  We consider an equation for a thin-film of fluid on a rotating cylinder and
present several new analytical and numerical results on steady state solutions.
First, we provide an elementary proof that both weak and classical steady
states must be strictly positive so long as the speed of rotation is nonzero.
Next, we formulate an iterative spectral algorithm for computing these steady
states. Finally, we explore a non-existence inequality for steady state
solutions from the recent work of Chugunova, Pugh, & Taranets.
