Remarks on the regularity criteria of generalized MHD and Navier-Stokes systems

TL;DR

This paper investigates simplified regularity criteria for 3D generalized MHD and Navier-Stokes systems, showing that regularity depends on specific components of the velocity's Jacobian or vorticity, thus potentially reducing complexity.

Contribution

It introduces new regularity criteria that depend on fewer components of the velocity Jacobian or vorticity, simplifying analysis of these systems.

Findings

Regularity criteria can be reduced to two diagonal Jacobian entries

Regularity depends on one vorticity component and one Jacobian entry

Simplifies understanding of conditions for system regularity

Abstract

We study the regularity criteria of the three dimensional generalized MHD and Navier-Stokes systems. In particular, we show that the regularity criteria of the generalized MHD system may be reduced to depend only on two diagonal entries of the Jacobian matrix of the velocity vector field or one vorticity component and one entry of the Jacobian matrix of the velocity vector field.