Nonlinear reynolds equation for lubrication of a rapidly rotating shaft

Using the homogenization theory, we derive the nonlinear Reynolds equation governing the process of lubrication of a slipper bearing with rapidly rotating shaft. We prove that this nonliner lubrication law is an approximation of the full Navier-Stokes equations in a thin cylinder with periodic roughness. The analyticity of the nonlinear function giving the relation between the velocity and the pressure drop is proved. The first term in its Taylor's expansion is the classical linear Reynolds law. Boundary layer correctors are computed.