English

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 T3 \mathbb{T}^3 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}
}

Comments

9pages

R2 v1 2026-06-24T03:23:14.816Z