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.

中文翻译：

---

流体动力学中的电扩散模型的拟中性极限和初始层问题

在本文中，我们研究了拟中性极限和由电流体动力学引起的电扩散模型的初始层问题，该问题是耦合的普朗克-能斯特-泊松方程和纳维-斯托克斯方程。与其他研究不同，我们认为实际情况是收费的流动性不同。对于一般光滑的掺杂轮廓和准备不充分的初始数据，在两种电荷迁移率之间的差异很小的假设下，通过加权加权严格证明了具有初始层结构的准中性极限能量方法与多尺度渐近展开。