1. CEREMADE, Université Paris-Dauphine, UMR CNRS 7534, place de Lattre de Tassigny, 75775 Paris cedex 16, France;2. Department of Mathematics, Mathematics Building, University of Maryland, College Park, MD 20742-4015, USA
Abstract:
We consider an equation modeling the evolution of a viscous liquid thin film wetting a horizontal solid substrate destabilized by an electric field normal to the substrate. The effects of the electric field are modeled by a lower order non-local term. We introduce the good functional analysis framework to study this equation on a bounded domain and prove the existence of weak solutions defined globally in time for general initial data (with finite energy).