Global existence of a strong solution to the initial value problem for the Nernst-Planck-Navier-Stokes system in high space dimensions

TL;DR

This paper proves the global existence of strong solutions for the Nernst-Planck-Navier-Stokes system in high-dimensional spaces, regardless of the number of ion species or initial data size.

Contribution

It establishes the existence of strong solutions in any space dimension for the NPNS system without restrictions on species count or initial conditions.

Findings

Strong solutions exist globally in high dimensions.

No restrictions on number of species or initial data size.

Results applicable to any space dimension N ≥ 3.

Abstract

We study the existence of a strong solution to the initial value problem for the Nernst-Planck-Navier-Stokes (NPNS) system in $\mathbb{R}^N, N\geq 3$. The system describes the electrodiffusion of ions in a viscous Newtonian fluid. A strong solution is obtained in any dimension of space without constraints on the number of species or the size of the given data.