Local well-posedness for the Hall-MHD system in optimal Sobolev spaces
Local well-posedness for the Hall-MHD system in optimal Sobolev spaces
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DOI：
10.1016/j.jde.2021.04.019
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发表时间：
2018-03
影响因子：
2.4
通讯作者：
Mimi Dai
中科院分区：
文献类型：
--
作者：
Mimi Dai
我们证明了具有霍尔效应的黏性电阻磁流体动力学系统在s （R 3）× H (s+ 1)−ε (R 3)中具有s - >2和任何足够小的ε >2使得s - ε >2的局域适定。这个空间是迄今为止系统Sobolev空间类中最大的局部适定性空间。根据系统中两个方程的优势尺度，它也是最优的。
We show that the viscous resistive magnetohydrodynamics system with Hall effect is locally well-posed in H s (R 3)× H s+ 1− ε (R 3) with s> 1 2 and any small enough ε> 0 such that s− ε> 1 2. This space is to date the largest local well-posedness space in the class of Sobolev spaces for the system. It is also optimal according to the predominant scalings of the two equations in the system.