Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024500 | Nonlinear Analysis: Real World Applications | 2017 | 27 Pages |
Abstract
This paper studies the Cauchy problem for a two-component high-order Camassa-Holm system proposed in Escher and Lyons (2015). First, we investigate the local well-posedness of the system in the Besov spaces Bp,rsÃBp,rsâ2 with s>max{3+1p,72,4â1p} and p,râ[1,â]. Second, by means of the Littlewood-Paley decomposition technique and the conservative property at hand, we derive a blow-up criteria for the strong solution. Finally, we study the Gevrey regularity and analyticity of the solutions to the system in the Gevrey-Sobolev spaces. In particular, we get a lower bound of the lifespan and the continuity of the data-to-solution mapping.
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Authors
Lei Zhang, Xiuting Li,