Hausdorff dimension of attractors for the two-dimensional Navier-Stokes equations with boundary conditions
type: Item
instance of: scholarly article
title: Hausdorff dimension of attractors for the two-dimensional Navier-Stokes equations with boundary conditions
zbMATH Open document ID: 0608.58031
DOI: 10.1007/BF01238931
author: André Lafon
published in: Communications in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: The author considers attracting sets in a viscous incompressible fluid in a region \(\Omega\) of \({\mathbb{R}}^ 2\) where the time evolution of the fluid is described by the Navier-Stokes equations with boundary conditions. Two kinds of boundary conditions are investigated: a given velocity and an imposed force on the boundary of \(\Omega\). Using earlier results by \textit{D. Ruelle} [ibid. 87, 287-302 (1982; Zbl 0546.76083); 93, 285-300 (1984; Zbl 0565.76031)] and \textit{E. Lieb} [ibid. 92, 473-480 (1984; Zbl 0598.76054)] the author derives explicit bounds (depending only on the data) for the entropy (Kolmogorov-Sinai invariant) and the Hausdorff dimension of the attractors under consideration.
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 3984173
zbMATH Keywords: viscous incompressible fluid
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: entropy
zbMATH Keywords: Kolmogorov-Sinai invariant
zbMATH Keywords: Hausdorff dimension
MaRDI profile type: Publication
cites work: Attractors of partial differential evolution equations and estimates of their dimension
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cites work: Q3695715
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full work available at URL: https://doi.org/10.1007/bf01238931
OpenAlex ID: W2053322447
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description: scientific article; zbMATH DE number 3984173