ANALYSIS OF THE NAVIER–STOKES–NERNST–PLANCK–POISSON SYSTEM

Abstract

We study a fluid-dynamical model based on a coupled Navier–Stokes–Nernst–Planck–Poisson system. Of special interest are the fluid velocity, concentrations of charged particles ranging from colloidal to nano size and the induced quasi-electrostatic potential, which all depend on an externally applied electrical field. For d ≤ 3, we prove existence and in some cases uniqueness of weak solutions. Moreover, we characterize solutions via energy laws, mass conservation, non-negativity and pointwise bounds. Furthermore, the system enjoys an entropy law. Existence of locally strong solutions is verified.