Quasineutral limit of the electro-diffusion model arising in Electrohydrodynamics

TL;DR

This paper rigorously justifies the quasineutral limit of the electro-diffusion model in electrohydrodynamics, demonstrating uniform Sobolev norm convergence as the Debye length approaches zero.

Contribution

It provides a rigorous mathematical proof of the quasineutral limit for the electro-diffusion model coupling Nernst-Planck-Poisson and Navier-Stokes equations.

Findings

Uniform estimates established with respect to Debye length

Sobolev norm convergence proved for the quasineutral limit

Energy analysis used for rigorous justification

Abstract

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.