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arXiv · 1102.0949

Electrified thin films: Global existence of non-negative solutions

Cyril Imbert·Antoine Mellet
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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).

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Cyril Imbert, Antoine Mellet. 2011-02-04. Electrified thin films: Global existence of non-negative solutions. https://doi.org/10.1016/j.anihpc.2012.01.003

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