#### 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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