Blow-up for the two-component Camassa-Holm system

Abstract

Following conservative solutions of the two-component Camassa-Holm system $u_t-u_{txx}+3u{u}_x-2u_x{u}_{xx}-u{u}_{xxx}+\rho {\rho }_x=0$, ${\rho }_t+(u\rho {)}_x=0$ along characteristics, we determine if wave breaking occurs in the nearby future or not, for initial data $u_0\in H^1(\mathbb{R})$ and ${\rho }_0\in L^2(\mathbb{R})$.

11 pages, 1 figure

References in corpus (2)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• On an integrable two-component Camassa-Holm shallow water system

Cited by in corpus (7)

• A Lagrangian view on complete integrability of the two-component Camassa-Holm system
• Solutions of the Camassa-Holm equation with accumulating breaking times
• A numerical study of variational discretizations of the Camassa-Holm equation
• A semi-discrete scheme derived from variational principles for global conservative solutions of a Camassa-Holm system
• Stumpons are non-conservative traveling waves of the Camassa-Holm equation
• Uniqueness of Dissipative Solution for Camassa-Holm Equation with Peakon-Antipeakon Initial Data
• Symmetries and multipeakon solutions for the modified two-component Camassa-Holm system