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

TL;DR

This paper proves the well-posedness of a free boundary barotropic fluid model in general relativity, accommodating general equations of state and non-zero vorticities, using Sobolev space estimates and coupled wave equations.

Contribution

It extends previous results by allowing more general equations of state and non-zero vorticities in the relativistic fluid model with a free boundary.

Findings

Established a priori estimates and well-posedness in Sobolev spaces.

Decomposed fluid and geometric quantities using parallel transport.

Analyzed fluid dynamics via coupled interior-boundary wave equations and geometric quantities through Bianchi equations.

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.