  The electro-diffusion model, which arises in electrohydrodynamics, is a
coupling between the Nernst-Planck-Poisson system and the incompressible
Navier-Stokes equations. For the generally smooth doping profile, the
quasineutral limit (zero-Debye-length limit) is justified rigorously in Sobolev
norm uniformly in time. The proof is based on the elaborate energy analysis and
the key point is to establish the uniform estimates with respect to the scaled
Debye length.
