Some new regularity criteria for the 3D MHD equations

AbstractIn this paper we consider the regularity criteria for solutions to the 3D incompressible magnetohydrodynamics (MHD) equations. The first one involves ∇hu=(∂1u,∂2u) and ∂3b. Then, the criterion concerning ∇hu and ∇hb=(∂1b,∂2b) is presented. Finally, we show that the weak solution (u,b) is actually regular, provided that u3, ∂3u, b and ∂3b are in suitable Serrin-type integrability classes, respectively