球对称下带退化粘性的可压缩Navier-Stokes方程的扩展解：整体存在性与无粘极限
Expanding solutions to the compressible Navier-Stokes equations with degenerate viscosities in spherical symmetry: global existence and inviscid limit
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中文总结 AI 辅助
本文针对球对称下带密度相关粘性的等熵可压缩Navier-Stokes方程的真空自由边界问题，在初始数据为特定扩展仿射解小扰动时构造了扩展整体解，并证明粘性系数趋于零时扰动解以显式速率收敛到可压缩Euler方程的解。
中文摘要 AI 辅助
本文致力于研究球对称下带密度相关粘性的等熵可压缩Navier-Stokes方程的真空自由边界问题的强解，该模型用于描述被真空包围的等熵可压缩粘性流的运动。当初始数据为绝热指数γ>1且粘性系数与流体密度ρ的γ次方成正比时的扩展仿射解的小扰动时，我们构造了一类扩展整体解。此外，当粘性系数趋于零时，我们证明了扰动解收敛到可压缩Euler方程的解，且粘性系数具有显式收敛速率。
英文摘要
This paper is devoted to studying the strong solutions to the vacuum free boundary problem for the isentropic compressible Navier-Stokes equations with density-dependent viscosities under spherical symmetry, which models the motions of isentropic compressible viscous flows surrounded by vacuum. We construct a class of expanding global solutions when the initial data is a small perturbation of the expanding affine solutions for the adiabatic exponent $γ>1$ and the viscosity coefficients proportional to $ρ^γ$, with $ρ$ being the fluid density. In addition, when the viscosity coefficients tend to zero, the perturbed solutions are proved to converge to the solutions to the compressible Euler equations with an explicit converging rate of viscosity coefficients.
