Capillary/gravity film flows on the surface of a rotating cylinder

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