# Partial regularity of suitable weak solutions of the Navier-Stokes-Planck-Nernst-Poisson equation

## TL;DR

This paper proves partial regularity of suitable weak solutions to a coupled Navier-Stokes-Planck-Nernst-Poisson system in three dimensions, showing smoothness outside a small singular set, extending classical results to a more complex PDE system.

## Contribution

It establishes the existence and partial regularity of suitable weak solutions for the Navier-Stokes-Planck-Nernst-Poisson equations, inspired by classical Navier-Stokes regularity theory.

## Key findings

- Existence of suitable weak solutions in 3D.
- Solutions are smooth outside a set of zero 1D parabolic Hausdorff measure.
- Extension of partial regularity results to coupled PDE systems.

## Abstract

In this paper, inspired by the seminal work by Caffarelli-Kohn-Nirenberg \cite{CKN} on the incompressible Navier-Stokes equation, we establish the existence of a suitable weak solution to the Navier-Stokes-Planck-Nernst-Poisson equation in dimension three, which is shown to be smooth away from a closed set whose $1$-dimensional parabolic Hausdorff measure is zero.