Some new regularity criteria for the 3D Navier-Stokes Equations

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Several types of new regularity criteria for Leray-Hopf weak solutions u to the 3D Navier-Stokes equations are obtained. Some of them are based on the third component u₃ of velocity under Prodi-Serrin index condition, another type is in terms of ω₃ and ∂₃u₃ with Prodi-Serrin index condition. And a very recent work of the authors, based on only one of the nine entries of the gradient tensor, is renovated.