The local well-posedness, blow-up criteria and Gevrey regularity of solutions for a two-component high-order Camassa–Holm system. (June 2017) - Zhang, Lei
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 B p, r s × B p, r s − 2 with s > max { 3 + 1 p, 7 2, 4 − 1 p } and p, r ∈ [ 1, ∞ ] . 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.