LAUSR

Abstract In this paper, with special choices of a sequence of low frequency and high frequency initial data g n , f n , based on the established existence estimates, by showing that the difference between the solutions initialled with f n + g n and f n will produce a positive lower bound independent of n in a small time, we show that the solution map of a Camassa-Holm-type equation proposed by Novikov is not uniformly continuous on the initial data in Besov spaces B p , r s ( R ) , s > 1 + 1 p , 1 ≤ p , r ≤ ∞ or s = 1 + 1 p , r = 1 , 1 ≤ p ∞ . Our result extends the previous non-uniform continuity in Sobolev spaces (Y. Mi et al., 2019) [29] to Besov spaces.