Abstract

We consider a layer of viscous incompressible fluid on a plate which can be vibrated vertically and we derive an equation which is non local in time for the linear evolution of the deformation of the surface in contact with the atmosphere. The equation is used to study the decay of a deformation of the surface. We characterize an interesting regime of high viscosity where the equation becomes local and we use it to study Faraday's instability. A new scenario is found for low frequency of the forcing. Key words : viscous fluid, Faraday's instability, lubrication regime.

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