The uniform attractor for the 2D non-autonomous Navier-Stokes flow in some unbounded domain
type: Item
instance of: scholarly article
title: The uniform attractor for the 2D non-autonomous Navier-Stokes flow in some unbounded domain
zbMATH Open document ID: 1057.35031
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-10-12T00:00:00Z
review text: The authors consider the Navier-Stokes equation on a region \(\Omega\subset\mathbb{R}^2\), where \(\Omega\) only has to satisfy the Poincaré inequality. The weak solutions define a semiprocess depending on an external force \(f\). The authors suppose \(f\in \mathcal{F}\), where \(\mathcal{F}\) is bounded (as a subset of \(L^\infty(\mathbb{R}^+,V')\) and \(V'\) is the dual of the space of divergence free functions in \(H_0^1(\Omega)\)) and positive invariant (i.e. \(s\mapsto f(s+h)\in \mathcal{F}\) for all \(h\geq 0\), \(f\in \mathcal{F}\)). Under these assumptions they prove the existence of a compact uniform (with respect to \(\mathcal{F}\)) attractor. In the case of \(f\) being a \(k\)-dimensional quasi-periodic external force, they also give an upper bound on the Hausdorff dimension of the attractor.
reviewed by: Thomas Elsken
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 2107301
zbMATH Keywords: uniform attractors
zbMATH Keywords: Non-autonomous systems
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: Hausdorff dimension
author: Yanren Hou
author: Kaitai Li
MaRDI profile type: Publication
full work available at URL: j.na.2004.02.031
OpenAlex ID: W2037968224
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DOI: 10.1016/J.NA.2004.02.031
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description: scientific article; zbMATH DE number 2107301