The local well-posedness in Besov spaces and non-uniform dependence on initial data for the interacting system of Camassa-Holm and Degasperis-Procesi equations

DOI10.1007/S00605-017-1110-6zbMath1406.35103OpenAlexW2765918203MaRDI QIDQ1799332

Shouming Zhou

Publication date: 18 October 2018

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

Full work available at URL: https://doi.org/10.1007/s00605-017-1110-6

zbMATH Keywords

Friedrichs regularization methodtransport equations theory

Mathematics Subject Classification ID

Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial value problems for systems of nonlinear higher-order PDEs (35G55)

Cites Work

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• Continuity and analyticity for a cross-coupled Camassa-Holm equation with waltzing peakons and compacton pairs
• The inverse spectral transform for the conservative Camassa-Holm flow with decaying initial data
• Well-posedness and persistence properties for the Novikov equation
• Non-uniform dependence on initial data for the CH equation on the line.
• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• The trajectories of particles in Stokes waves
• Global conservative solutions of the Camassa-Holm equation
• A Camassa-Holm equation interacted with the Degasperis-Procesi equation
• Well-posedness and blow-up phenomena for the interacting system of the Camassa-Holm and Degasperis-Procesi equations
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• On the inverse spectral problem for the Camassa-Holm equation
• Wave breaking for nonlinear nonlocal shallow water equations
• A note on well-posedness for Camassa-Holm equation.
• On the Cauchy problem for an integrable equation with peakon solutions
• On asymptotically equivalent shallow water wave equations
• A few remarks on the Camassa-Holm equation.
• Stability of the Camassa-Holm solitons
• The Cauchy problem for the Fokas-Olver-Rosenau-Qiao equation
• On the scattering problem for the Camassa-Holm equation
• Dressing Method for the Degasperis-Procesi Equation
• Inverse scattering transform for the Degasperis–Procesi equation
• Particle trajectories in extreme Stokes waves
• Inverse scattering transform for the Camassa–Holm equation
• A two-component generalization of the Degasperis–Procesi equation
• Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation
• Long-time Asymptotics for the Camassa–Holm Equation
• Well posedness and blow-up solution for a new coupled Camassa–Holm equations with peakons
• A shallow water equation on the circle
• Camassa–Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water waves
• Stability of peakons
• An integrable shallow water equation with peaked solitons
• Commutator estimates
• The Cauchy problem for the Novikov equation

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