Electrified thin films: Global existence of non-negative solutions

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• 作者：C. Imbert^a ; ^{Cyril.Imbert@ens.fr} ; A. Mellet^b
• 关键词：35G25 ; 35K25 ; 35A01 ; 35B09
• 刊名：Annales de l'Institut Henri Poincare (C) Non Linear Analysis
• 出版年：2012
• 出版时间：May-June, 2012
• 年：2012
• 卷：29
• 期：3
• 页码：413-433
• 全文大小：235 K

文摘

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).