The local well-posedness, blow-up and global solution of a new integrable system in Besov spaces

2024/06/23 by Zheng, Pei, Yin, Zhaoyang
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.16022

Abstract

In this paper, we first establish the local well-posednesss for the Cauchy problem of a N-peakon system in the sense of Hadamard in both critical Besov spaces and supercritical Besov spaces. Second, we gain a blow-up criterion. According to blow-up criterion wemreach a precise blow-up criterion. Under a sign condition, we reach the existence of global solution. Finally, based on the first-order difference method, we give a simulation example of the blow-up of the equation and the properties of the global solution.

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