Interior epsilon-regularity theory for the solutions of the magneto-micropolar equations with a perturbation term

TL;DR

This paper establishes an interior epsilon-regularity theory for solutions to the Magneto-Micropolar equations with a perturbation term, extending regularity results to models used in liquid crystals and polymers.

Contribution

It develops a partial regularity theory for the Magneto-Micropolar equations incorporating a perturbation term, which is relevant for applications beyond classical fluid models.

Findings

Proves epsilon-regularity under certain conditions

Extends regularity results to perturbed Magneto-Micropolar systems

Provides a framework for analyzing fluid models with additional forces

Abstract

We develop here a particular version of the partial regularity theory for the Magneto-Micropolar equations (MMP) where a perturbation term is added. These equations are used in some special cases, such as in the study of the evolution of liquid cristals or polymers, where the classical Navier-Stokes equations are not an accurate enough model. The incompressible Magneto-Micropolar system is composed of three coupled equations: the first one is based in the Navier-Stokes system, the second one considers mainly the magnetic field while the last equation introduces the microrotation field representing the angular velocity of the rotation of the fluid particles. External forces are considered and a specific perturbation term is added as it is quite useful in some applications.