Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation with cubic nonlinearity

DOI10.1016/j.na.2016.12.003zbMath1356.35060OpenAlexW2563959531MaRDI QIDQ504372

Zhaoyang Yin, Min Li

Publication date: 16 January 2017

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2016.12.003

zbMATH Keywords

Besov spacesLittlewood-Paley theorylocal well-posednessblow-up criterionBesov space \(B_{p,r}^s\)

Mathematics Subject Classification ID

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

Related Items

Blow-up phenomena and travelling wave solutions to the periodic integrable dispersive Hunter-Saxton equation, On wave-breaking phenomena for a new generalized two-component shallow water wave system, Formation of singularity of solution to a nonlinear shallow water equation, Wave-breaking phenomena for the generalized Camassa-Holm equation with dual-power nonlinearities, Infinite propagation speed and asymptotic behavior for a generalized Camassa-Holm equation with cubic nonlinearity, The Cauchy problem of a weakly dissipative shallow water equation, Revisit to wave breaking phenomena for the periodic Dullin–Gottwald–Holm equation, On local-in-space blow-up scenarios for a weakly dissipative rotation-Camassa–Holm equation, Blow-up phenomena and persistence properties for an integrable two-component peakon system, Weak well-posedness for the integrable modified Camassa-Holm equation with the cubic nonlinearity, Blow-up issues for the weakly dissipative periodic b-family of equations revisited, Blow-up scenario for a generalized Camassa–Holm equation with both quadratic and cubic nonlinearity

Cites Work

• Remarks on the well-posedness of Camassa-Holm type equations in Besov spaces
• The Cauchy problem for the integrable Novikov equation
• 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
• 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
• The Hamiltonian structure of the Camassa-Holm equation
• Stokes waves
• Global existence for a new periodic integrable equation.
• On asymptotically equivalent shallow water wave equations
• Traveling wave solutions of the Degasperis-Procesi equation
• A few remarks on the Camassa-Holm equation.
• Periodic and solitary-wave solutions of the Degasperis-Procesi equation
• Global weak solutions for a new periodic integrable equation with peakon solutions
• Existence of permanent and breaking waves for a shallow water equation: a geometric approach
• 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 uniqueness in critical spaces for compressible Navier-Stokes equations
• Traveling wave solutions of the Camassa-Holm 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
• 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
• Edge waves along a sloping beach
• Global solutions to a new integrable equation with peakons
• Well-posedness and global existence for the Novikov equation
• Equatorially trapped nonlinear water waves in a -plane approximation with centripetal forces
• On Gerstner's Water Wave
• The Cauchy problem for the Novikov equation
• The Cauchy problem for the Novikov equation
• On the Cauchy problem for the Camassa-Holm equation
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