Non-uniform dependence for the Camassa-Holm and Novikov equations in low regularity Besov spaces

Abstract

In the paper, we consider the initial value problem to the Camassa-Holm and Novikov equations on the real-line case. We show that both the solution maps of Camassa-Holm and Novikov equations are not uniformly continuous on the initial data in Besov spaces B s p,r (R) with s > 1 and 1 ≤ p, r < ∞. Our result improves the previous work given by Li et al.