On Characteristic Exponents in Turbulence
Ruelle has found upper bounds to the magnitude and to the number of non-negative characteristic exponents for the Navier-Stokes flow of an incompressible fluid in a domain Ω. The latter is particularly important because it yields an upper bound to the Hausdorff dimension of attracting sets. However, Ruelle’s bound on the number has three deficiences : (i) it relies on some unproved conjectures about certain constants; (ii) it is valid only in dimensions ≧ 3 and not 2 ; (iii) it is valid only in the limit Ω-→ ∞. In this paper these deficiences are remedied and, in addition, the final constants in the inequality are improved.
KeywordsIncompressible Fluid Hausdorff Dimension Characteristic Exponent Sharp Constant Large Volume Limit
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