Glasnik Matematicki, Vol. 39, No.1 (2004), 77-100.

DERIVATION OF THE REYNOLDS TYPE EQUATION WITH MAMORY EFFECTS, GOVERNING TRANSIENT FLOW OF LUBRICANT

Antonija Duvnjak

Faculty of Electrical Engineering and Computing, Department of Applied Mathematics, University of Zagreb, Unska 3, 10000 Zagreb, Croatia
e-mail: antonija.duvnjak@gsf.de


Abstract.   In this paper we derive the Reynolds type lubrication equation with memory effects for lubrication of a rotating shaft. Starting from the nonstationary Stokes equations and using the asymptotic expansion we obtain a law that is nonlocal in time and gives a linear connection between velocity and pressure gradient. Our law tends to the classical Reynolds equation when time tends to infinity. We prove a convergence theorem for velocity and pressure in appropriate functional space.

2000 Mathematics Subject Classification.   35B25, 35Q30.

Key words and phrases.   Nonstationary Stokes system, nonlocal Reynolds equation.


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