Stability of Boundary Layers for the Nonisentropic Compressible Circularly Symmetric 2D Flow
Stability of Boundary Layers for the Nonisentropic Compressible Circularly Symmetric 2D Flow
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DOI：
10.1137/130906507
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发表时间：
2014-01
期刊：
影响因子：
--
通讯作者：
Cheng-Jie Liu;Ya-Guang Wang
中科院分区：
文献类型：
--
作者：
Cheng-Jie Liu;Ya-Guang Wang
本文研究了具有不可渗透边界条件的二维外域中非等熵可压缩纳维-斯托克斯方程初始边值问题的圆对称解在粘度和导热系数以相同速率趋于零时的渐近行为。通过多尺度分析，得出远离边界的非等熵可压缩粘性流可以用相应的无粘流来近似，在边界附近存在解的主阶展开式中的角速度、密度和温度的边界层，而径向速度和压力没有主阶的边界层。速度和温度的边界层由非线性抛物线系统描述。我们证明了边界层的稳定性，并严格证明了在 L^{\infty}$ 空间中对于小粘度和 L 中的热传导极限的解的渐近行为。
In this paper, we study the asymptotic behavior of circularly symmetric solutions to the initial boundary value problem of the nonisentropic compressible Navier--Stokes equations in a two-dimensional exterior domain with impermeable boundary conditions when the viscosities and the heat conduction coefficient tend to zero at the same rate. By multiscale analysis, we obtain that away from the boundary the nonisentropic compressible viscous flow can be approximated by the corresponding inviscid flow, and near the boundary there are boundary layers for the angular velocity, density, and temperature in the leading order expansions of solutions, while the radial velocity and pressure do not have boundary layers in the leading order. The boundary layers of velocity and temperature are described by a nonlinear parabolic system. We prove the stability of boundary layers and rigorously justify the asymptotic behavior of solutions in the $L^{\infty}$ space for the small viscosities and heat-conduction limit in the L...