Quasi-neutral limit and the initial layer problem of the electro-diffusion model arising in electro-hydrodynamics. (June 2021)

• Record Type: Journal Article
• Authors: Wang, Shu; Jiang, Limin
• Is Part Of: Nonlinear analysis. Volume 59(2021)
• Publication Date: 2021-06
• Subjects: Quasi-neutral limit -- Initial layer -- Weighted energy functional -- Energy method -- Multiple scaling asymptotic expansions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103266
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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.