Problem. Gyroscopic Analogy. 2.3. Vorticity Algorithms for Incompressible Euler and Navier-Stokes Fluids. The d = 2 Case. 2.4. Vorticity Algorithms for Incompressible Euler and Navier-Stokes Fluids. The d = 3 Case --
3. Analytical Theories and Mathematical Aspects. 3.1. Spectral Method and Local Existence, Regularity and Uniqueness Theorems for Euler and Navier-Stokes Equations, d [greater than or equal to] 2. 3.2. Weak Global Existence Theorems for NS. Autoregularization, Existence, Regularity and Uniqueness for d = 2. 3.3. Regularity: Partial Results for the NS Equation in d = 3. The Theory of Leray. 3.4. Fractal Dimension of Singularities of the Navier-Stokes Equation, d = 3. 3.5. Local Homogeneity and Regularity. CKN Theory --
4. Incipient Turbulence and Chaos. 4.1. Fluid Theory in the Absence of Existence and Uniqueness Theorems for the Basic Fluid Dynamics Equations. Truncated NS Equations. (The Rayleigh and Lorenz Models). 4.2. Onset of Chaos. Elements of Bifurcation Theory. 4.3. Bifurcation Theory. End of the Onset of Turbulence. 4.4. Dynamical Tables --
5. Ordering Chaos. 5.1. Quantitative Description of Chaotic Motions Before Developed Turbulence. Continuous Spectrum. 5.2. Timed Observations. Random Data. 5.3. Dynamical Systems Types. Statistics on Attracting Sets. 5.4. Dynamical Bases and Lyapunov Exponents. 5.5. SRB Statistics. Attractors and Attracting Sets. Fractal Dimension. 5.6. Ordering of Chaos. Entropy and Complexity. 5.7. Symbolic Dynamics. Lorenz Model. Ruelle's Principle --
6. Developed Turbulence. 6.1. Functional Integral Representation of Stationary Distributions. 6.2. Phenomenology of Developed Turbulence and the Kolmogorov Laws. 6.3. The Shell Model. Multifractal Statistics --
7. Statistical Properties of Turbulence. 7.1. Viscosity, Reversibility, and Irreversible Dissipation. 7.2. Reversibility, Axiom C, Chaotic Hypothesis. 7.3. Chaotic Hypothesis, Fluctuation Theorem and Onsager Reciprocity. Entropy Driven Intermittency. 7.4. The Structure of the Attractor for the Navier-Stokes Equations. Dissipative Euler Equations. Barometric Formula.
Series Title: Texts and monographs in physics.
Other Titles: Ipotesi per una introduzione alla meccanica dei fluidi.
Responsibility: Giovanni Gallavotti.

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"Gallavotti's remarkable new book, Foundations of Fluid Dynamics, takes a fresh look at the essential formulation and phenomenology of fluid dynamics as reflected in the research of the 70s, 80s and Read more...

 
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