Temporary list of contents of the english version of the book
"Fluid dynamics" by Giovanni Gallavotti



Sec (CHAPTER I: Generalities on Continua)[1]
Sec (\${1.1} Continua)[1]
Sec (\${1.2} General and incompressible equations.)[15]
Sec (\${1.3} The rescaling method and estimates of the approximations)[25]
Sec (\${1.4} Elements of hydrostatics)[32]
Sec (\${1.5} The convection problem. Rayleigh's equations)[43]
Sec (\${1.6} Kinematics: incompressible fields, vector potentials, decompositions of a general field)[53]
Sec (\${1.7} Vorticity conservation in Euler equation. Clebsch potentials and Hamiltonian form of Euler equations. Bidimensional fluids)[66]
Sec (CHAPTER II: Empirical algorithms. Analytical theories)[83]
Sec (\${2.1} Incompressible Euler and Navier--Stokes fluidodynamics. First empirical solutions algorithms. Auxiliary friction and heat equation comparison methods)[83]
Sec (\${2.2} Another class of empirical algorithms. Spectral method. Stokes problem. Gyroscopic analogy)[99]
Sec (\${2.3} Vorticity algorithms for incompressible Euler and Navier--Stokes fluids. The $d=2$ case)[118]
Sec (\${2.4} Vorticity algorithms for incompressible Euler and Navier--Stokes fluids. The $d=3$ case)[126]
Sec (CHAPTER III: Analytical theories and mathematical aspects)[141]
Sec (\${3.1} Spectral method and local existence, regularity and uniqueness theorems for Euler and Navier--Stokes equations, $d\ge 2$)[141]
Sec (\${3.2} Weak global existence theorems for NS. Autoregularization, existence, regularity and uniqueness for $d=2$)[156]
Sec (\${3.3} Regularity: partial results for the NS equation in $d=3$. The theory of Leray)[174]
Sec (\${3.4} Fractal dimension of singularities of the Navier--Stokes equation, $d=3$)[194]
Sec (\${3.5} Local homogeneity and regularity. CKN theory)[202]
Sec (CHAPTER IV: Incipient turbulence and chaos)[223]
Sec (\${4.1} Fluids theory in absence of existence and uniqueness theorems for the basic fluidodynamics equations. Truncated NS equations. The Rayleigh's and Lorenz' models)[223]
Sec (\${4.2} Onset of chaos. Elements of bifurcation theory)[235]
Sec (\${4.3} Chaos scenarios)[253]
Sec (\${4.4} Dynamical tables)[269]
Sec (CHAPTER V: Ordering chaos)[281]
Sec (\${5.1} Quantitative description of chaotic motions before developed turbulence. Continuous spectrum)[281]
Sec (\${5.2} Timed observations. Random data.)[299]
Sec (\${5.3} Dynamical systems types. Statistics on attracting sets)[311]
Sec (\${5.4} Dynamical bases and Lyapunov exponents)[322]
Sec (\${5.5} SRB Statistics. Attractors and attracting sets. Fractal dimension.)[341]
Sec (\${5.6} Ordering of Chaos. Entropy and complexity)[357]
Sec (\${5.7} Symbolic dynamics. Lorenz model. Ruelle's principle)[369]
Sec (CHAPTER VI: Developed turbulence)[391]
Sec (\${6.1} Functional integral representation of stationary distributions)[391]
Sec (\${6.2} Phenomenology of developed turbulence and Kolmogorov laws)[400]
Sec (\${6.3} The shell model. Multifractal statistics)[419]
Sec (CHAPTER VII: Statistical properties of turbulence)[429]
Sec (\${7.1} Viscosity, reversibility and irreversible dissipation)[429]
Sec (\${7.2} Reversibility, axiom C, chaotic hypothesis.)[440]
Sec (\${7.3} Chaotic hypothesis, fluctuation theorem and Onsager reciprocity. Entropy driven intermittency)[451]
Sec (\${7.4} The structure of the attractor for the Navier--Stokes equations)[465]
Sec (Bibliography)[479]
Sec (Name index)[487]
Sec (Subject index)[488]
Sec (Citations index)[494]