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

Published 1 Jun 2021 in math.AP | (2106.00540v2)

Abstract: In the paper, by constructing a initial data $u_{0}\in B^{{\sigma}_{p,\infty}$} with $\sigma-2>\max{1+\frac 1 p, \frac 3 2}$, 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 $B^{{\sigma}_{p,\infty}$,} which implies that the ill-posedness for the higher dimensional Camassa-Holm equations in $B^{{\sigma}_{p,\infty}$.}