Eigenvalue regularity criterion for the MHD equations with fractional magnetic diffusion

In this paper, we discuss the eigenvalue regularity criterion of the MHD equations with fractional magnetic diffusion in the three-dimensional whole space. We show that the results established by Neustupa-Penel[8,9,10] and Miller[7] can be extended to MHD equations with fractional magnetic diffusion. The proof involves combining the evolution equation for the strain tensor with the delicate structure of the nonlinear terms. As a by-product, we also obtain some new regularity criterion for the generalized MHD equations