Partial regularity of suitable weak solutions to the multi-dimensional generalized magnetohydrodynamics equations

TL;DR

This paper investigates the partial regularity of suitable weak solutions to multi-dimensional fractional magnetohydrodynamics equations, extending previous results to include endpoint cases and more general external forces.

Contribution

It extends partial regularity results for fractional MHD equations to include the endpoint case and broader external force conditions, with new interior regularity criteria.

Findings

Includes the endpoint case =3/4 for fractional MHD equations.

Allows external forces in more general parabolic Morrey spaces.

Provides interior regularity criteria based on scaled mixed norms.

Abstract

In this paper, we are concerned with the partial regularity of the suitable weak solutions to the fractional MHD equations in $\mathbb{R}^{n}$ for $n=2,\,3$. In comparison with the work of the 3D fractional Navier-Stokes equations obtained by Tang and Yu in [24, Commun. Math. Phys. 334: 1455--1482, 2015], our results include their endpoint case $\alpha=3/4$ and the external force belongs to more general parabolic Morrey space. Moreover, we prove some interior regularity criteria just via the scaled mixed norm of the velocity for the suitable weak solutions to the fractional MHD equations.