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Attractor dimension estimate for plane shear flow of micropolar fluid with free boundary

✍ Scribed by Mahdi Boukrouche; Grzegorz Łukaszewicz

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 174 KB
Volume: 28
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.630

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✦ Synopsis

This research is motivated by a problem from lubrication theory. We consider a free boundary problem of a two-dimensional boundary-driven micropolar uid ow. The existence of a unique global-in-time solution of the problem and the global attractor for the associated semigroup are known.

In this paper we estimate the dimension of the global attractor in terms of the given data and the geometry of the domain of the ow by establishing a new version of the Lieb-Thirring inequality with constants depending explicitly on the geometry of the domain. We also obtain some new estimates for the Navier-Stokes shear ows.

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