In this paper, we first prove the global well-posedness of 3-D anisotropic Navier-Stokes system provided that the vertical viscous coefficient of the system is sufficiently large compared to some critical norm of the initial data. Then we shall construct a family of initial data, $u_{0,\nu},$ which vary fast enough in the vertical variable and which are not small in the space, $BMO^{-1}.$ Yet $u_{0,\nu}$ generates a unique global solution to the classical 3-D Navier-Stokes system provided that $\nu$ is sufficiently large.

中文翻译：

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具有大垂直粘性系数的 3-D 各向异性 Navier-Stokes 系统的全局适定性

在本文中，我们首先证明了 3-D 各向异性 Navier-Stokes 系统的全局适定性，前提是该系统的垂直粘性系数与初始数据的某些临界范数相比足够大。然后我们将构建一个初始数据族 $u_{0,\nu},$ 在垂直变量中变化足够快并且在空间中不小$BMO^{-1}。$ 然而 $u_{ 0,\nu}$ 生成经典 3-D Navier-Stokes 系统的唯一全局解，前提是 $\nu$ 足够大。