An improved nonlinear Reynolds equation for a thin flow of a viscous incompressible fluid

A scalar nonlinear second-order equation describing a fluid flow between two closely spaced rigid walls is constructed on the basis of an asymptotic analysis of the Navier-Stokes equations. This equation takes into account the convective term and the surface curvature; it improves the Reynolds equation and provides a two-term asymptotics for the solution to the initial problem. Integral and pointwise error estimates are obtained. It is demonstrated that the one-dimensional model cannot be improved further.