Well-posedness and wave breaking for a class of integrable equations

DOI10.1007/s00209-022-03124-2zbMath1498.35453OpenAlexW4293760362MaRDI QIDQ2081426

Yong-Hui Zhou, Shuguan Ji

Publication date: 13 October 2022

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-022-03124-2

zbMATH Keywords

blow-up rateglobal solutionslocal well-posednesswave breaking

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (3)

On the Cauchy problem for a weakly dissipative coupled Camassa-Holm system ⋮ Globally conservative weak solutions for a class of nonlinear dispersive wave equations beyond wave breaking ⋮ Wave breaking and asymptotic analysis of solutions for a class of weakly dissipative nonlinear wave equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Korteweg-de Vries equation
• Global weak solutions and blow-up structure for the Degasperis-Procesi equation
• Global conservative solutions of the Camassa-Holm equation
• Formation and dynamics of shock waves in the Degasperis-Procesi equation
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Semigroups of linear operators and applications to partial differential equations
• On the structure of a family of quasilinear equations arising in shallow water theory
• Wave breaking for nonlinear nonlocal shallow water equations
• On asymptotically equivalent shallow water wave equations
• Global weak solutions for a shallow water equation
• The initial value problem for a generalized Boussinesq equation.
• Global weak solutions for a new periodic integrable equation with peakon solutions
• On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
• Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
• Existence of permanent and breaking waves for a shallow water equation: a geometric approach
• Invariants and wave breaking analysis of a Camassa-Holm type equation with quadratic and cubic non-linearities
• On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation
• Global weak solutions to the Novikov equation
• Global existence and blow-up phenomena for the Degasperis-Procesi equation
• Wave breaking and global solutions of the weakly dissipative periodic Camassa-Holm type equation
• On the weak solutions to a shallow water equation
• On the scattering problem for the Camassa-Holm equation
• Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation
• Global existence and blow-up phenomena for the peakon $b$-family of equations
• Stability of peakons for the Degasperis-Procesi equation
• Generalizations of the Camassa–Holm equation
• Commutator estimates and the euler and navier-stokes equations
• Multi-peakons and a theorem of Stieltjes
• Global weak solutions for a shallow water equation
• A shallow water equation on the circle
• Stability of peakons
• An integrable shallow water equation with peaked solitons
• Well-posedness and global existence for the Novikov equation
• Global existence of weak solutions to the Camassa-Holm equation
• The Cauchy problem of the modified CH and DP equations
• The Cauchy problem for the Novikov equation

This page was built for publication: Well-posedness and wave breaking for a class of integrable equations