On the global well-posedness and Gevrey regularity of some electrodiffusion models

TL;DR

This paper investigates the global existence, uniqueness, and Gevrey regularity of solutions to certain electrodiffusion models involving ionic concentrations and fluid flow, in a periodic two-dimensional setting.

Contribution

It establishes the global well-posedness and Gevrey regularity for electrodiffusion models coupled with Euler or Darcy fluid equations, advancing understanding of their mathematical properties.

Findings

Proved global well-posedness of the models

Established Gevrey regularity of solutions

Analyzed models with both Euler and Darcy fluid dynamics

Abstract

We consider the Nernst-Planck equations describing the nonlinear time evolution of multiple ionic concentrations in a two-dimensional incompressible fluid. The velocity of the fluid evolves according to either the Euler or Darcy's equations, both forced nonlinearly by the electric forces generated by the presence of charged ions. We address the global well-posedness and Gevrey regularity of the resulting electrodiffusion models in the periodic setting.