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The periodic Cauchy problem for a two-component non-isospectral cubic Camassa-Holm system.
- Source :
-
Journal of Differential Equations . Jan2020, Vol. 268 Issue 3, p1270-1305. 36p. - Publication Year :
- 2020
-
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 B 2 , r s (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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 268
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 139528287
- Full Text :
- https://doi.org/10.1016/j.jde.2019.08.043