In this paper, the multi-dimensional (M-D) isentropic compressible Navier–Stokes equations with degenerate viscosities (ICNS) is considered in the whole space. We show that for a certain class of initial data with local vacuum, the regular solution of the corresponding Cauchy problem will blow up in finite time, no matter how small and smooth the initial data are. It is worth pointing out that local existence of regular solution considered in this paper has been established.

中文翻译：

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多维可压缩退化 Navier-Stokes 方程的奇点形成

在本文中，在整个空间中考虑了具有退化粘度的多维（MD）等熵可压缩纳维-斯托克斯方程（ICNS）。我们证明，对于某一类具有局部真空的初始数据，无论初始数据多么小和多么平滑，相应的柯西问题的正则解都会在有限时间内爆炸。值得指出的是，本文所考虑的正则解的局部存在性已经成立。