We introduce a weak formulation for a system of electrostatic and hydrodynamic equations modelling the electrophoretic motion of charged particles in ionized fluids. We obtain a local in time existence theorem, using the results established in [11] and properties of the solutions of the Poisson-Boltzmann equation. These properties follows from singular integral operators techniques.
Poisson-Boltzmann equation; singular integral operators; Stokes problem; electrophoresis
