  Motivated by models for thin films coating cylinders in two physical cases
proposed by V.I. Kerchman and A.L. Frenkel, we analyze the dynamics of
corresponding thin film models. The models are governed by nonlinear,
fourth-order, degenerate, parabolic PDEs. We prove, given positive and suitably
regular initial data, the existence of weak solutions in all length scales of
the cylinder, where all solutions are only local in time. We also prove that
given a length constraint on the cylinder, long-time and global in time weak
solutions exist. This analytical result is motivated by numerical work on
related models in the Ph.D. Thesis of R. Ogrosky in conjunction with multiple
further works jointly worked on by combinations of Camassa, Forest, Lee, the
first author, Ogrosky, Olander, and Vaughn.
