This work gives a survey of the results obtained in a series of papers by Boukrouche & Lukaszewicz (2004, 2005a,b, 2007) and Boukrouche, Lukaszewicz, & Real (2006) in which we consider the problem of the existence and finite dimensionality of attractors for some classes of twodimensional turbulent boundary-driven flows (Problems I–IV below). The flows admit mixed, non-standard boundary conditions and also time-dependent driving forces (Problems III and IV). We are interested in the dependence of the dimension of the attractors on the geometry of the flow domain and on the boundary conditions. This research is motivated by problems from lubrication theory. Our results generalize some earlier ones devoted to the.
