Some new regularity criteria for the 3D MHD equations

In this paper we consider the regularity criteria for solutions to the 3D incompressible magnetohydrodynamics (MHD) equations. The first one involves ∇ h u = ( ∂ 1 u , ∂ 2 u ) and ∂ 3 b . Then, the criterion concerning ∇ h u and ∇ h b = ( ∂ 1 b , ∂ 2 b ) is presented. Finally, we show that the weak solution ( u , b ) is actually regular, provided that u 3 , ∂ 3 u , b and ∂ 3 b are in suitable Serrin-type integrability classes, respectively.