# American Institute of Mathematical Sciences

May  2015, 35(5): 2041-2051. doi: 10.3934/dcds.2015.35.2041

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

 1 Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim

Received  June 2014 Revised  August 2014 Published  December 2014

Following conservative solutions of the two-component Camassa--Holm system $u_t-u_{txx}+3uu_x-2u_xu_{xx}-uu_{xxx}+\rho\rho_x=0$, $\rho_t+(u\rho)_x=0$ 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 $\rho_0\in L^2(\mathbb{R})$.
Citation: Katrin Grunert. Blow-up for the two-component Camassa--Holm system. Discrete & Continuous Dynamical Systems - A, 2015, 35 (5) : 2041-2051. doi: 10.3934/dcds.2015.35.2041
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