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Attractors representing turbulent flows. (English) Zbl 0567.35070
Mem. Am. Math. Soc. 314, 67 p. (1985).
Physical investigations of 3-dimensional turbulence lead to the conclusion that for \(t\to \infty\) the turbulence flow has only a finite number d of degrees of freedom; in particular, Kolmogorov, Landau and Lifschitz obtained upper estimates for that number d in terms of such physical quantities as Reynolds number Re and dissipation length. The authors prove that under the hypothesis that singularities do not develop in 3-dimensional flows these inequalities are true for some natural mathematical formalizations of d, Re etc., e.g. d is interpreted as a Hausdorff dimension of an attractor.
Reviewer: C.Ya.Kreĭnovich

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
35A20 Analyticity in context of PDEs
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