Electrified thin films: Global existence of non-negative solutions

Cyril Imbert (1) , Antoine Mellet (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Department of Mathematics [College Park]

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).

Mots clés: Higher order equation; Non-local equation; Thin film equation; Non-negative solutions

Domaines: Equations aux dérivées partielles [math.AP]

Cyril Imbert, Antoine Mellet. Electrified thin films: Global existence of non-negative solutions. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2012, 29 (3), pp.413-433. ⟨10.1016/j.anihpc.2012.01.003⟩. ⟨hal-00563372v4⟩