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arXiv · 2410.01616

Well-posedness for the free boundary barotropic fluid model in general relativity

Zeming Hao·Wei Huo·Shuang Miao
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Abstract

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.

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Zeming Hao, Wei Huo, Shuang Miao. 2024-10-02. Well-posedness for the free boundary barotropic fluid model in general relativity. https://arxiv.org/abs/2410.01616

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