JournalsaihpcVol. 29, No. 3pp. 413–433

Electrified thin films: Global existence of non-negative solutions

  • C. Imbert

    CEREMADE, Université Paris-Dauphine, UMR CNRS 7534, place de Lattre de Tassigny, 75775 Paris cedex 16, France

  • A. Mellet

    Department of Mathematics, Mathematics Building, University of Maryland, College Park, MD 20742-4015, USA
Electrified thin films: Global existence of non-negative solutions cover
Download PDF

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).

Cite this article

C. Imbert, A. Mellet, Electrified thin films: Global existence of non-negative solutions. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 3, pp. 413–433

DOI 10.1016/J.ANIHPC.2012.01.003