Summary: This paper derives regularity criteria for generalized magnetohydrodynamics (MHD) equations, a system of equations resulting from replacing the Laplacian -
in the usual MHD equations by a fractional Laplacian (-
. These criteria impose assumptions on the velocity field alone and sharpen a result of C. He
and Z. Xin
[J. Differ. Equations 213, No. 2, 235–254 (2005; Zbl 1072.35154
)]. In addition, these criteria apply to incompressible Navier-Stokes equations and improve some existing results.