Regularity criteria via one directional derivative of the velocity in anisotropic Lebesgue spaces to the 3D Navier-Stokes equations

In this paper, we consider the regularity criterion for 3D incompressible Navier-Stokes equations in terms of one directional derivative of the velocity in anisotropic Lebesgue spaces. More precisely, it is proved that u becomes a regular solution if the ∂3u satisfies [Formula presented] where [Formula presented] and [Formula presented]. © 2021