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 ∇hu=(∂1u,∂2u)∇hu=(∂1u,∂2u) and ∂3b∂3b. Then, the criterion concerning ∇hu∇hu and ∇hb=(∂1b,∂2b)∇hb=(∂1b,∂2b) is presented. Finally, we show that the weak solution (u,b)(u,b) is actually regular, provided that u3u3, ∂3u∂3u, bb and ∂3b∂3b are in suitable Serrin-type integrability classes, respectively.