Global solutions to the Nernst-Planck-Euler system on bounded domain

TL;DR

This paper proves the existence of global strong solutions for the Nernst-Planck-Euler system in two-dimensional bounded domains, accommodating large data and inhomogeneous boundary conditions, advancing the mathematical understanding of ionic fluid models.

Contribution

It establishes the first global existence results for the Nernst-Planck-Euler system with large data and inhomogeneous boundary conditions in two dimensions.

Findings

Global strong solutions exist for large data in 2D bounded domains.

The results apply to systems with either two species or identical diffusivities and ionic valences.

The proof utilizes energy estimates, characteristic line integration, and elliptic/parabolic regularity theory.

Abstract

We show that the Nernst-Planck-Euler system, which models ionic electrodiffusion in fluids, has global strong solutions for arbitrarily large data in the two dimensional bounded domains. The assumption on species is either there are two species or the diffusivities and the absolute values of ionic valences are the same if the species are arbitrarily many. In particular, the boundary conditions for the ions are allowed to be inhomogeneous. The proof is based on the energy estimates, integration along the characteristic line and the regularity theory of elliptic and parabolic equations.