Non-uniform Dependence on Initial Data for the Camassa–Holm Equation in the Critical Besov Space - Li, Jinlu; Wu, Xing; Yu, Yanghai; Zhu, Weipeng (Journal of mathematical fluid mechanics, 2021)
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 uniformly continuous remains open. In the paper, we aim at solving the open question left in the previous works (Li et al. in J Differ Equ 269:8686–8700, 2020a; J Math Fluid Mech 22:50, 2020b) and giving a negative answer to this problem.