Nonuniform dependence and well-posedness for the generalized Camassa–Holm equation

DOI10.1080/00036811.2018.1430785zbMath1415.35100OpenAlexW2792410671MaRDI QIDQ5379319

Yongsheng Mi, Linsong Wang, Bo-ling Guo, Chun-Lai Mu

Publication date: 28 May 2019

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

Full work available at URL: https://doi.org/10.1080/00036811.2018.1430785

zbMATH Keywords

Besov spaceslocal well-posednessCamassa-Holm type equationGalerkin-type approximation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial value problems for nonlinear higher-order PDEs (35G25) Cauchy-Kovalevskaya theorems (35A10)

Cites Work

• Local well-posedness and blow-up phenomena for a generalized Camassa-Holm equation with peakon solutions
• Global existence and blow-up phenomena for the weakly dissipative Novikov equation
• Well-posedness and persistence properties for the Novikov equation
• Nonuniform dependence and well posedness for the periodic Hunter-Saxton equation.
• Non-uniform dependence on initial data for the CH equation on the line.
• Analyticity of periodic traveling free surface water waves with vorticity
• Blow-up phenomenon for the integrable Novikov equation
• On well-posedness of the Degasperis-Procesi equation
• Dissipative solutions for the Camassa-Holm equation
• On the Cauchy problem for the periodic \(b\)-family of equations and of the non-uniform continuity of Degasperis-Procesi equation
• The trajectories of particles in Stokes waves
• Global conservative solutions of the Camassa-Holm equation
• On geodesic exponential maps of the Virasoro group
• Non-uniform dependence on initial data of solutions to the Euler equations of hydrodynamics
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa-Holm type equation
• On the Stokes conjecture for the wave of extreme form
• Pseudodifferential operators and nonlinear PDE
• On the inverse spectral problem for the Camassa-Holm equation
• Wave breaking for nonlinear nonlocal shallow water equations
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• Stokes waves
• Traveling wave solutions of the Degasperis-Procesi equation
• Periodic and solitary-wave solutions of the Degasperis-Procesi equation
• Partial differential equations. 2: Qualitative studies of linear equations
• The Cauchy problem for a 4-parameter family of equations with peakon traveling waves
• The Cauchy problem for the Fokas-Olver-Rosenau-Qiao equation
• On the scattering problem for the Camassa-Holm equation
• A note on the Cauchy problem of the Novikov equation
• Inverse scattering transform for the Degasperis–Procesi equation
• An extension of integrable peakon equations with cubic nonlinearity
• Inverse scattering transform for the Camassa–Holm equation
• GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
• Integrable peakon equations with cubic nonlinearity
• Non-Uniform Dependence for the Periodic CH Equation
• Generalizations of the Camassa–Holm equation
• A shallow water equation on the circle
• Wave Structure and Nonlinear Balances in a Family of Evolutionary PDEs
• Multi-peakon solutions of the Degasperis–Procesi equation
• Stability of peakons
• An integrable shallow water equation with peaked solitons
• Well-posedness and global existence for the Novikov equation
• Waves in shallow water, with emphasis on the tsunami of 2004
• Integrable Nonlinear Wave Equations and Possible Connections to Tsunami Dynamics
• Propagation of very long water waves, with vorticity, over variable depth, with applications to tsunamis
• Particle trajectories in solitary water waves
• Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View
• Multisoliton solutions of the Degasperis–Procesi equation and their peakon limit
• The Cauchy problem for the Novikov equation
• Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation in the critical Besov space
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