Global existence of solutions for the Hall-MHD equations

TongKeun Chang; Bataa Lkhagvasuren; MinSuk Yang

Global existence of solutions for the Hall-MHD equations

Analysis of PDEs 2023-10-27 v1

Authors: TongKeun Chang , Bataa Lkhagvasuren , MinSuk Yang

Abstract

In this paper, we study the global well-posedness of the incompressible Hall-MHD system for small initial data $( u_0, b_0) \in \dot B^{\frac3p -1}_{p,5} (\mathbb{R}) \times \Big( \dot B^{\frac3p -1}_{p,5} (\mathbb{R}) \cap \dot B^{\frac3p}_{p,1}(\mathbb{R}) \Big)$ for $1 < p < 5$ . We get the result under the weaker regularity and integrability conditions of the initial data than the previous works. We also give integral formulae for the solution.

Keywords

hall-mhd equations global well-posedness incompressible system besov spaces small initial data integral formulae

Cite

@article{arxiv.2310.17398,
  title  = {Global existence of solutions for the Hall-MHD equations},
  author = {TongKeun Chang and Bataa Lkhagvasuren and MinSuk Yang},
  journal= {arXiv preprint arXiv:2310.17398},
  year   = {2023}
}

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