Two regularity criteria for the 3D MHD equations

TL;DR

This paper introduces two new regularity criteria for the 3D incompressible MHD equations, based on derivatives of velocity and pressure, advancing understanding of solution regularity conditions.

Contribution

It presents novel regularity criteria involving derivatives of velocity and pressure, providing new conditions for the smoothness of solutions to the 3D MHD equations.

Findings

Established a regularity criterion based on velocity derivative in one direction.

Proved a regularity condition involving boundedness of pressure derivative in one direction.

Contributed to the theoretical understanding of solution regularity in MHD equations.

Abstract

This work establishes two regularity criteria for the 3D incompressible MHD equations. The first one is in terms of the derivative of the velocity field in one-direction while the second one requires suitable boundedness of the derivative of the pressure in one-direction.