  We study the flow of two immiscible fluids located on a solid bottom, where
the lower fluid is Newtonian and the upper fluid is a non-Newtonian Ellis
fluid. Neglecting gravitational effects, we consider the formal asymptotic
limit of small film heights in the two-phase Navier--Stokes system. This leads
to a strongly coupled system of two parabolic equations of fourth order with
merely H\"older-continuous dependence on the coefficients. For the case of
strictly positive initial film heights we prove local existence of strong
solutions by abstract semigroup theory. Uniqueness is proved by energy methods.
Under additional regularity assumptions, we investigate asymptotic stability of
the unique equilibrium solution, which is given by constant film heights.
