The Cauchy problem and blow-up phenomena for a new integrable two-component peakon system with cubic nonlinearities

Li, Xiuting; Zhang, Lei

doi:10.3934/dcds.2017140

Cited by 2 publications

(1 citation statement)

References 42 publications

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“…With the initial data satisfying some certain conditions, it was shown that the 2CH system admits global solutions [26,28]. Furthermore, for the Cauchy problem for some high-order 2CH systems, see for example [20,35,47] and the references therein.…”

Section: Lei Zhang and Bin Liumentioning

confidence: 99%

Well-posedness, blow-up criteria and gevrey regularity for a rotation-two-component camassa-holm system

Zhang¹,

Liu²

2018

Discrete &Amp; Continuous Dynamical Systems - A

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In this paper, we are concerned with the Cauchy problem for a new two-component Camassa-Holm system with the effect of the Coriolis force in the rotating fluid, which is a model in the equatorial water waves. We first investigate the local well-posedness of the system in B s p,r × B s−1 p,r with s > max{1 + 1 p , 3 2 , 2 − 1 p }, p, r ∈ [1, ∞] by using the transport theory in Besov space. Then by means of the logarithmic interpolation inequality and the Osgood's lemma, we establish the local well-posedness in the critical Besov space B 3/2 2,1 × B 1/2 2,1 , and we present a blow-up result with the initial data in critical Besov space by virtue of the conservation law. Finally, we study the Gevrey regularity and analyticity of solutions to the system in a range of Gevrey-Sobolev spaces in the sense of Hardamard. Moreover, a precise lower bound of the lifespan is obtained.

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