Abstract
We derive equations describing the motion of a viscous incompressible capillary film on the surface of a rotating cylinder in the transverse gravity field. As a result, we obtain an equation for the film thickness that has fourth order in two space variables and first order in time. We study both space-periodic solutions in the axial coordinate and localized solutions of this equation in the stationary case. We also discuss the stability of stationary solutions. Analysis of the one-dimensional problem shows that its solution strongly depends on the Galileo number and that such a solution does not exist if this number is large. Bibliography: 15 titles.
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