Some theoretical results concerning diphasic flows in thin films

We are interested in a model for diphasic fluids in thin flows taking into account both the hydrodynamical and the chemical effects at the interface between the two fluids. A limit problem in thin curved channels is introduced heuristically. It is a system coupling the Reynolds equation and the Cahn–Hilliard equation. We study the mathematical properties of this system, and prove an existence result under some smallness condition on the data.