English

Non-uniform continuous dependence and continuous dependence for the non-resistive MHD equations

Analysis of PDEs 2018-11-26 v2

Abstract

In this paper, we establish the continuous dependence for the non-resistive MHD equations in Sobolev spaces. Our obtained result fills considerably the recent result [C. Fefferman, D. McCormick, J. Robinson and J. Rodrigo, Higher order commutator estimates and local existence for the non-resistive MHD equations and related models, J. Funct. Anal. 267 (2014), 1035--1056] for the continuous dependence on initial data. We also show that this result is optimal. More precisely, we proved that the data-to-solution map is not uniform continuous dependence in Sobolev spaces.

Keywords

Cite

@article{arxiv.1811.00375,
  title  = {Non-uniform continuous dependence and continuous dependence for the non-resistive MHD equations},
  author = {Jinlu Li and Zhaoyang Yin and Weipeng Zhu},
  journal= {arXiv preprint arXiv:1811.00375},
  year   = {2018}
}

Comments

20 pages

R2 v1 2026-06-23T05:00:36.039Z