Electrified thin films: Global existence of non-negative solutions
  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). 
Cyril Imbert (CEREMADE), Antoine Mellet
math.AP