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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.01884 |
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| _version_ | 1866911788565528576 |
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| author | Chen, Li Luo, Zhen Wang, Yucheng |
| author_facet | Chen, Li Luo, Zhen Wang, Yucheng |
| contents | In this paper, we consider the chemotaxis-shallow water system in $\mathbb{R}^2$. We establish the local existence of classical solution without assuming the initial height is small or has a small perturbation near a constant. The far field behavior of the height is a constant which could be either vacuum or non-vacuum. The initial data is allowed vacuum and the spatial measure of the set of vacuum can be arbitrarily large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01884 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local existence of classical solution to the chemotaxis-shallow water system with vacuum in $\mathbb{R}^2$ Chen, Li Luo, Zhen Wang, Yucheng Analysis of PDEs In this paper, we consider the chemotaxis-shallow water system in $\mathbb{R}^2$. We establish the local existence of classical solution without assuming the initial height is small or has a small perturbation near a constant. The far field behavior of the height is a constant which could be either vacuum or non-vacuum. The initial data is allowed vacuum and the spatial measure of the set of vacuum can be arbitrarily large. |
| title | Local existence of classical solution to the chemotaxis-shallow water system with vacuum in $\mathbb{R}^2$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.01884 |