The ill-posedness for the rotation Camassa-Holm equation in Besov space $B^{1}_{\infty,1}(\mathbb{R})$

Abstract

In this paper, we present a construction of $u_{0}\in B^{1}_{\infty,1}$ and get the local ill-posedness for the rotation Camassa-Holm equation modelling the equatorial water waves with the weak Coriolis effect by proving the norm inflation.