A CONTINUOUS INTERPOLATION BETWEEN CONSERVATIVE AND DISSIPATIVE SOLUTIONS FOR THE TWO-COMPONENT CAMASSA–HOLM SYSTEM

DOI10.1017/fms.2014.29zbMath1315.35186arXiv1402.1060OpenAlexW2963364851MaRDI QIDQ5496787

Katrin Grunert, Helge Holden, Xavier Raynaud

Publication date: 28 January 2015

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.1060

zbMATH Keywords

global weak solutionconservative solutionLagrangian coordinatestwo-component Camassa-Holm systemdissipative solution

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30)

Related Items (17)

Lipschitz metric for conservative solutions of the two-component Camassa-Holm system ⋮ Stability of the Camassa-Holm multi-peakons in the dynamics of a shallow-water-type system ⋮ Stability of the Camassa-Holm peakons in the dynamics of a shallow-water-type system ⋮ Ghostpeakons and characteristic curves for the Camassa-Holm, Degasperis-Procesi and Novikov equations ⋮ Existence and regularity for global weak solutions to the 𝜆-family water wave equations ⋮ Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy ⋮ On measures of accretion and dissipation for solutions of the Camassa–Holm equation ⋮ A LIPSCHITZ METRIC FOR THE CAMASSA–HOLM EQUATION ⋮ A convergent numerical algorithm for \(\alpha\)-dissipative solutions of the Hunter-Saxton equation ⋮ Existence and Lipschitz stability for α-dissipative solutions of the two-component Hunter–Saxton system ⋮ Blow-up for the two-component Camassa-Holm system ⋮ Uniqueness of dissipative solution for Camassa-Holm equation with peakon-antipeakon initial data ⋮ Transfer of energy in Camassa-Holm and related models by use of nonunique characteristics ⋮ The general peakon–antipeakon solution for the Camassa–Holm equation ⋮ Generic Regularity of Conservative Solutions to Camassa--Holm Type Equations ⋮ A view of the peakon world through the lens of approximation theory ⋮ Lipschitz stability for the Hunter–Saxton equation

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