  We consider the initial value problem for the Nernst-Planck equations coupled
to the incompressible Euler equations in $\mathbb T^2$. We prove global
existence of weak solutions for vorticity in $L^p$. We also obtain global
existence and uniqueness of smooth solutions. We show that smooth solutions of
the Nernst-Planck-Navier-Stokes equations converge to solutions of the
Nernst-Planck-Euler equations as viscosity tends to zero. All the results hold
for large data.
