  This study investigates the nonlinear stability and dynamics of
gravity-driven viscous films on a vertical rotating cylinder, considering both
outer and inner surface flows with slip conditions at the cylinder wall. We
develop an asymptotic model for the combined effects of rotation and wall
slippage. Linear stability analysis indicates that wall slippage enhances
instability on both surfaces, while rotation has differing impacts: it
amplifies instability due to slip for outer surface flow but reduces it for
inner surface flow. A weakly nonlinear stability analysis is then conducted to
explore the combined impact of rotation and wall slip on flow stability beyond
the linear regime, including the bifurcation of the nonlinear evolution
equation for both surfaces. The traveling wave solution of the model is
analyzed, showing how rotation affects nonlinear wave speed with a slippery
wall. A stability analysis of the traveling wave solutions is also performed.
Numerical simulations of the nonlinear evolution of the free surface reveal
that increasing slip length enhances the choke phenomenon in inner surface
flow, while rotation can delay this effect. Additionally, simulations show that
for flow along the outer surface of a slippery rotating cylinder, the film
tends to break up into droplets in the presence of rotation.
