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 known constant for t > 0. The mathematical model consists of a coupled system formed by the Reynolds variational inequality for incompressible fluids and Newton's Second Law. We study the steady states of the problem and the

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... global existence and uniqueness of the time-dependent problem. We assume one degree of freedom for the position of the surface. We consider different cases depending on the geometry of the upper surface.