Quasi-neutral limit of Nernst-Planck-Navier-Stokes system

Abstract

In this paper, we investigate the quasi-neutral limit of Nernst-Planck-Navier-Stokes system in a smooth bounded domain $\Omega$ of ${\mathbb{R}}^d$ for $d=2,3,$ with ``electroneutral boundary conditions" and well-prepared data. We first prove by using modulated energy estimate that the solution sequence converges to the limit system in the norm of $L^{\infty }((0,T);L^2(\Omega ))$ for some positive time $T.$ In order to justify the limit in a stronger norm, we need to construct both the initial layers and weak boundary layers in the approximate solutions.