On a generalized Camassa–Holm equation with the flow generated by velocity and its gradient

DOI10.1080/00036811.2016.1151498zbMath1362.35101OpenAlexW2346350659WikidataQ58285788 ScholiaQ58285788MaRDI QIDQ2968012

Huijun He, Zhaoyang Yin

Publication date: 9 March 2017

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

Full work available at URL: https://doi.org/10.1080/00036811.2016.1151498

zbMATH Keywords

critical Besov spacesblow-up ratelocal well-posednessblow-up criterionsupercritical Besov spaces

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Initial value problems for nonlinear higher-order PDEs (35G25) Blow-up in context of PDEs (35B44)

Related Items (7)

On the Cauchy problem for a Camassa-Holm type equation with cubic and quartic nonlinearities ⋮ Persistence properties and blow-up phenomena for a generalized Camassa-Holm equation ⋮ On the Cauchy problem for a modified Camassa-Holm equation ⋮ Blow-up phenomena and the local well-posedness and ill-posedness of the generalized Camassa-Holm equation in critical Besov spaces ⋮ The Cauchy problem of the rotation Camassa–Holm equation in equatorial water waves ⋮ The Cauchy problem for a generalized Novikov equation ⋮ Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation in the critical Besov space

Cites Work

• Unnamed Item
• The Cauchy problem for the integrable Novikov equation
• 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
• Formation and dynamics of shock waves in the Degasperis-Procesi equation
• Well-posedness and global existence for a generalized Degasperis-Procesi equation
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Wave breaking for nonlinear nonlocal shallow water equations
• Stokes waves
• Global existence for a new periodic integrable equation.
• On asymptotically equivalent shallow water wave equations
• Global weak solutions for a shallow water equation
• Traveling wave solutions of the Degasperis-Procesi equation
• Periodic and solitary-wave solutions of the Degasperis-Procesi equation
• Global weak solutions for a new periodic integrable equation with peakon solutions
• Local well-posedness and blow-up criteria for a two-component Novikov system in the critical Besov space
• Global weak solutions to the Novikov equation
• Global existence and blow-up phenomena for the Degasperis-Procesi equation
• On the weak solutions to a shallow water equation
• On the scattering problem for the Camassa-Holm equation
• A note on the Cauchy problem of the Novikov equation
• Fourier Analysis and Nonlinear Partial Differential Equations
• Global weak solutions for the Novikov equation
• On the Cauchy problem for the Degasperis-Procesi equation
• Inverse scattering transform for the Degasperis–Procesi equation
• GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
• Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation
• Integrable peakon equations with cubic nonlinearity
• Variational derivation of the Camassa-Holm shallow water equation
• Generalizations of the Camassa–Holm equation
• A shallow water equation on the circle
• A note on the uniqueness of solutions of ordinary differential equations
• Stability of peakons
• An integrable shallow water equation with peaked solitons
• Global solutions to a new integrable equation with peakons
• The Cauchy problem for the Novikov equation
• The Cauchy problem for the Novikov equation
• On the Cauchy problem for the Camassa-Holm equation

This page was built for publication: On a generalized Camassa–Holm equation with the flow generated by velocity and its gradient