Sisällysluettelo:
“…The Navier-
Stokes Equations -- Turbulence: Where the Interests of Engineers and Mathematicians Overlap -- Elements of the Theories of Turbulence of Kolmogorov and Kraichnan -- Function Spaces, Functional Inequalities, and Dimensional Analysis -- Elements of the Mathematical Theory of the Navier-
Stokes Equations -- Energy and Enstrophy -- Boundary Value Problems -- Helmholtz-Leray Decomposition of Vector Fields -- Weak Formulation of the Navier-
Stokes Equations -- Function Spaces -- The
Stokes Operator -- Existence and Uniqueness of Solutions: The Main Results -- Analyticity in Time -- Gevrey Class Regularity and the Decay of the Fourier Coefficients -- Function Spaces for the Whole-Space Case -- The No-Slip Case with Moving Boundaries -- Dissipation Rate of Flows -- Nondimensional Estimates and the Grashof Number -- Mathematical Complements -- Proofs of Technical Results in Chapter II -- Finite Dimensionality of Flows -- Determining Modes -- Determining Nodes -- Attractors and Their Fractal Dimension -- Approximate Inertial Manifolds -- Proofs of Technical Results in Chapter III -- Stationary Statistical Solutions of the Navier-
Stokes Equations, Time Averages, and Attractors -- Mathematical Framework, Definition of Stationary Statistical Solutions, and Banach Generalized Limits -- Invariant Measures and Stationary Statistical Solutions in Dimension 2 -- Stationary Statistical Solutions in Dimension 3 -- Attractors and Stationary Statistical Solutions…”
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