Boundary Layer Stability¶in Real Vanishing Viscosity Limit
Boundary Layer Stability¶in Real Vanishing Viscosity Limit
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DOI：
10.1007/s002200100486
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发表时间：
2001-02
影响因子：
2.4
通讯作者：
D. Serre;K. Zumbrun
中科院分区：
文献类型：
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作者：
D. Serre;K. Zumbrun
在以前的文献[20]中，发展了一种用于研究边界层稳定性的Evans函数机。在那里，分析仅限于强抛物型扰动，即近似于公式ut+（F（u））x= v（B（u）ux）x$（v <$1）与“椭圆”矩阵B。然而，真实的模型，如气体流动的Euler方程的Navier-Stokes近似，涉及不完全抛物扰动：B是不可逆的在一般情况下，我们首先适应埃文斯函数到这个现实的框架，假设边界不是特征，无论是双曲一阶系统t+（F（u））x= 0，也不为扰动系统。然后，我们将其应用到各种气体流动的边界层。我们展示了一些例子，一个完美的气体不稳定的边界层，当粘度占主导地位的热导率。
In the previous paper [20], an Evans function machinery for the study of boundary layer stability was developed. There, the analysis was restricted to strongly parabolic perturbations, that is to an approximation of the formut+(F(u))x=ν(B(u)ux)x$ (ν≪1) with an “elliptic” matrixB. However, real models, like the Navier–Stokes approximation of the Euler equations for a gas flow, involve incompletely parabolic perturbations:Bis not invertible in general.We first adapt the Evans function to this realistic framework, assuming that the boundary is not characteristic, neither for the hyperbolic first order systemut+(F(u))x= 0, nor for the perturbed system. We then apply it to the various kinds of boundary layers for a gas flow. We exhibit some examples of unstable boundary layers for a perfect gas, when the viscosity dominates heat conductivity.