1201.5753 (Grzegorz Łukaszewicz)

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

Grzegorz Łukaszewicz

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.

View original: http://arxiv.org/abs/1201.5753