Global dynamics of viscous gaseous stars in a physical vacuum
Abstract
The study of vacuum is important in understanding compressible flows. In particular, physical vacuum, which ensures a finite, nontrivial pressure-induced acceleration in the normal direction on the moving boundary, naturally arises in the study of the motion of gaseous stars. In this paper, we analyze the free boundary problem for the three-dimensional compressible Navier--Stokes--Poisson equations with degenerate viscosities for self-gravitating viscous gaseous stars. For the spherically symmetric and barotropic motion, we establish the global existence of the unique classical solution without any restriction on the size of the initial data. Our solutions are classical up to the moving boundary for positive times, and preserve the physical vacuum boundary behavior of the Lane--Emden star configuration.
Related
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- Global regularity and sharp decay rates for the one-dimensional hypo-viscous compressible Navier-Stokes equations in critical Besov spaces
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BibTeX
@misc{wang2026global,
title = {{Global dynamics of viscous gaseous stars in a physical vacuum}},
author = {Demin Wang and Jiawen Zhang and Shengguo Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.09189},
eprint = {2607.09189},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.09189},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Global dynamics of viscous gaseous stars in a physical vacuum
AU - Demin Wang
AU - Jiawen Zhang
AU - Shengguo Zhu
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2607.09189
UR - https://arxiv.org/abs/2607.09189
AB - The study of vacuum is important in understanding compressible flows. In particular, physical vacuum, which ensures a finite, nontrivial pressure-induced acceleration in the normal direction on the moving boundary, naturally arises in the study of the motion of gaseous stars. In this paper, we analyze the free boundary problem for the three-dimensional compressible Navier--Stokes--Poisson equations with degenerate viscosities for self-gravitating viscous gaseous stars. For the spherically symmetric and barotropic motion, we establish the global existence of the unique classical solution without any restriction on the size of the initial data. Our solutions are classical up to the moving boundary for positive times, and preserve the physical vacuum boundary behavior of the Lane--Emden star configuration.
ER -