Local well-posedness and blow-up phenomenon for a generalization two-component Camassa–Holm system

In this paper, a new generalized two-component Camassa–Holm system is derived via the energy variational approach. This system has two parameters which depend on the energy functional. The initial value problem is investigated. The local well-posedness is obtained when the initial density is away fr...

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Veröffentlicht in:Journal of evolution equations 2019-12, Vol.19 (4), p.935-963
Hauptverfasser: Chen, Yuhui, Huang, Jingchi, Luo, Wei, Yu, Fang
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Sprache:eng
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Zusammenfassung:In this paper, a new generalized two-component Camassa–Holm system is derived via the energy variational approach. This system has two parameters which depend on the energy functional. The initial value problem is investigated. The local well-posedness is obtained when the initial density is away from vacuum. Taking advantage of the method of characteristics and the conservation laws, we prove the blow-up criteria. According to the blow-up criteria, we can prove the finite time blow-up result under some suitable condition. Moreover, we give some exact expression of traveling solutions.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-019-00503-x