  Models and simulations of the flow of thin films of fluids have many
important applications in industrial and natural processes. We consider the
motion of a thin layer of an incompressible, Newtonian fluid over an arbitrary
solid, stationary curved substrate. Earlier work by Roy, et al has modeled slow
fluid flows in which inertia is negligible. However, in many applications a
model expressed in terms of both the fluid layer thickness and the average
lateral velocity is needed to resolve faster dynamics. Here we use centre
manifold techniques to derive such a non-dimensional, approximate model of the
three dimensional flow.
