Non-uniform dependence on initial data for the Camassa-Holm equation in the critical Besov space

Jinlu Li; Xing Wu; Yanghai Yu; Weipeng Zhu

Non-uniform dependence on initial data for the Camassa-Holm equation in the critical Besov space

Analysis of PDEs 2020-07-10 v1

Authors: Jinlu Li , Xing Wu , Yanghai Yu , Weipeng Zhu

Abstract

Whether or not the data-to-solution map of the Cauchy problem for the Camassa-Holm equation and Novikov equation in the critical Besov space $B_{2,1}^{3/2}(\R)$ is not uniformly continuous remains open. In the paper, we aim at solving the open question left the previous works in \cite{Li3,Li4} and give a positive answer to this problem.

Keywords

Camassa-Holm equation Novikov equation critical Besov space data-to-solution map non-uniform continuity

Cite

@article{arxiv.2007.04501,
  title  = {Non-uniform dependence on initial data for the Camassa-Holm equation in the critical Besov space},
  author = {Jinlu Li and Xing Wu and Yanghai Yu and Weipeng Zhu},
  journal= {arXiv preprint arXiv:2007.04501},
  year   = {2020}
}

Comments

arXiv admin note: text overlap with arXiv:2001.00290

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