The continuous dependence and non-uniform dependence of the rotation Camassa-Holm equation in Besov spaces

Abstract

In this paper, we first establish the local well-posedness and continuous dependence for the rotation Camassa-Holm equation modelling the equatorial water waves with the weak Coriolis effect in nonhomogeneous Besov spaces $B_{p,r}^s$ with $s>1+1/p$ or $s=1+1/p,p\in [1,+\infty ),r=1$ by a new way: the compactness argument and Lagrangian coordinate transformation, which removes the index constraint $s>3/2$ and improves our previous work \cite{guoy1}. Then, we prove the solution is not uniformly continuous dependence on the initial data in both supercritical and critical Besov spaces.

21 pages

References in corpus (1)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations