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This is a Quantitative Study study.

October 13, 2025Open Access

Global Strong Solutions to the Three-Dimensional Axisymmetric Compressible Navier-Stokes Equations with Large Initial Data and Vacuum

Key Points

Global existence of strong and weak solutions is established, indicating robustness of the Navier-Stokes equations under certain conditions.
The study finds that shear viscosity being a positive constant is essential for the global solutions to be valid over time.
The solutions are derived without any restrictions on the size of initial data, suggesting flexibility in modeling various fluid scenarios.
This work emphasizes the importance of considering initial density that can vanish, introducing challenges and complexities in solutions.

Abstract

This paper investigates the three-dimensional axisymmetric compressible Navier-Stokes equations with slip boundary conditions in a cylindrical domain that excludes the axis. For initial density allowed to vanish, the global existence and large time asymptotic behavior of strong and weak solutions are established, provided the shear viscosity is a positive constant and the bulk one is a power function of density with the power bigger than four-thirds. It should be noted that this result is obtained without any restrictions on the size of initial data.

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Cite This Study

Qinghua Lei (Sun,) studied this question.

synapsesocial.com/papers/68ecfebf950606aabec09420 https://doi.org/https://doi.org/10.48550/arxiv.2509.11260