LAUSR

Abstract We consider the extension criterion of strong solutions to the Navier–Stokes equations in R N . 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 L q , 3 / 2 q ∞ , of the vorticity contribute to such an extension criterion. Furthermore, the critical case q = ∞ originally treated by Kato–Ponce [8] in R N is also generalized in such a way that [ N / 2 ] components of vortex matrix are redundant for the extension criterion.