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On the blow up solutions to a two-component cubic Camassa-Holm system with peakons

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  • 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 $ L^\infty $-norm of the strong solution within its lifespan. As a result, two new blow-up solutions with certain initial profiles are established.

    Mathematics Subject Classification: 35B44, 35G25, 35Q35.


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