Logarithmical regularity criteria in terms of pressure for the three dimensional nonlinear dissipative system modeling electro-diffusion

TL;DR

This paper develops new logarithmic regularity criteria for a complex electro-diffusion system, linking pressure conditions to system regularity in advanced mathematical spaces.

Contribution

It introduces logarithmic regularity criteria based on pressure and its gradient in Besov spaces for the Navier--Stokes/Poisson--Nernst--Planck system, advancing mathematical understanding.

Findings

Established new regularity criteria involving pressure.

Linked pressure conditions to system regularity in Besov spaces.

Enhanced theoretical framework for electro-diffusion models.

Abstract

In this paper, logarithmically improved regularity criteria for the Navier--Stokes/Poisson--Nernst--Planck system are established in terms of both the pressure and the gradient of pressure in the homogeneous Besov space.