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The electro-diffusion model, which arises in electrohydrodynamics, is acoupling between the Nernst-Planck-Poisson system and the incompressibleNavier-Stokes equations. For the generally smooth doping profile, thequasineutral limit (zero-Debye-length limit) is justified rigorously in Sobolevnorm uniformly in time. The proof is based on the elaborate energy analysis andthe key point is to establish the uniform estimates with respect to the scaledDebye length.

Quasineutral limit of the electro-diffusion model arising in Electrohydrodynamics