Well-posedness and Continuity Properties of the Degasperis-Procesi equation in critical Besov space

Abstract

In this paper, we obtain the local-in-time existence and uniqueness of solution to the Degasperis-Procesi equation in $B_{\infty ,1}^1(\mathbb{R})$. Moreover, we prove that the data-to-solution of this equation is continuous but not uniformly continuous in $B_{\infty ,1}^1$.