Equilibrium Problems in Fluid-Structure Interactions: The Eldrod and Adams Model.

This paper investigates the dynamic behavior of a lubricated mechanical system in the incompressible fluid case. The main objective is to develop a rigorous mathematical model describing the motion of the upper surface subjected to lubrication effects. The model is based on the quasistationary Reynolds equation, which governs the pressure distribution within the lubricant film, coupled with Newton’s second law to characterize the vertical displacement of the moving surface.

We establish theoretical results concerning the existence and uniqueness of solutions to the coupled differential system arising from this model. In addition, we identify conditions under which global solutions fail to exist, providing insight into possible mechanical instabilities or breakdown of the lubrication regime.

A detailed numerical analysis is performed to investigate the influence of key physical parameters, particularly the film thickness parameter $a$ and the pressure field $p$, on the overall system dynamics. Various computational experiments are carried out to illustrate the evolution of these parameters and their interaction with the mechanical response of the system.

The obtained results contribute to a deeper understanding of lubricated contact mechanisms and highlight the critical role of fluid-structure interaction in determining system stability. These findings may support the design and optimization of engineering devices involving thin film lubrication and moving rigid surfaces.