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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.08397 |
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| _version_ | 1866913388499566592 |
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| author | Thompson, Ryan C. |
| author_facet | Thompson, Ryan C. |
| contents | In this paper, we consider a generalized two component Camassa-Holm system. Based on local well-posedness results and lifespan estimates, we establish sharpness of continuity on the data-to-solution map by showing that it is not uniformly continuous from product Sobolev spaces $H^s \times H^{s}$ to $C([0,T]; H^s \times H^{s})$. The proof of nonuniform dependence is based upon approximate solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08397 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Note on a Generalized Two Component Camassa-Holm System in Sobolev Spaces Thompson, Ryan C. Analysis of PDEs 35Q53 In this paper, we consider a generalized two component Camassa-Holm system. Based on local well-posedness results and lifespan estimates, we establish sharpness of continuity on the data-to-solution map by showing that it is not uniformly continuous from product Sobolev spaces $H^s \times H^{s}$ to $C([0,T]; H^s \times H^{s})$. The proof of nonuniform dependence is based upon approximate solutions. |
| title | A Note on a Generalized Two Component Camassa-Holm System in Sobolev Spaces |
| topic | Analysis of PDEs 35Q53 |
| url | https://arxiv.org/abs/2406.08397 |