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The Israel-Stewart equations with a physical vacuum boundary
Abstract
We establish local existence for the nonlinear Israel--Stewart equations describing a relativistic viscous fluid with a physical vacuum free boundary. Compared with ideal fluids with a physical vacuum, the relaxation equation for the bulk viscosity introduces further derivative loss. The problem is compounded by the degenerate nature of the equations of motion on the free boundary. In this work, we construct solutions in weighted Sobolev spaces via a Nash--Moser iteration. Since the domain moves, the iteration is carried out in Lagrangian coordinates, while the linearized operator at each iterate is inverted on the Eulerian domain with the local well-posedness of the linearized equations established in our earlier work.
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BibTeX
@misc{zhong2026israelstewart,
title = {{The Israel-Stewart equations with a physical vacuum boundary}},
author = {Runzhang Zhong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26533},
eprint = {2610.26533},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26533},
}
RIS
TY - UNPB
TI - The Israel-Stewart equations with a physical vacuum boundary
AU - Runzhang Zhong
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26533
UR - https://arxiv.org/abs/2610.26533
AB - We establish local existence for the nonlinear Israel--Stewart equations describing a relativistic viscous fluid with a physical vacuum free boundary. Compared with ideal fluids with a physical vacuum, the relaxation equation for the bulk viscosity introduces further derivative loss. The problem is compounded by the degenerate nature of the equations of motion on the free boundary. In this work, we construct solutions in weighted Sobolev spaces via a Nash--Moser iteration. Since the domain moves, the iteration is carried out in Lagrangian coordinates, while the linearized operator at each iterate is inverted on the Eulerian domain with the local well-posedness of the linearized equations established in our earlier work.
ER -