Geometric regularity criterion for NSE: the cross product of velocity and vorticity 1: $u imes om$

在 [Chae, Dongho. On the regularity conditions of suitable weak solutions of the 3D Navier-Stokes equations. J. Math. Fluid Mech. 12 (2010), no. 2, 171--180] 中, 作者证明了如果
$$u imesf{om}{|om|}in L^p(0,T;L^q(bR^3)),quadf{2}{p}+f{3}{q}=1,quad 3<qleqinfty,$$
或
$$om imesf{u}{|u|}in L^p(0,T;L^q(bR^3)),quadf{2}{p}+f{3}{q}=2,quad f{3}{2}<qleqinfty,$$
则解光滑.