Geometric regularity criterion for NSE: the cross product of velocity and vorticity 3: $u\times \f{\om}{|\om|}\cdot \f{\vLm^\be u}{|\vLm^\be u|}$

在 [Chae, Dongho; Lee, Jihoon. On the geometric regularity conditions for the 3D Navier-Stokes equations. Nonlinear Anal. 151 (2017), 265--273] 中, 作者证明了如果
$$u\times \f{\om}{|\om|}\cdot \f{\vLm^\be u}{|\vLm^\be u|}\in L^p(0,T;L^q(\bbR^3)),\quad \f{2}{p}+\f{3}{q}=1,\quad 3<q\leq\infty,\quad 1\leq \be\leq 2,$$
则解光滑.