Geometric regularity criterion for NSE: the cross product of velocity and vorticity 4: $ucdot om$

在 [Berselli, Luigi C.; Córdoba, Diego. On the regularity of the solutions to the 3D Navier-Stokes equations: a remark on the role of the helicity. C. R. Math. Acad. Sci. Paris 347 (2009), no. 11-12, 613--618] 中, 作者证明了如果
$$|u(x+y,t)cdot om(x,t)|leq c_1|y||u(x+y,t)||om(x,t), |y|leq del,$$
则解光滑.