# Ill-posedness for the Camassa-Holm and related equations in Besov spaces

@article{Li2022IllposednessFT,
title={Ill-posedness for the Camassa-Holm and related equations in Besov spaces},
author={Jinlu Li and Yanghai Yu and WeiPeng Zhu},
journal={Journal of Differential Equations},
year={2022}
}
• Published 13 April 2021
• Mathematics
• Journal of Differential Equations
17 Citations
Ill-posedness for the higher dimensional Camassa-Holm equations in Besov spaces
• Mathematics
• 2021
In the paper, by constructing a initial data u0 ∈ B σ p,∞ with σ−2 > max{1+ 1 p , 3 2 }, we prove that the corresponding solution to the higher dimensional Camassa-Holm equations starting from u0 is
On the Cauchy problem for a weakly dissipative Camassa-Holm equation in critical Besov spaces
• Mathematics
• 2022
In this paper, we mainly consider the Cauchy problem of a weakly dissipative Camassa-Holm equation. We first establish the local well-posedness of equation in Besov spaces Bs p,r with s > 1+ 1 p and
The ill-posedness for the rotation Camassa-Holm equation in Besov space $B^{1}_{\infty,1}(\mathbb{R})$
• Mathematics
• 2022
In this paper, we present a construction of u0 ∈ B 1 ∞,1 and get the local ill-posedness for the rotation Camassa-Holm equation modelling the equatorial water waves with the weak Coriolis effect by
Well-posedness and continuity properties of the Degasperis-Procesi equation in critical Besov space
• Mathematics
Monatshefte für Mathematik
• 2022
In this paper, we obtain the local-in-time existence and uniqueness of solution to the Degasperis-Procesi equation in B ∞,1(R). Moreover, we prove that the data-to-solution of this equation is
Non-uniform dependence for the Camassa-Holm and Novikov equations in low regularity Besov spaces
• Mathematics
• 2021
In the paper, we consider the initial value problem to the Camassa-Holm and Novikov equations on the real-line case. We show that both the solution maps of Camassa-Holm and Novikov equations are not
The Cauchy problem for coupled system of the generalized Camassa-Holm equations
• Mathematics
AIMS Mathematics
• 2022
Local well-posedness for the Cauchy problem of coupled system of generalized Camassa-Holm equations in the Besov spaces is established by employing the Littlewood-Paley theory and a priori estimate
Ill_posedness for a two_component Novikov system in Besov space
• Mathematics
• 2022
In this paper, we consider the Cauchy problem for a two-component Novikov system on the line. By specially constructed initial data (ρ0, u0) in B s−1 p,∞(R) × B p,∞(R) with s > max{2 + 1 p , 5 2 }
Ill-posedness for the two component Degasperis-Procesi equation in critical Besov space
• Mathematics
• 2022
: In this paper, we study the Cauchy problem for the two component Degasperis-Procesi equation in critical Besov space B 1 ∞ , 1 ( R ). By presenting a new construction of initial data, we proved the
A P ] 8 J an 2 02 2 Ill-posedness for the Camassa-Holm equation in B 1 p , 1 ∩ C 0 , 1
• Mathematics
• 2022
In this paper, we study the Cauchy problem for the Camassa-Holm equation on the real line. By presenting a new construction of initial data, we show that the solution map in the smaller space B p,1 ∩
Sharp ill-posedness for the generalized Camassa–Holm equation in Besov spaces
• Mathematics
Journal of Evolution Equations
• 2022
In this paper, we consider the Cauchy problem for the generalized Camassa–Holm equation that containing, as its members, three integrable equations: the Camassa–Holm equation, the Degasperis–Procesi

## References

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• Mathematics
• 2020
Whether or not the data-to-solution map of the Cauchy problem for the Camassa-Holm equation and Novikov equation in the critical Besov space $B_{2,1}^{3/2}(\R)$ is not uniformly continuous remains
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In this paper, we examine the break-down phenomenon for a particular type of solution to the Camassa-Holm equation-namely, a peakon-antipeakon interaction with equal magnitude. We will show, in
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The purpose of this paper is to investigate the Cauchy problem of the Camassa-Holm equation. By using the abstract method proposed and studied by T. Kato and priori estimates, the existence and
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This work studies the initial value problem for a Camassa–Holm type equation with cubic nonlinearities that has been recently discovered by Vladimir Novikov to be integrable. For s > 3/2, using a
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