In this paper, we consider the initial value problem of the incompressible Hall-MHD system and prove the global well-posedness in the scaling critical class \({\dot{B}}_{p,\infty }^{-1+\frac{3}{p}}(\mathbb {R}^3)\times ({\dot{B}}_{p,\infty }^{-1+\frac{3}{p}}(\mathbb {R}^3) \cap L^{\infty }(\mathbb {R}^3))\) for \(3< p < \infty \). Moreover, we also refine the smallness conditions and show that our global well-posedness holds for initial data whose \({\dot{B}}_{p,\infty }^{-1+\frac{3}{p}}(\mathbb {R}^3)\)-norm is large, provided that some weaker norm is sufficiently small.

在本文中，我们考虑不可压缩霍尔MHD系统的初值问题，并证明了缩放临界类\({\dot{B}}_{p,\infty }^{-1+ \frac{3}{p}}(\mathbb {R}^3)\times ({\dot{B}}_{p,\infty }^{-1+\frac{3}{p}}( \mathbb {R}^3) \cap L^{\infty }(\mathbb {R}^3))\)对于\(3< p < \infty \)。此外，我们还改进了小条件，并表明我们的全局适定性适用于初始数据，其\({\dot{B}}_{p,\infty }^{-1+\frac{3}{p} }(\mathbb {R}^3)\) -范数很大，前提是某些较弱的范数足够小。