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

In this paper, we study regularity of weak solutions to the incompressible Navier–Stokes equations in R3× (0 , T). The main goal is to establish the regularity criterion via the gradient of one velocity component in some multiplier spaces. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.