Abstract
This paper is concerned with the Cauchy problem for a two- component cubic Camassa-Holm system with peakons, which is a natural multi-component extension of the single Fokas-Olver-Rosenau-Qiao equation. By sufficiently exploiting the fine structure of the system, we derive two useful conservation laws which turns out an exponential increase estimate for the \begin{document}$ L^\infty $\end{document} -norm of the strong solution within its lifespan. As a result, two new blow-up solutions with certain initial profiles are established.
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