Some new regularity criteria for the 3D MHD equations

Abstract 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.

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