Abstract We consider a simplified compressible Navier-Stokes equations with cylindrical symmetry when viscosity coefficient λ and heat conductivity coefficient κ depend on temperature. We obtain global existence of strong solution and vanishing shear viscosity limit to the initial-boundary value problem in Eulerian coordinates. The analysis for the global existence is based on the assumption that μ = const . > 0 , 1 c ˜ θ m ≤ λ ( θ ) ≤ c ˜ ( 1 + θ m ) , κ ( θ ) = θ q , for m ∈ ( 0 , 1 ] , q ≥ m . For the part of vanishing shear viscosity limit, we require in addition that 1 c ˜ ( 1 + θ m ) ≤ λ ( θ ) ≤ c ˜ ( 1 + θ m ) . In the paper, the acceleration effect in one direction is neglected, however, we do not need any smallness assumption for the initial data.

中文翻译：

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关于具有温度相关粘度的简化可压缩 Navier-Stokes 方程

摘要 当粘度系数λ 和导热系数κ 取决于温度时，我们考虑了简化的具有圆柱对称性的可压缩Navier-Stokes 方程。我们获得了欧拉坐标中初边界值问题的强解和消失剪切粘度极限的全局存在性。全局存在性的分析基于 μ = const 的假设。> 0 , 1 c ˜ θ m ≤ λ ( θ ) ≤ c ˜ ( 1 + θ m ) , κ ( θ ) = θ q , 对于 m ∈ ( 0 , 1 ] , q ≥ m . 对于消失剪切部分粘度极限，我们另外要求 1 c ˜ ( 1 + θ m ) ≤ λ ( θ ) ≤ c ˜ ( 1 + θ m ) . 在本文中，一个方向的加速度效应被忽略，但我们不需要对初始数据进行任何小的假设。