Constantin, P.; Foiaş, Ciprian; Temam, R. 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 Cited in 10 ReviewsCited in 124 Documents MSC: 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids 35A20 Analyticity in context of PDEs Keywords:turbulence; degrees of freedom; upper estimates; Hausdorff dimension; attractor PDFBibTeX XMLCite \textit{P. Constantin} et al., Attractors representing turbulent flows. Providence, RI: American Mathematical Society (AMS) (1985; Zbl 0567.35070) Full Text: DOI