Geometric regularity criterion for NSE: the cross product of velocity and vorticity 1: $u\times \om$
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
$$u\times\f{\om}{|\om|}\in L^p(0,T;L^q(\bbR^3)),\quad\f{2}{p}+\f{3}{q}=1,\quad 3<q\leq\infty,$$
或
$$\om\times\f{u}{|u|}\in L^p(0,T;L^q(\bbR^3)),\quad\f{2}{p}+\f{3}{q}=2,\quad \f{3}{2}<q\leq\infty,$$
则解光滑.
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