Quasineutral limit of the electro-diffusion model arising in electrohydrodynamics

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.