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

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

2012-01-27

arxiv.org/abs/1201.5753v1

Physics

Mathematical Physics

24 pages, submitted to Nonlinear Analysis RWA

Scientific paper

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 $l$-trajectories. This research is motivated by a problem from lubrication theory.

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