On existence and uniqueness of the equilibrium state for an improved Nernst-Planck-Poisson system

Abstract

This work deals with a model for a mixture of charged constituents introduced in [W. Dreyer et al. Overcoming the shortcomings of the Nernst-Planck model. emphPhys. Chem. Chem. Phys., 15:7075-7086, 2013]. The aim of this paper is to give a first existence and uniqueness result for the equilibrium situation. A main difference to earlier works is a momentum balance involving the gradient of pressure and the Lorenz force which persists in the stationary situation and gives rise to the dependence of the chemical potentials on the particle densities of every species.