In this paper, we prove the global well-posedness of the 3-D generalized incompressible Navier–Stokes equations in critical Besov spaces under a polynomial smallness assumption on the initial data. Moreover, we construct a class of initial data with large vertical component, which satisfies that polynomial condition but cannot satisfy the exponential condition in Liu (2020).

中文翻译：

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3D广义不可压缩Navier–Stokes方程的全局大型解

在本文中，我们在初始数据的多项式小假设下，证明了临界Besov空间中3-D广义不可压缩Navier-Stokes方程的整体适定性。此外，我们构造了一类具有大垂直分量的初始数据，该数据满足多项式条件，但不能满足Liu（2020）的指数条件。