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July  2020, 40(7): 4565-4576. doi: 10.3934/dcds.2020191

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

 1 School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China 2 Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China

Received  December 2019 Revised  January 2020 Published  April 2020

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.

Citation: Kai Yan. On the blow up solutions to a two-component cubic Camassa-Holm system with peakons. Discrete & Continuous Dynamical Systems - A, 2020, 40 (7) : 4565-4576. doi: 10.3934/dcds.2020191
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