Asymptotic description of a viscous fluid layer

We prove that the exact non local equation derived by the present authors f or the temporal linear evolution of the surface of a viscous incompressible fluid reduces asymptotically for high viscosity to a second order Mathieu type equation proposed recently by Cerda and Tirapegui. The equation descri bes a strongly damped pendulum and the conditions of validity of the asympt otic regime are given in terms of the relevant physical parameters.