  We derive a novel and rigorous correction to the classical Reynolds
lubrication approximation for fluids with viscosity depending upon the
pressure. Our analysis shows that the pressure dependence of viscosity leads to
additional nonlinear terms related to the shear-rate and arising from a non
negligible cross-film pressure. We present a numerical comparison between the
classical Reynolds equation and our modified equation and conclude that the
modified equation leads to the prediction of higher pressures and viscosities
in the flow domain.
