Global existence of weak solutions of a model for electrolyte solutions   - Part 2: Multicomponent case
  This paper analytically investigates the Darcy-Poisson-Nernst-Planck system. This system is a mathematical model for electrolyte solutions. In this paper, we consider electrolyte solutions, which consist of a neutral fluid and multiple suspended charged chemical species with arbitrary valencies. We prove global existence and uniqueness of weak solutions in two space dimensions. 
Matthias Herz and Peter Knabner
math.AP