Asymptotic Description of a Viscous Fluid Layer

Abstract

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