A new regularity criterion for weak solutions to the Navier–Stokes equations

Abstract

In this paper we obtain a new regularity criterion for weak solutions to the 3-D Navier–Stokes equations. We show that if any one component of the velocity field belongs to L α ( [ 0 , T ) ; L γ ( R 3 ) ) with 2 α + 3 γ ⩽ 1 2 , 6 < γ ⩽ ∞ , then the weak solution actually is regular and unique.