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arXiv · 2106.10501

Global small solutions to the inviscid Hall-MHD system

Xiaoping Zhai·Yongsheng Li·Yajuan Zhao
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Abstract

The local existence of smooth solutions to the inviscid Hall-MHD system has been obtained since Chae, Degond and Liu [Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire, {31} (2014), 555--565]. However, as we known, how to construct the global small solutions to the inviscid Hall-MHD system is still an open problem. In the present paper, we give a positive answer in $ \mathbb{T}^3$ when the initial magnetic field is close to a background magnetic field satisfying the Diophantine condition.

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Xiaoping Zhai, Yongsheng Li, Yajuan Zhao. 2021-06-19. Global small solutions to the inviscid Hall-MHD system. https://doi.org/10.1007/s00021-021-00620-z

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