Existence theory for a Poisson-Nernst-Planck model of electrophoresis

A system modeling the electrophoretic motion of a charged rigid macromolecule immersed in a incompressible ionized fluid is considered. The ionic concentration is governing by the Nernst-Planck equation coupled with the Poisson equation for the electrostatic potential, Navier-Stokes and Newtonian equations for the fluid and the macromolecule dynamics, respectively. A local in time existence result for suitable weak solutions is established, following the approach of Desjardins and Esteban [Comm. Partial Diff. Eq., 25 (2000), 1399--1414].