Regularity criteria for the 3D MHD equations in term of velocity

TL;DR

This paper establishes new regularity criteria for the 3D incompressible MHD equations based on velocity and its fractional derivatives, extending existing results using anisotropic Lebesgue space interpolation.

Contribution

It introduces generalized regularity criteria involving velocity and fractional derivatives in anisotropic Lebesgue spaces for the 3D MHD equations.

Findings

Regularity criteria involving velocity in anisotropic Lebesgue spaces

Criteria based on fractional derivatives of velocity

Generalization of known regularity results

Abstract

In this paper we consider three-dimensional incompressible magnetohydrodynamics equations. By using interpolation inequalities in anisotropic Lebesgue space, we provide regularity criteria involving the velocity or alternatively involving the fractional derivative of velocity in one direction, which generalize some known results.