The local well-posedness, blow-up and global solution of a new integrable system in Besov spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929396899643392 |
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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 |