Nowhere-uniform continuity of the solution map of the Camassa-Holm equation in Besov spaces

Abstract: In the paper, we gave a strengthening of our previous work in 32 and proved that the data-to-solution map for the Camassa-Holm equation is nowhere uniformly continuous in $B^s_{p,r}(\R)$ with $s>\max{1+1/{p},3/2}$ and $(p,r)\in [1,\infty]\times[1,\infty)$. The method applies also to the b-family of equations which contain the Camassa-Holm and Degasperis-Procesi equations.