Abstract: The Poisson-Nernst-Planck (PNP) model is a well-studied system of equations, which describes the movement of charged particles, oftentimes ions, in a solvent. However, in narrow domains ions become crowded and repulsion may appear, which is not taken into account by the classical PNP equations. Thus, a modification is needed to consider this behavior.
In this talk, a Poisson-Nernst-Planck cross-diffusion system with steric effects is presented. Related systems are reviewed and compared to the proposed model in the context of both application and mathematical treatment. Using entropy methods the existence of global weak solutions, a weak-strong uniqueness property as well as the exponential convergence towards the thermal equilibrium are outlined. Moreover, the mathematical difficulties arising in the analysis of the steric PNP system are discussed. Finally, the results of a numerical simulation are shown.