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

Fuente: arXiv
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Main Authors: Zheng, Pei, Yin, Zhaoyang
Format: Preprint
Published: 2024
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author Zheng, Pei
Yin, Zhaoyang
author_facet Zheng, Pei
Yin, Zhaoyang
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_16022
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The local well-posedness, blow-up and global solution of a new integrable system in Besov spaces
Zheng, Pei
Yin, Zhaoyang
Analysis of PDEs
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.
title The local well-posedness, blow-up and global solution of a new integrable system in Besov spaces
topic Analysis of PDEs
url https://arxiv.org/abs/2406.16022