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.
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