Lack of contact in a lubricated system
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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.