A logarithmically improved regularity criterion for the MHD equations in terms of one directional derivative of the pressure

Abstract

In this paper, a logarithmically improved regularity criterion for the incompressible magnetohydrodynamics equation is established in terms of the derivative of the pressure in one direction. It is shown that if the partial derivative of the pressure satisfies the logarithmical Serrin-type condition

then the solution (u, b) remains smooth on . Compared to the Navier–Stokes result, there is a logarithmic correction involving b in the denominator. This is an extension of earlier regularity results in the Serrin’s type space with

Keywords:

• MHD equations
• regularity criteria
• partial derivatives

AMS Subject Classifications:

• 35Q35
• 35B65
• 76D05

Notes

No potential conflict of interest was reported by the authors.