Non-uniform continuity on initial data for a Camassa-Holm-type equation in Besov space (Q2227580)

This paper deals with the Cauchy problem for the Novikov integrable quadratic quasi-linear scalar evolution equation \[ (1-\partial_x^2)u_t =\partial_x(2-\partial_x)(1+\partial_x)u^2. \] The authors show that its solution map is not uniformly continuous with respect to the initial data in Besov spaces \[ B^s_{p,r}(\mathbb{R}), \] with \[ s > 1 + \frac{1}{p},\qquad 1 \le p,r \le \infty, \] or \[ s = 1 + \frac{1}{p},\qquad r = 1,\qquad 1 \le p < \infty. \]