On pullback attractors for a class of two-dimensional turbulent shear flows

We consider a two-dimensional Navier–Stokes shear flow with time dependent boundary driving. We establish the existence of a unique global in time solution of the considered problem and then the existence of the pullback attractor for the associated evolutionary process. In the end, we estimate from above the dimension of the attractor in terms of given data.This research is motivated by a problem from lubrication theory.