E. Marusic-Paloka, Department of Mathematics, University of Zagreb, Bijenicka 30, 10000 Zagreb, CROATIA
Abstract. In this paper, using the asymptotic expansion, we prove that the Reynolds lubrication equation is an approximation of the full Navier--Stokes equations in thin gap between two coaxial cylinders in relative motion. Boundary layer correctors are computed. The error estimate in terms of domain thickness for the asymptotic expansion is given. The corrector for classical Reynolds approximation is computed.
AMSclassification. 35B25, 35B40, 76D08
Keywords. Lubrication, Reynolds equation, Navier-Stokes system, lower-dimensional approximation