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  and properties of the solutions of the Poisson-Boltzmann equation. These properties follows from singular integral operators techniques.
Matemática aplicada e computacional. Rio de Janeiro. Vol. 25, no. 1 (2006), p. 1-26.