English

Ill-posedness for the Cauchy problem of the modified Camassa-Holm equation in $B^0_{\infty,1}$

Analysis of PDEs 2023-10-25 v1

Abstract

In this paper, we prove the norm inflation and get the ill-posedness for the modified Camassa-Holm equation in B,10B_{\infty,1}^0. Therefore we completed all well-posedness and ill-posedness problem for the modified Camassa-Holm equation in all critical spaces Bp,11pB_{p,1}^\frac{1}{p} with p[1,]p\in[1,\infty].

Keywords

Cite

@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}
}