  We consider the problem of a rigid surface moving over a flat plane. The
surfaces are separated by a small gap filled by a lubricant fluid. The relative
position of the surfaces is unknown except for the initial time $t=0$. The
total load applied over the upper surface is a know constant for $t>0$. The
mathematical model consists in a coupled system formed by Reynolds variational
inequality for incompressible fluids and Newton$^{\prime}$s second Law. In this
paper we study the global existence and uniqueness of solutions of the
evolution problem when the position of the surface presents only one degree of
freedom, under extra assumptions on its geometry. The existence of steady
states is also studied.
