On Characteristic Exponents in Turbulence

Elliott H. Lieb
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Elliott H. Lieb: Princeton University, Departments of Mathematics and Physics

A chapter in Inequalities, 2002, pp 305-312 from Springer

Abstract: Abstract 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.

Keywords: Incompressible Fluid; Hausdorff Dimension; Characteristic Exponent; Sharp Constant; Large Volume Limit (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55925-9_25

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DOI: 10.1007/978-3-642-55925-9_25

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