DERIVATION OF THE REYNOLDS EQUATION FOR LUBRICATION OF A ROTATING SHAFT

A. DUVNJAK and E. MARUSIC-PALOKA

Address. A. Duvnjak, Faculty of Electrical Engineering and Computing, University of Zagreb, Department of Applied Mathematics, Unska 3, 10000 Zagreb, CROATIA

E. Marusic-Paloka, Department of Mathematics, University of Zagreb, Bijenicka 30, 10000 Zagreb, CROATIA

E-mail: emarusic@math.hr

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