Navier-Stokes equations with regularity in two entries of the velocity gradient tensor

This paper concerns itself the regularity criteria for the three-dimensional Navier-Stokes equations. In particular, it is proved that if∂1u3,∂3u3∈L163(0,T;L2(R3)),or∂1u3,∂2u3∈L8(0,T;L2(R3)),then the solution is in fact smooth on (0,T).