Attractor dimension and small length scale estimates for the three-dimensional Navier - Stokes equations
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It is shown that a rigorous estimate for the fractal dimension of the global attractor of the three-dimensional incompressible Navier-Stokes equations on periodic boundary conditions is given by dF≤ c(L/λk)4.8where L is the box length and λkis a Kolmogorov length defined by λk-1= (ε̄/v3)1/4with the energy dissipation rate given by ε̄ = vL-3sup, ∫Ω|ω|2dV. By interpreting the dimension of the attractor as the number of degrees of freedom of the system, we obtain an estimate for an average natural length scale ℓ for the flow which is given by ℓ/L ≥ c (λk/L)1.6.
author list (cited authors)
Gibbon, J. D., & Titi, E. S.