Asymptotic justification of the Reynolds equation for a spherical bearing
Analysis of PDEs
2026-06-29 v1
Abstract
To our knowledge, there is no rigorous mathematical justification of the Reynolds equation for a spherical bearing. In this article, we demonstrate that the solution of the Stokes problem in a domain between two closely spaced spheres converges, as the distance between the spheres approaches zero, to the solution of a "Reynolds equation".
Cite
@article{arxiv.2606.30148,
title = {Asymptotic justification of the Reynolds equation for a spherical bearing},
author = {Guy Bayada and José M. Rodríguez and Raquel Taboada-Vázquez},
journal= {arXiv preprint arXiv:2606.30148},
year = {2026}
}