Ill-posedness of the Camassa–Holm and related equations in the critical space

2018/08/09 by Zihua Guo, Xingxing Liu, Luc Molinet +1 · 14 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Mathematical Physics Problems #Advanced Differential Equations and Dynamical Systems

paper · doi:10.1016/j.jde.2018.08.013

Citations

• Global Conservative Solutions of the Camassa–Holm Equation
• Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation
• Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation
• Wave breaking for nonlinear nonlocal shallow water equations

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• A new result for the local well-posedness of the Camassa-Holm type equations in critial Besov spaces B^1+(1)/(p)_p,1,1≤ p
• Stability of peakons for the generalized modified Camassa-Holm equation
• Non-uniform dependence on initial data for the Camassa-Holm equation in Besov spaces
• Non-uniform dependence for higher dimensional Camassa-Holm equations in Besov spaces
• Non-uniform dependence on initial data for the Camassa-Holm equation in the critical Besov space
• Blow-up phenomenon, ill-posedness and peakon solutions for the periodic Euler-Poincaré equations
• The well-posedness, ill-posedness and non-uniform dependence on initial data for the Fornberg-Whitham equation in Besov spaces
• The local well-posedness, global existence and ill-posedness for the fifth order Camassa-Holm model
• Non-uniform dependence for the two-component Camassa-Holm shallow water system
• On the Cauchy problem for the Hunter-Saxton equation on the line
• Ill-posedness for the Burgers equation in Sobolev spaces
• Ill-posedness for the Camassa-Holm and related equations in Besov spaces
• Well-posedness for the dispersive Hunter-Saxton equation
• The continuous dependence and non-uniform dependence of the rotation Camassa-Holm equation in Besov spaces