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Main Authors: Hao, Zeming, Huo, Wei, Miao, Shuang
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2410.01616
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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