Global existence of solutions for the Poisson–Nernst–Planck system with steric effects

Abstract

In this work, we study the global existence of a modified Poisson–Nernst–Planck system with steric effects. This model involves cross-diffusion and non-local terms. The main idea of the proof is to approximate the system by truncating the diffusion matrix and apply the Schauder’s fixed-point theorem. Moreover, we obtain L2 uniform in time estimates from the energy inequality (3.5). The global existence then follows.