Foundations of Fluid Dynamics

By: Giovanni Gallavotti

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Hardcover | 29 March 2005

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514 Pages

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22.86 x 15.88 x 3.18

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The imagination is struck by the substantial conceptual identity between the problems met in the theoretical study of physical phenomena. It is absolutely unexpected and surprising, whether one studies equilibrium statistical me- chanics, or quantum field theory, or solid state physics, or celestial mechanics, harmonic analysis, elasticity, general relativity or fluid mechanics and chaos in turbulence. So when in 1988 I was made chair of Fluid Mechanics at the Universita La Sapienza, not out of recognition of work I did on the subject (there was none) but, rather, to avoid my teaching mechanics, from which I could have a strong cultural influence on mathematical physics in Rome, I was not excessively worried, although I was clearly in the wrong place. The subject is wide, hence in the last decade I could do nothing else but go through books and libraries looking for something that was within the range of the methods and experiences of my past work. The first great surprise was to realize that the mathematical theory of fluids is in an even more primitive state than I was aware of. Nevertheless it still seems to me that a detailed analysis of the mathematical problems is essential for anyone who wishes to do research into fluids. Therefore, I dedicated (Chap. 3) all the space necessary to a complete exposition of the theories of Leray, of Scheffer and of Caffarelli, Kohn and Nirenberg, taken directly from the original works.

Industry Reviews

"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 90s. [...] Foundations of Fluid Dynamics is strongly recommended, by this reviewer, for acquisition by academic libraries and for the use of anyone with a serious interest in the mathematical foundations of fluid dynamics." (J.H. Lienhard, Applied Mechanics Review, 55/4, 2002)

"This is an advanced textbook suitable for higher level graduate coursework and as a research reference work. [...] All in all, this book presents a broad range of topics in sufficient depth to make it relatively self-contained." (Mathematical Reviews 2003e)

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You Can Find This Book In

Non-Fiction Science Physics Classical Mathematics Fluid Mechanics Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Fluids Hydraulics & Pneumatics Science in General Maths for Scientists

Technology in General Maths for Engineers Mechanical Engineering

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Paperback

Published: 7th December 2010

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Continua and Generalities About Their Equations	p. 1
Continua	p. 1
Equations of Motion of a Fluid in General. Ideal and Incompressible Cases. Incompressible Euler, Navier-Stokes and Navier-Stokes-Fourier Equations	p. 15
The Rescaling Method and Estimates of the Approximations	p. 24
Elements of Hydrostatics	p. 31
The Convection Problem. Rayleigh's Equations	p. 43
Kinematics: Incompressible Fields, Vector Potentials, Decompositions of a General Field	p. 53
Vorticity Conservation in the Euler Equation. Clebsch Potentials and Hamiltonian Form of Euler Equations. Bidimensional Fluids	p. 66
Empirical Algorithms	p. 83
Incompressible Euler and Navier-Stokes Fluid Dynamics. First Empirical Solutions Algorithms. Auxiliary Friction and Heat Equation Comparison Methods	p. 83
Another Class of Empirical Algorithms. Spectral Method. Stokes Problem. Gyroscopic Analogy	p. 99
Vorticity Algorithms for Incompressible Euler and Navier-Stokes Fluids. The d = 2 Case	p. 120
Vorticity Algorithms for Incompressible Euler and Navier-Stokes Fluids. The d = 3 Case	p. 128
Analytical Theories and Mathematical Aspects	p. 143
Spectral Method and Local Existence, Regularity and Uniqueness Theorems for Euler and Navier-Stokes Equations, d [greater than or equal to] 2	p. 143
Weak Global Existence Theorems for NS. Autoregularization, Existence, Regularity and Uniqueness for d = 2	p. 159
Regularity: Partial Results for the NS Equation in d = 3. The Theory of Leray	p. 176
Fractal Dimension of Singularities of the Navier-Stokes Equation, d = 3	p. 197
Local Homogeneity and Regularity. CKN Theory	p. 205
Incipient Turbulence and Chaos	p. 227
Fluid Theory in the Absence of Existence and Uniqueness Theorems for the Basic Fluid Dynamics Equations. Truncated NS Equations. (The Rayleigh and Lorenz Models)	p. 227
Onset of Chaos. Elements of Bifurcation Theory	p. 239
Bifurcation Theory. End of the Onset of Turbulence	p. 259
Dynamical Tables	p. 275
Ordering Chaos	p. 287
Quantitative Description of Chaotic Motions Before Developed Turbulence. Continuous Spectrum	p. 287
Timed Observations. Random Data	p. 307
Dynamical Systems Types. Statistics on Attracting Sets	p. 319
Dynamical Bases and Lyapunov Exponents	p. 330
SRB Statistics. Attractors and Attracting Sets. Fractal Dimension	p. 351
Ordering of Chaos. Entropy and Complexity	p. 367
Symbolic Dynamics. Lorenz Model. Ruelle's Principle	p. 380
Developed Turbulence	p. 403
Functional Integral Representation of Stationary Distributions	p. 403
Phenomenology of Developed Turbulence and the Kolmogorov Laws	p. 412
The Shell Model. Multifractal Statistics	p. 431
Statistical Properties of Turbulence	p. 441
Viscosity, Reversibility, and Irreversible Dissipation	p. 441
Reversibility, Axiom C, Chaotic Hypothesis	p. 452
Chaotic Hypothesis, Fluctuation Theorem and Onsager Reciprocity. Entropy Driven Intermittency	p. 463
The Structure of the Attractor for the Navier-Stokes Equations. Dissipative Euler Equations. Barometric Formula	p. 477
Bibliography	p. 491
Name Index	p. 501
Subject Index	p. 503
Citations Index	p. 511
Table of Contents provided by Blackwell. All Rights Reserved.

Foundations of Fluid Dynamics

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Hardcover

Industry Reviews

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Other Editions and Formats

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