The Cauchy problem for a generalized Camassa–Holm equation with the velocity potential

DOI10.1080/00036811.2016.1267342zbMath1461.35108OpenAlexW2570278578WikidataQ58253253 ScholiaQ58253253MaRDI QIDQ5856156

Bohuan Lin, Zhaoyang Yin

Publication date: 24 March 2021

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2016.1267342

zbMATH Keywords

blow-uplocal well-posednesscuspon weak solutionsgeneralized Camassa-Holm equation with the velocity potential

Mathematics Subject Classification ID

Wave equation (35L05) Initial value problems for nonlinear higher-order PDEs (35G25) Blow-up in context of PDEs (35B44)

Cites Work

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• An exact solution for equatorial geophysical water waves with an underlying current
• Analyticity of periodic traveling free surface water waves with vorticity
• On the well-posedness of the Degasperis-Procesi equation
• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Global weak solutions and blow-up structure for the Degasperis-Procesi equation
• The trajectories of particles in Stokes waves
• Global conservative solutions of the Camassa-Holm equation
• Well-posedness and global existence for a generalized Degasperis-Procesi equation
• Wave breaking for nonlinear nonlocal shallow water equations
• Global existence for a new periodic integrable equation.
• 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
• Traveling wave solutions of the Degasperis-Procesi equation
• A few remarks on the Camassa-Holm equation.
• Existence of permanent and breaking waves for a shallow water equation: a geometric approach
• Global existence and blow-up phenomena for the Degasperis-Procesi equation
• Local-in-space criteria for blowup in shallow water and dispersive rod equations
• Traveling wave solutions of the Camassa-Holm equation
• On the scattering problem for the Camassa-Holm equation
• Fourier Analysis and Nonlinear Partial Differential Equations
• On the Cauchy problem for the Degasperis-Procesi equation
• Inverse scattering transform for the Degasperis–Procesi equation
• Inverse scattering transform for the Camassa–Holm equation
• GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
• Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation
• Long-time Asymptotics for the Camassa–Holm Equation
• Generalizations of the Camassa–Holm equation
• A shallow water equation on the circle
• Breakdown of the Camassa-Holm equation
• An integrable shallow water equation with peaked solitons
• Edge waves along a sloping beach
• Global solutions to a new integrable equation with peakons
• Equatorially trapped nonlinear water waves in a -plane approximation with centripetal forces
• On Gerstner's Water Wave
• Particle trajectories in solitary water waves
• On the Blow-up Phenomena for the Degasperis-Procesi Equation
• The Cauchy problem for the Novikov equation

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