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Attractors and neoattractors for 3D stochastic Navier-Stokes equations

Cutland, N.J. and Keisler, H.J. (2005) Attractors and neoattractors for 3D stochastic Navier-Stokes equations. Stochastics and Dynamics, 5 (4). pp. 487-533. ISSN 0219-4937

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Abstract

In nonstandard analysis was used to construct a (standard) global attractor for the 3D stochastic Navier–Stokes equations with general multiplicative noise, living on a Loeb space, using Sell's approach. The attractor had somewhat ad hoc attracting and compactness properties. We strengthen this result by showing that the attractor has stronger properties making it a neo-attractor — a notion introduced here that arises naturally from the Keisler–Fajardo theory of neometric spaces.

To set this result in context we first survey the use of Loeb space and nonstandard techniques in the study of attractors, with special emphasis on results obtained for the Navier–Stokes equations both deterministic and stochastic, showing that such methods are well-suited to this enterprise.

Item Type: Article
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 10 Feb 2009 12:48
Last Modified: 10 Feb 2009 12:48
Published Version: http://dx.doi.org/10.1142/S0219493705001559
Status: Published
Publisher: World Scientific Publishing Co
Identification Number: 10.1142/S0219493705001559
URI: http://eprints.whiterose.ac.uk/id/eprint/7534

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