A REGULARITY CRITERION FOR THE NAVIER-STOKES EQUATIONS IN TERMS OF THE HORIZONTAL DERIVATIVES OF THE TWO VELOCITY COMPONENTS

In this article, we consider the regularity for weak solutions to the Navier-Stokes equations in R-3. It is proved that if the horizontal derivatives of the two velocity components del(h)(u) over tilde is an element of L2/(2-r) (0, T; (M) over dot(2,3/r)(R-3)), for 0 < r < 1, then the weak solution is actually strong, where (M) over dot(2,3/r) is the critical Morrey-Campanato space and (u) over tilde = (u(1), u(2), 0), del(h)(u) over tilde = (partial derivative(1)u(1), partial derivative(2)u(2), 0).