Some theoretical results concerning diphasic fluids in thin films

Abstract : 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 films" is introduced heuristically. It is a system coupling the Reynolds equation and the hydrodynamical Cahn-Hilliard equation. We study the mathematical properties of this system, and prove an existence result under some smallness condition on the data.
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Guy Bayada, Laurent Chupin, Bérénice Grec. Some theoretical results concerning diphasic fluids in thin films. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2015, 116, pp.153-179. ⟨10.1016/j.na.2014.12.020⟩. ⟨hal-00383732v2⟩

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