Global well-posedness for the compressible Navier--Stokes equations in 3D bounded domains under a new smallness condition
Year: 2026
Type: preprint
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 $L^2$. 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.
Source: arXiv (Cornell University)
Authors: Xu, Lin, Zhong, Xin
Institution: Southwest University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1306563017, G2771458480
OpenAlex ID: W7222986328