Quasi-neutral limit and the initial layer problem of the electro-diffusion model arising in electro-hydrodynamics

In this paper we study quasi-neutral limit and the initial layer problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck–Nernst–Poisson and Navier–Stokes equations. Different from other studies, we consider the physical case that the mobilities of the charges are different. For the generally smooth doping profile and for the ill-prepared initial data, under the assumption that the difference between the mobilities of two kinds of charges is very small, the quasi-neutral limit with an initial layer structure is rigorously proved by using the weighted energy method coupled with multi-scaling asymptotic expansions.