Lack of contact in a lubricated system

Abstract

Abstract.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 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.

An inverse problem for the compressible Reynolds equation

“…For the incompressible case there is a larger number of references, mainly concerning numerical simulations. See for instance [7], [5], [6] and the survey [1] for more details.…”

On a variational inequality on elasto-hydrodynamic lubrication

“…This approach has been used in different fluid-rigid structure interaction problems in the field (see for instance [4][5][6][7]). It is not difficult to prove that g is well defined, continuous and satisfies…”