Global existence of weak solutions of a model for electrolyte solutions - Part 2: Multicomponent case

TL;DR

This paper proves the global existence and uniqueness of weak solutions for a complex electrolyte solution model involving multiple charged species in two dimensions.

Contribution

It extends the analysis of the Darcy-Poisson-Nernst-Planck system to multicomponent electrolyte solutions, establishing global weak solutions in 2D.

Findings

Proved global existence of weak solutions in 2D

Established uniqueness of solutions

Analyzed multicomponent electrolyte systems

Abstract

This paper analytically investigates the Darcy-Poisson-Nernst-Planck system. This system is a mathematical model for electrolyte solutions. In this paper, we consider electrolyte solutions, which consist of a neutral fluid and multiple suspended charged chemical species with arbitrary valencies. We prove global existence and uniqueness of weak solutions in two space dimensions.