On the Cauchy problem for a class of shallow water wave equations with \((k+1)\)-order nonlinearities

DOI10.1016/j.jmaa.2016.07.056zbMath1354.35119OpenAlexW2494369549MaRDI QIDQ323793

Bin Liu, Lei Zhang

Publication date: 10 October 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.07.056

zbMATH Keywords

well-posednessanalyticityblow-up criteriaGevrey regularity\((k+1)\)-order nonlinearitiesshallow water wave equations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Blow-up in context of PDEs (35B44) Strong solutions to PDEs (35D35)

Related Items

Well-posedness and blow-up phenomena for an integrable three-component Camassa-Holm system ⋮ Well-posedness, blow-up criteria and Gevrey regularity for a rotation-two-component Camassa-Holm system ⋮ Local and global pathwise solutions for a stochastically perturbed nonlinear dispersive PDE ⋮ Global weak solutions to a nonlinear equation with fourth order nonlinearities ⋮ The Cauchy problem of a weakly dissipative shallow water equation ⋮ Blow-up phenomena and peakons for the gFQXL/gCH-mCH equation ⋮ The Cauchy problem and blow-up phenomena for a new integrable two-component peakon system with cubic nonlinearities ⋮ The periodic Cauchy problem for a two-component non-isospectral cubic Camassa-Holm system ⋮ The dynamic properties of solutions for a nonlinear shallow water equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Cauchy problem for the integrable Novikov equation
• Continuity properties of the data-to-solution map for the generalized Camassa-Holm equation
• Well-posedness and persistence properties for the Novikov equation
• Analyticity of periodic traveling free surface water waves with vorticity
• The trajectories of particles in Stokes waves
• Global conservative solutions of the Camassa-Holm equation
• On geodesic exponential maps of the Virasoro group
• Formation and dynamics of shock waves in the Degasperis-Procesi equation
• A note on a theorem of Nirenberg
• Wave breaking for nonlinear nonlocal shallow water equations
• A note on well-posedness for Camassa-Holm equation.
• On asymptotically equivalent shallow water wave equations
• Analyticity of the Cauchy problem for an integrable evolution equation
• Global weak solutions for a shallow water equation
• Peakon solutions of the Novikov equation and properties of the data-to-solution map
• A few remarks on the Camassa-Holm equation.
• Global weak solutions for a new periodic integrable equation with peakon solutions
• On the Cauchy problem for the modified Novikov equation with peakon solutions
• The existence of global strong and weak solutions for the Novikov equation
• Existence of permanent and breaking waves for a shallow water equation: a geometric approach
• The Cauchy problem for the generalized Camassa-Holm equation in Besov space
• On the uniqueness in critical spaces for compressible Navier-Stokes equations
• An abstract form of the nonlinear Cauchy-Kowalewski theorem
• On the weak solutions to a shallow water equation
• On the scattering problem for the Camassa-Holm equation
• Fourier Analysis and Nonlinear Partial Differential Equations
• The Periodic Cauchy Problem for Novikov's Equation
• GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
• Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation
• Generalizations of the Camassa–Holm equation
• A shallow water equation on the circle
• Stability of peakons
• An integrable shallow water equation with peaked solitons
• Gevrey regularity and analyticity for Camassa-Holm type systems
• Particle trajectories in solitary water waves
• Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View
• The Cauchy problem for a generalized Camassa-Holm equation
• On the Cauchy problem for a generalized Camassa-Holm equation
• The Cauchy problem for the Novikov equation
• On the Cauchy problem for the Camassa-Holm equation

This page was built for publication: On the Cauchy problem for a class of shallow water wave equations with \((k+1)\)-order nonlinearities