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- W2971376170 abstract "In this paper, we study the periodic Cauchy problem for a two-component non-isospectral cubic Camassa-Holm system which includes the Fokas-Olver-Rosenau-Qiao (FORQ) or modified Camassa-Holm (MCH) equation and the two-component MCH system as two special cases. The system is integrable in the sense of possessing a non-isospectral Lax pair with the spectrum depending on time t, and admits multi-peakon solutions in an explicit form. Furthermore, we establish the local well-posedness for the system in the Besov space B2,rs(T) with s>3/2, 1≤r≤∞, where the key ingredients include the Friedrichs regularization method, the Littlewood-Paley decomposition theory, and the transport theory in Besov spaces. Then we derive a precise blow-up criteria, which is dependent of the parameters α(t) and γ(t). Moreover, by the intrinsic structure of the system, we obtain a new blow-up result for strong solutions with sufficient conditions on the initial data and parameters. The entire proof procedure relies upon a newly derived transport equation which is involved in nonlocal velocity term along the characteristic curves." @default.
- W2971376170 created "2019-09-12" @default.
- W2971376170 creator A5024741363 @default.
- W2971376170 creator A5073574798 @default.
- W2971376170 date "2020-01-01" @default.
- W2971376170 modified "2023-09-25" @default.
- W2971376170 title "The periodic Cauchy problem for a two-component non-isospectral cubic Camassa-Holm system" @default.
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- W2971376170 doi "https://doi.org/10.1016/j.jde.2019.08.043" @default.
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