A regularity criterion of Serrin-type for the Navier-Stokes equations involving the gradient of one velocity component.

In the present paper we prove that a weak Leray solution to the Navier-Stokes equations in R³ × (0, T] is regular provided the gradient of one component belongs to the Prodi-Serrin class ∇u³ Є L4(0, T; L²). [ABSTRACT FROM AUTHOR]