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Local well-posedness for the Hall-MHD system in optimal Sobolev spaces
Journal of Differential Equations ( IF 2.4 ) Pub Date : 2021-04-23 , DOI: 10.1016/j.jde.2021.04.019 Mimi Dai
中文翻译:
最佳Sobolev空间中Hall-MHD系统的局部适定性
更新日期:2021-04-23
Journal of Differential Equations ( IF 2.4 ) Pub Date : 2021-04-23 , DOI: 10.1016/j.jde.2021.04.019 Mimi Dai
We show that the viscous resistive magnetohydrodynamics system with Hall effect is locally well-posed in with and any small enough such that . 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.
中文翻译:
最佳Sobolev空间中Hall-MHD系统的局部适定性
我们表明,具有霍尔效应的粘性电阻磁流体动力学系统在局部位置良好。 和 还有足够小的 这样 。迄今为止,该空间是该系统Sobolev空间类别中最大的局部适定性空间。根据系统中两个方程的主要比例,它也是最佳的。