  We consider the Nernst-Planck equations describing the nonlinear time
evolution of multiple ionic concentrations in a two-dimensional incompressible
fluid. The velocity of the fluid evolves according to either the Euler or
Darcy's equations, both forced nonlinearly by the electric forces generated by
the presence of charged ions. We address the global well-posedness and Gevrey
regularity of the resulting electrodiffusion models in the periodic setting.
