Ill-posedness for a generalized Camassa-Holm equation with higher-order nonlinearity in the critical Besov space

DOI10.1007/s00605-023-01864-9arXiv2303.00887MaRDI QIDQ6124256

Wei Deng, Xing Wu, Weipeng Zhu, Min Li

Publication date: 27 March 2024

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.00887

zbMATH Keywords

ill-posednesscritical Besov spacegeneralized Camassa-Holm equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53)

Cites Work

• Remarks on the well-posedness of Camassa-Holm type equations in Besov spaces
• Non-uniform dependence on initial data for the CH equation on the line.
• Blow-up, zero \(\alpha\) limit and the Liouville type theorem for the Euler-poincaré equations
• Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces
• The trajectories of particles in Stokes waves
• Global conservative solutions of the Camassa-Holm equation
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Wave breaking for nonlinear nonlocal shallow water equations
• Stokes waves
• A note on well-posedness for Camassa-Holm equation.
• Ill-posedness of the Camassa-Holm and related equations in the critical space
• Existence of permanent and breaking waves for a shallow water equation: a geometric approach
• Ill-posedness for the Cauchy problem of the Camassa-Holm equation in \(B_{\infty, 1}^1(\mathbb{R})\)
• Non-uniform dependence on initial data for the generalized Camassa-Holm-Novikov equation in Besov space
• The Cauchy problem for the generalized Camassa-Holm equation in Besov space
• Non-uniform dependence on initial data for the Camassa-Holm equation in the critical Besov space
• Ill-posedness for the Camassa-Holm and related equations in Besov spaces
• Well-posedness and continuity properties of the Degasperis-Procesi equation in critical Besov space
• On the weak solutions to a shallow water equation
• Fourier Analysis and Nonlinear Partial Differential Equations
• GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
• Non-Uniform Dependence for the Periodic CH Equation
• An integrable shallow water equation with peaked solitons
• Local Well-Posedness and Orbital Stability of Solitary Wave Solutions for the Generalized Camassa–Holm Equation
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