Premium
Attractor dimension estimate for plane shear flow of micropolar fluid with free boundary
Author(s) -
Boukrouche Mahdi,
Łukaszewicz Grzegorz
Publication year - 2005
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.630
Subject(s) - attractor , mathematics , domain (mathematical analysis) , boundary (topology) , flow (mathematics) , semigroup , mathematical analysis , shear flow , dimension (graph theory) , plane (geometry) , no slip condition , geometry , boundary value problem , classical mechanics , mixed boundary condition , physics , pure mathematics
Abstract This research is motivated by a problem from lubrication theory. We consider a free boundary problem of a two‐dimensional boundary‐driven micropolar fluid flow. 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 flow 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 flows. Copyright © 2005 John Wiley & Sons, Ltd.