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

Abstract: In this paper, we consider the global spherically symmetric strong solution to the compressible Navier-Stokes equations with far-field vacuum and density-denpendent degenerate viscosity which is referenced from Bresch-Vasseur-Yu \cite{B-V-Y 2021}. For the 1D Navier-Stokes equations, Wen-Zhang \cite{W-Z SIAM 2025} have considered the Cauchy problem which established the dependence relationship $γ-δ-\frac{1}{p}\ge0$ within the $W<sup>{2,p}(\mathbb{R})$ and $p\ge 2$. In contrast, the solution space of this paper is $H<sup>2[a,+\infty)$, $a&gt;0$ and $δ$ satisfies $1&gt;δ\gtrsim0.7427$. This result can be regarded as the first one on spherically symmetric strong solutions to the 3D Navier-Stokes equations with the viscosity proposed in \cite{B-V-Y 2021} and far-field vacuum.