On the existence of an exponential attractor for a planar shear flow with the Tresca friction condition

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• 作者：Grzegorz ?ukaszewicz ; ^{glukasz@mimuw.edu.pl}
• 关键词：Lubrication theory ; Navier&ndash ; Stokes equation ; Global solution ; Exponential attractor
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2013
• 出版时间：June, 2013
• 年：2013
• 卷：14
• 期：3
• 页码：1585-1600
• 全文大小：275 K

文摘

We consider a two-dimensional nonstationary Navier-Stokes shear flow with a subdifferential boundary condition on a part of the boundary of the flow domain, namely, with a boundary driving subject to the Tresca law. There exists a unique global in time solution of the considered problem which is governed by a variational inequality. Our aim is to prove the existence of a global attractor of a finite fractional dimension and of an exponential attractor for the associated semigroup. We use the method of -trajectories. This research is motivated by a problem from lubrication theory.