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arXiv · 2406.16022

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

Pei Zheng·Zhaoyang Yin
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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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Pei Zheng, Zhaoyang Yin. 2024-06-23. The local well-posedness, blow-up and global solution of a new integrable system in Besov spaces. https://arxiv.org/abs/2406.16022

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