Global small solutions to the inviscid Hall-MHD system
Analysis of PDEs
2021-09-29 v1
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 when the initial magnetic field is close to a background magnetic field satisfying the Diophantine condition.
Keywords
Cite
@article{arxiv.2106.10501,
title = {Global small solutions to the inviscid Hall-MHD system},
author = {Xiaoping Zhai and Yongsheng Li and Yajuan Zhao},
journal= {arXiv preprint arXiv:2106.10501},
year = {2021}
}
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9pages