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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/2410.01616 |
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| _version_ | 1866914962740346880 |
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| author | Hao, Zeming Huo, Wei Miao, Shuang |
| author_facet | Hao, Zeming Huo, Wei Miao, Shuang |
| contents | In the framework of general relativity, the dynamics of a general barotropic fluid are coupled to the Einstein equations, which govern the structure of the underlying spacetime. We establish a priori estimates and well-posedness in Sobolev spaces for this model with a free boundary. Within the frame parallel-transported by the fluid velocity, we decompose the fluid and geometric quantities. The fluid components are estimated via a coupled interior-boundary wave equation, while the geometric quantities are analyzed through the Bianchi equations. Compared to a previous work, the results in present paper allow general equations of state and non-zero vorticities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01616 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness for the free boundary barotropic fluid model in general relativity Hao, Zeming Huo, Wei Miao, Shuang Analysis of PDEs In the framework of general relativity, the dynamics of a general barotropic fluid are coupled to the Einstein equations, which govern the structure of the underlying spacetime. We establish a priori estimates and well-posedness in Sobolev spaces for this model with a free boundary. Within the frame parallel-transported by the fluid velocity, we decompose the fluid and geometric quantities. The fluid components are estimated via a coupled interior-boundary wave equation, while the geometric quantities are analyzed through the Bianchi equations. Compared to a previous work, the results in present paper allow general equations of state and non-zero vorticities. |
| title | Well-posedness for the free boundary barotropic fluid model in general relativity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.01616 |