Extension criterion via partial components of vorticity on strong solutions to the Navier-Stokes equations in higher dimensions

We consider the extension criterion of strong solutions to the Navier-Stokes equations in RN. It is proved that among N(N−1)/2 components of the vorticity, [N/2] components are negligible for the criterion whether the time local solutions can be extended beyond the critical time. Our result may be regarded as generalization to the higher dimensional case of Chae-Choe [4] in the 3D case which showed that only two components in Lq, 3/2