Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations. (English) Zbl 0582.35092

Constantin, P.; Foiaş, Ciprian

Commun. Pure Appl. Math. 38, 1-27 (1985).

The fractal and Hausdorff dimension of the universal attractor for the Navier-Stokes equation are estimated in terms of the Grashof number, improving the previous estimations. The equations governing the transport of finite-dimensional volume elements in the phase space are established, and the existence of a critical dimension (such that every volume depassing this dimension decays exponentially in time) is proved. The authors show that upper bounds for the fractal and Hausdorff dimension of the attractor may be obtained in terms of the global Lyapunov exponents [replacing the local exponents used in the J. L. Kaplan-J. A. Yorke conjecture, Lect. Notes Math. 730, 204-227 (1979; Zbl 0448.58020)].

Reviewer: G.Pasa

MSC:

35Q30	Navier-Stokes equations
35B40	Asymptotic behavior of solutions to PDEs
37C70	Attractors and repellers of smooth dynamical systems and their topological structure

Keywords:

Kaplan-Yorke formulas; dimension; universal attractor; Navier-Stokes equation; Grashof number; critical dimension; global Lyapunov exponents

Citations:

Zbl 0448.58020

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