Three-dimensional perturbations of the radial-rotational spread–sink of a viscous cylindrical layer

Abstract

The temporal evolution of the three-dimensional pattern of perturbations superposed on a radialrotational spread or sink of a viscous layer the parameters of which depend on the radial coordinate and time has been studied. The motion of the layer boundaries is specified both in the main motion and in the perturbed motion. Based on the integral relations method applied to the linearized problem in perturbations, sufficient estimates of exponential stability (in particular, on a finite time interval) of the main motion have been derived.