REGULARITY CRITERION FOR 3D NAVIER-STOKES EQUATIONS IN BESOV SPACES

Several regularity criterions of Leray-Hopf weak solutions u to the 3D Navier-Stokes equations are obtained. The results show that a weak solution u becomes regular if the gradient of velocity component del(h)u (or del u(3)) satisfies the additional conditions in the class of L-q(0, T; <(B)over dot>(s)(p,r)(R-3)), where del(h) = (partial derivative(x1), partial derivative(x2)) is the horizontal gradient operator. Besides, we also consider the anisotropic regularity criterion for the weak solution of Navier-Stokes equations in R-3. Finally, we also get a further regularity criterion, when give the sufficient condition on partial derivative(3)u(3).