Non-uniform dependence of the data-to-solution map for the rotation b -family system

In this paper, we consider the Cauchy problem for a generalized rotation b-family system on the real line and prove that the data-to-solution map of this problem is not uniformly continuous in Bp,rs×Bp,rs−1. We have removed the restriction of μ(b+1)=Aσ in Holmes et al. [Nonuniform dependence of the R-b-family system in Besov spaces. Z Angew Math Mech. 2021;101(8):18] and Yang [Non-uniform continuity of the solution map to the rotation-two-component Camassa–Holm system. J Differ Equ. 2020;268:4423–4463].