Global existence for the higher-order Camassa-Holm shallow water equation

DOI10.1016/J.NA.2010.12.002zbMath1210.35194OpenAlexW2048385796MaRDI QIDQ631719

Pin Zhang, Lixin Tian, Li-Meng Xia

Publication date: 14 March 2011

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.2010.12.002

zbMATH Keywords

conservation lawglobal existencelocal well-posednesshigher-order Camassa-Holm equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (12)

On the Cauchy problem for a higher-order \(\mu\)-Camassa-Holm equation ⋮ Lipschitz metric for the periodic second-order Camassa-Holm equation ⋮ Stability of traveling wave solutions for the second-order Camassa-Holm equation ⋮ Orbital stability of pseudo-peakons for the fifth-order Camassa-Holm type equation ⋮ Stability of disturbance decomposition near traveling wave solutions for the second-order Camassa-Holm equation ⋮ Blow-up solution near the traveling waves for the second-order Camassa-Holm equation ⋮ The Cauchy problem for a weakly dissipative 2-component Camassa-Holm system ⋮ Infinite propagation speed and asymptotic behavior for a generalized fifth-order Camassa–Holm equation ⋮ The effect of a noise on the stochastic modified Camassa–Holm equation ⋮ Traveling solutions and evolution properties of the higher order Camassa-Holm equation ⋮ Orbital stability and dynamical behaviors of solitary waves for the Camassa-Holm equation with quartic nonlinearity ⋮ Analytical properties for the fifth-order b-family Novikov model

Cites Work

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