A remark on the global regularity for the 3D Navier–Stokes equations

In this paper, we investigate the case of Prodi–Serrin type regularity criterion involving u3u3 and ∂3uh∂3uh. More precisely, it is shown that Leray’s weak solutions of the three-dimensional Navier–Stokes equations become regular if the third component of velocity (or the gradient of the velocity field) satisfies the additional end-point Prodi–Serrin type condition.