Robinson, James C. Low dimensional attractors arise from forcing at small scales. (English) Zbl 1040.35063 Physica D 181, No. 1-2, 39-44 (2003). Summary: Standard estimates of the dimension of the attractor of the 2D Navier-Stokes equations are given in terms of a dimensionless Grashof number that measures the total amount of energy injected into the flow. However, this result takes no account of whether the forcing is concentrated at large or small scales. By a simple modification of the usual argument, this paper provides a bound that is linear in a modified Grashof number that reflects the spatial structure of the forcing. In particular, as a fixed amount of energy is injected at progressively smaller scales then the dimension of the attractor decreases. Cited in 3 Documents MSC: 35Q30 Navier-Stokes equations 37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:2D Navier-Stokes equations; Grashof number; spatial forcing structure; scales PDFBibTeX XMLCite \textit{J. C. Robinson}, Physica D 181, No. 1--2, 39--44 (2003; Zbl 1040.35063) Full Text: DOI References: [1] Constantin, P.; Foias, C., Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations, Commun. Pure Appl. Math., 38, 1-27 (1985) · Zbl 0582.35092 [2] P. Constantin, C. Foias, R. Temam, Attractors representing turbulent flows, Mem. Am. Math. Soc. 53 (1985).; P. Constantin, C. Foias, R. Temam, Attractors representing turbulent flows, Mem. Am. Math. 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