Electrified thin films: Global existence of non-negative solutions

Mellet, Antoine; Imbert, Cyril

Mellet, Antoine; Imbert, Cyril (2012), Electrified thin films: Global existence of non-negative solutions, Annales de l'Institut Henri Poincaré. Analyse non linéaire, 29, 3, p. 413-433. http://dx.doi.org/10.1016/j.anihpc.2012.01.003

Type

Article accepté pour publication ou publié

External document link

ttp://hal.archives-ouvertes.fr/hal-00563372/fr/

Date

2012

Journal name

Annales de l'Institut Henri Poincaré. Analyse non linéaire

Volume

Number

Publisher

Elsevier

Pages

413-433

Abstract (EN)

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).

Subjects / Keywords

Non-negative solutions; Thin film equation; Non-local equation; Higher order equation