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

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
$$u imes f{om}{|om|}cdot f{vLm^e u}{|vLm^e u|}in L^p(0,T;L^q(bR^3)),quad f{2}{p}+f{3}{q}=1,quad 3<qleqinfty,quad 1leq eleq 2,$$
则解光滑.