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Global well-posedness for the compressible Navier--Stokes equations in 3D bounded domains under a new smallness condition
Abstract
We investigate the three-dimensional barotropic compressible Navier--Stokes equations involving vacuum in a bounded domain with Navier-slip boundary conditions. It is shown that such a model admits a unique global strong solution provided the gradient of the initial velocity and the initial pressure deviation are suitably small in L2. In particular, \textit{the smallness threshold depends only on the known parameters and the prescribed density bounds.} Our result provides a new analytical framework for the global well-posedness theory of the compressible Navier--Stokes equations.
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BibTeX
@misc{xu2026global,
title = {{Global well-posedness for the compressible Navier--Stokes equations in 3D bounded domains under a new smallness condition}},
author = {Lin Xu and Xin Zhong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23091},
eprint = {2610.23091},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23091},
}
RIS
TY - UNPB
TI - Global well-posedness for the compressible Navier--Stokes equations in 3D bounded domains under a new smallness condition
AU - Lin Xu
AU - Xin Zhong
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23091
UR - https://arxiv.org/abs/2610.23091
AB - We investigate the three-dimensional barotropic compressible Navier--Stokes equations involving vacuum in a bounded domain with Navier-slip boundary conditions. It is shown that such a model admits a unique global strong solution provided the gradient of the initial velocity and the initial pressure deviation are suitably small in L^2. In particular, \textit{the smallness threshold depends only on the known parameters and the prescribed density bounds.} Our result provides a new analytical framework for the global well-posedness theory of the compressible Navier--Stokes equations.
ER -