Analysis on a generalized two-component Novikov system
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916883844825088 |
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| author | Zhou, Yonghui Li, Xiaowan Ji, Shuguan Qiao, Zhijun |
| author_facet | Zhou, Yonghui Li, Xiaowan Ji, Shuguan Qiao, Zhijun |
| contents | In this paper, we study the Cauchy problem for a generalized two-component Novikov system with weak dissipation. We first establish the local well-posedness of solutions by using the Kato's theorem. Then we give the necessary and sufficient condition for the occurrence of wave breaking in a finite time. Finally, we investigate the persistence properties of strong solutions in the weighted $L^{p}(\mathbb{R})$ spaces for a large class of moderate weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04290 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis on a generalized two-component Novikov system Zhou, Yonghui Li, Xiaowan Ji, Shuguan Qiao, Zhijun Analysis of PDEs Mathematical Physics In this paper, we study the Cauchy problem for a generalized two-component Novikov system with weak dissipation. We first establish the local well-posedness of solutions by using the Kato's theorem. Then we give the necessary and sufficient condition for the occurrence of wave breaking in a finite time. Finally, we investigate the persistence properties of strong solutions in the weighted $L^{p}(\mathbb{R})$ spaces for a large class of moderate weights. |
| title | Analysis on a generalized two-component Novikov system |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2508.04290 |