A generalized regularity criterion for 3D Navier–Stokes equations in terms of one velocity component

In this article, we study the global regularity of the 3D Navier–Stokes equations in terms of one velocity component. In particular, we establish a new version of regularity criterion in the framework of the anisotropic Lebesgue space. It is a generalization of the notable work of C. Cao and E.S. Titi (2011) [3].