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An Improved Nonlinear Reynolds Equation for a Thin Flow of a Viscous Incompressible Fluid

Videman, J. H.; Nazarov, S.A.

Vestnik State Petersburg University: Mathematics, 41 (2008), 171-175

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.