In this paper, we prove the norm inflation and get the ill-posedness for the modified Camassa-Holm equation in B∞,10. Therefore we completed all well-posedness and ill-posedness problem for the modified Camassa-Holm equation in all critical spaces Bp,1p1 with p∈[1,∞].
@article{arxiv.2310.15749,
title = {Ill-posedness for the Cauchy problem of the modified Camassa-Holm equation in $B^0_{\infty,1}$},
author = {Zhen He and Zhaoyang Yin},
journal= {arXiv preprint arXiv:2310.15749},
year = {2023}
}