Electrified thin films: Global existence of non-negative solutions

TL;DR

This paper proves the global existence of non-negative weak solutions for a mathematical model describing the evolution of an electrified viscous thin film on a solid substrate, incorporating non-local electric effects.

Contribution

It introduces a functional analysis framework to establish the existence of solutions for the electrified thin film equation on bounded domains, extending previous results.

Findings

Global existence of weak solutions proven

Solutions are non-negative and defined for all time

Applicable to general initial data with finite energy

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).