论文标题
Navier的本地各向异性规律标准 - 涡流方程
A locally anisotropic regularity criterion for the Navier--Stokes equation in terms of vorticity
论文作者
论文摘要
在本文中，我们将证明一个规律性标准可以保证Navier的解决方案 - 史托克斯方程必须保持平稳，只要涡度仅限于飞机的涡度限制在规模关键空间$ l^4_t l^2_x $中，平面可能会在空间和时间上随着平面的梯度而变化。这扩展了Chae和Choe先前的工作，以确保Navier-Stokes方程的溶液必须保持平稳，只要涡度仅限于固定平面，在关键的混合混合Lebesgue空间中仍处于固定平面的限制。该规则性标准也可以看作是根据两个涡度组成部分和BeirãoDaVeiga和Berselli的规律性标准在Chae和Cho的规律性标准之间插值，并根据涡度方向的梯度。
In this paper, we will prove a regularity criterion that guarantees solutions of the Navier--Stokes equation must remain smooth so long as the the vorticity restricted to a plane remains bounded in the scale critical space $L^4_t L^2_x$, where the plane may vary in space and time as long as the gradient of the vector orthogonal to the plane remains bounded. This extends previous work by Chae and Choe that guaranteed that solutions of the Navier--Stokes equation must remain smooth as long as the vorticity restricted to a fixed plane remains bounded in family of scale critical mixed Lebesgue spaces. This regularity criterion also can be seen as interpolating between Chae and Choe's regularity criterion in terms of two vorticity components and Beirão da Veiga and Berselli's regularity criterion in terms of the gradient of vorticity direction.
