Sharp ill-posedness for the generalized Camassa–Holm equation in Besov spaces
نویسندگان
چکیده
In this paper, we consider the Cauchy problem for generalized Camassa–Holm equation that containing, as its members, three integrable equations: equation, Degasperis–Procesi and Novikov equation. We present a new unified method to prove sharp ill-posedness in $$B^s_{p,\infty }$$ with $$s>\max \{1+1/p, 3/2\}$$ $$1\le p\le \infty $$ sense solution map starting from $$u_0$$ is discontinuous at $$t = 0$$ metric of . Our result covers improves previous work given Li et al. (J Differ Equ 306:403–417, 2022), solving an open left (2022).
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ژورنال
عنوان ژورنال: Journal of Evolution Equations
سال: 2022
ISSN: ['1424-3199', '1424-3202']
DOI: https://doi.org/10.1007/s00028-022-00792-9