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

Kai Yan

doi:10.3934/dcds.2020191

Article Contents

2020, Volume 40, Issue 7: 4565-4576. Doi: 10.3934/dcds.2020191

This issue Previous Article Large spectral gap induced by small delay and its application to reduction Next Article Corrigendum to "The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension" [Discrete Contin. Dyn. Syst., 36 (2016), 5743–5761]

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

Kai Yan^1,2,

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

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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 $ L^\infty $-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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Mathematics Subject Classification: 35B44, 35G25, 35Q35.

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