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Gallavotti G. Foundation of Fluid Mechanics

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Gallavotti G. Foundation of Fluid Mechanics
Roma, 2000. 502 p
The imagination is stricken 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 mechanics, or quantum fleld theory, or solid state physics, or celestial mechanics, harmonic analysis, elasticity, general relativity or fluid mechanics and chaos in turbulence
Generalities on Continua
General and incompressible equations
The rescaling method and estimates of the approximations
Elements of hydrostatics
The convection problem. Rayleigh's equations
Kinematics: incompressible fields, vector potentials, decompositions of a general field
Vorticity conservation in Euler equation. Clebsch potentials and Hamiltonian form of Euler equations. Bidimensional fiuids
Empirical algorithms. Analytical theories
Incompressible Euler and Navier-Stokes fiuidodynamics. First empirical solutions algorithms. Auxiliary friction and heat equation comparison methods
Another class of empirical algorithms. Spectral method. Stokes problem. Gyroscopic analogy
Vorticity algorithms for incompressible Euler and Navier-Stokes fiuids. The d = 2 case
Vorticity algorithms for incompressible Euler and Navier-Stokes fiuids. The d = 3 case
Analytical theories and mathematical aspects
Spectral method and local existence, regularity and uniqueness theorems for Euler and Navier-Stokes equations, d
Weak global existence theorems for NS. Autoregularization, existence, regularity and uniqueness for d =
Regularity: partial results for the NS equation in d =
The theory of Leray
Fractal dimension of singularities of the Navier-Stokes equation, d =
Local homogeneity and regularity. CKN theory
Incipient turbulence and chaos
Fluids theory in absence of existence and uniqueness theorems for the basic fiuidodynamics equations. Truncated NS equations. The Rayleigh's and Lorenz' models
Onset of chaos. Elements of bifurcation theory
Chaos scenarios
Dynamical tables
Ordering chaos
Quantitative description of chaotic motions before developed turbulence. Continuous
Timed observations. Random data
Dynamical systems types. Statistics on attracting sets
Dynamical bases and Lyapunov exponents
SRB Statistics. Attractors and attracting sets. Fractal dimension
Ordering of Chaos. Entropy and complexity
Symbolic dynamics. Lorenz model. Ruelle's principle
Developed turbulence
Functional integral representation of stationary distributions
Phenomenology of developed turbulence and Kolmogorov laws
he shell model. Multifractal statistics
Statistical properties of turbulence
Viscosity, reversibility and irreversible dissipation
Reversibility, axiom C, chaotic hypothesis
Chaotic hypothesis, fluctuation theorem and Onsager reciprocity. Entropy driven intermittency
The structure of the attractor for the Navier-Stokes equations
Author index
Subject index
Citations index
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