Analysis of a parabolic compressible first-order slip Reynolds equation with discontinuous coefficients

We study a lubricated system consisting of two bodies in proximity. The flow of air is considered as a lubricated flow and the air pressure pp satisfies the first-order slip Reynolds equation ∂∂t[ph]+Λ⋅∇[hp]=∇⋅[(h3p+λh2)∇p], where hh is the normalized gap thickness with can be discontinuous in space. We prove the existence and uniqueness of a nonnegative weak solution by using an implicit time semi-discretization scheme.