On liquid crystal flows with free-slip boundary conditions

In this paper, we study a coupled dynamic system describing nematic liquid crystal flows. The system was motivated by the Ericksen-Leslie equations mo deling the flow of nematic liquid crystals. The purpose of studying the sim plified system is to understand the flow properties of more complicated mat erials, the material configurations, as well as the interactions between th em. Unlike in the previous studies where the Dirichlet boundary conditions are prescribed, we consider here the free-slip boundary conditions which po ssess a number of distinct advantages. The results in this paper form the a nalytical background for the forthcoming numerical simulations of the syste m.