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 |
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Hauptverfasser: | , , , |
Format: | Artikel |
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. |
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ISSN: | 1424-3199 1424-3202 |
DOI: | 10.1007/s00028-019-00503-x |