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

Nonnegative Weak Solutions of Thin Film Equations Related to Viscous Flows in Cylindrical Geometries