In this paper, we study two characteristic properties of thin confined liquids under shear : the induced velocity profile in the liquid at low shear rates, and the shear-dependent thinning of the effective viscosity. Our approach is based on the coupling between a time-dependent Ginzburg-Landau equation for a local order parameter and a local velocity field. Special attention is given to the role of the lateral nonuniformity of the liquid-wall interactions in determining these properties. We derive the Brinkman equation for the velocity profile and obtain a power low dependence of the viscosity on shear rate in the thinning regime, eta(eff)similar to gamma(-alpha) with 2/3 less than or equal to alpha less than or equal to 1.