Upper Bound on the Dimension of the Attractor for Nonhomogeneous Navier-Stokes Equations
Our aim in this article is to derive an upper bound on the dimension of the attractor for Navier-Stokes equations with nonhomogeneous boundary conditions. in space dimension two, for flows in general domains with prescribed tangential velocity at the boundary, we obtain a bound on the dimension of the attractor of the form csript R signe3/2, where script R signe is the Reynolds number. This improves significantly on previous bounds which were exponential in script R signe. Keywords: Navier-Stokes equations, background flows, channel flows, Taylor-Couette flows, global attractor, functional invariant set, Hausdorff and fractal dimensions, energy dissipation rate, Reynolds number.
A. Miranville and X. Wang, "Upper Bound on the Dimension of the Attractor for Nonhomogeneous Navier-Stokes Equations," Discrete and Continuous Dynamical Systems, vol. 2, no. 1, pp. 95 - 110, American Institute of Mathematical Sciences (AIMS), Jan 1996.
The definitive version is available at https://doi.org/10.3934/dcds.1996.2.95
Mathematics and Statistics
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01 Jan 1996