A note on the regularity criterion for the 3D Navier–Stokes equations via the gradient of one velocity component

In this paper, we consider the regularity criterion for weak solutions to the 3D Navier–Stokes equations. We show that if∇u3∈L327(0,T;L2(R3)), then the solution is smooth on (0,T)(0,T), which improves the regularity condition ∇u3∈L245(0,T;L2(R3)) in [42].