Non-uniform dependence for higher dimensional Camassa-Holm equations in Besov spaces

Abstract

In this paper, we investigate the dependence on initial data of solutions to higher dimensional Camassa-Holm equations. We show that the data-to-solution map is not uniformly continuous dependence in Besov spaces $B_{p,r}^s({\mathbb{R}}^d),s>\max \{1+\frac{d}{2},\frac{3}{2}\}$.