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arXiv · 2604.20670

Global spherically symmetric solutions to the isothermal compressible Navier-Stokes equations with far-field vacuum

Xingyang Zhang
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Abstract

In this paper, we consider the global spherically symmetric strong solutions to the compressible Navier-Stokes equations with far-field vacuum and density-dependent degenerate viscosity, following the framework proposed by Bresch-Vasseur-Yu \cite{B-V-Y 2021}. For the 1D Navier-Stokes equations, Wen-Zhang \cite{W-Z SIAM 2025} considered the Cauchy problem which established the dependence relationship $γ-δ-\frac{1}{p}\ge0$ within the $W^{2,p}(\mathbb{R})$ and $p\ge 2$. In this paper, we establish the global existence and uniqueness of strong solutions in $H^2([a,+\infty))$, $a>0$. In particular, we remove the restriction relating ($γ$, $δ$, $p$), and instead assume that $δ> 0.7427$. This result can be regarded as the first one on spherically symmetric strong solutions to the 3D Navier-Stokes equations with density-dependent viscosity proposed in \cite{B-V-Y 2021} and far-field vacuum.

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Xingyang Zhang. 2026-05-04. Global spherically symmetric solutions to the isothermal compressible Navier-Stokes equations with far-field vacuum. https://arxiv.org/abs/2604.20670

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