Rayleigh–Taylor instability of a thin liquid layer in the presence of three-dimensional perturbations

We consider the evolution of small three-dimensional perturbations of an accelerated thin liquid layer. The analytical solutions obtained correspond to various types of initial perturbations: in the form of a layer, in the initial velocities, and in the thickness of the layer. Depending on the dimensionless parameters which characterize the initial data, the perturbations can increase exponentially with time, remain bounded, and change the phase.