We prove the global solutions to the incompressible Hall-magnetohydrodynamics (Hall-MHD) equations with small or some large initial data in $\mathbb R^n (n \geq 3)$. Especially, Fujita–Kato type initial data as the incompressible Navier–Stokes equations are allowed. We also study the large time behavior of the solutions and obtain an optimal decay rate in the general Besov spaces. Different from all the previous wellposedness results in [6, 7, 21], the initial energy we considered here may not be finite.

中文翻译：

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霍尔-磁流体动力学方程解的整体适度性和长时间行为

我们用$ \ mathbb R ^ n（n \ geq 3）$中的初始数据来证明了不可压缩的霍尔磁流体力学（Hall-MHD）方程的整体解。特别是，允许​​使用Fujita-Kato类型的初始数据作为不可压缩的Navier-Stokes方程。我们还研究了解的长时间行为，并在一般Besov空间中获得了最佳的衰减率。有别于[6，7，21]中所有先前的适度结果，我们在此处考虑的初始能量可能不是有限的。