Ill-posedness for the Cauchy problem of the Camassa-Holm equation in \(B_{\infty, 1}^1(\mathbb{R})\)

DOI10.1016/j.jde.2022.04.020zbMath1496.35319arXiv2112.10081OpenAlexW4224988722MaRDI QIDQ2137833

Yingying Guo, Weikui Ye, Zhaoyang Yin

Publication date: 11 May 2022

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.10081

zbMATH Keywords

Banach algebracritical Besov spacesCamassa-Holm equationill-posednessnorm inflation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Ill-posed problems for PDEs (35R25) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial value problems for nonlinear higher-order PDEs (35G25) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (7)

Energy conservation and well-posedness of the Camassa-Holm equation in Sobolev spaces ⋮ Existence and uniqueness of the globally conservative solutions for a weakly dissipative Camassa–Holm equation in time weighted H1(R) space ⋮ Ill-posedness for a generalized Camassa-Holm equation with higher-order nonlinearity in the critical Besov space ⋮ The well-posedness for the Camassa-Holm type equations in critical Besov spaces \(B_{p , 1}^{1 + \frac{ 1}{ p}}\) with \(1 \leq p < + \infty \) ⋮ Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces: revisited ⋮ Non-uniform continuity of the generalized Camassa-Holm equation in Besov spaces ⋮ The well-posedness, ill-posedness and non-uniform dependence on initial data for the Fornberg-Whitham equation in Besov spaces

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