The spectrum of the linearized operator around the Couette flow of the compressible Navier–Stokes equations between two concentric rotating cylinders is studied when the Mach number is sufficiently small. It is shown that, for sufficiently small Mach numbers, the linearized operator around the Couette flow has a critical eigenvalue which crosses the origin when the rotating speed of the cylinder increases. The critical eigenvalue and the associated eigenprojection converge to the ones for the incompressible Navier–Stokes equations as the Mach number goes to zero.

中文翻译：

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关于两个同心圆柱之间可压缩库特流的线性化算子的谱

当马赫数足够小时，研究了两个同心旋转圆柱体之间可压缩的Navier-Stokes方程的Couette流周围的线性化算子的频谱。结果表明，对于足够小的马赫数，围绕库埃特流的线性化算子具有一个临界特征值，该临界特征值在圆柱体的转速增加时会越过原点。当马赫数变为零时，不可压缩的Navier–Stokes方程的临界特征值和相关的特征投影收敛到那些。