Ill-posedness for the higher dimensional Camassa-Holm equations in Besov spaces

Abstract

In the paper, by constructing a initial data $u_0\in B^{\ddot{I}}{ƒ}_{p,\infty }$ with $\ddot{I}ƒ-2>\max \{1+\frac{1}{p},\frac{3}{2}\}$, we prove that the corresponding solution to the higher dimensional Camassa-Holm equations starting from $u_0$ is discontinuous at $t=0$ in the norm of $B^{\ddot{I}}{ƒ}_{p,\infty }$, which implies that the ill-posedness for the higher dimensional Camassa-Holm equations in $B^{\ddot{I}}{ƒ}_{p,\infty }$.

13 pages. arXiv admin note: text overlap with arXiv:2104.05973 by other authors