The formation of singularity of strong solutions to the two-dimensional (2D) Cauchy problem of the compressible Navier-Stokes equations with variable viscosity is considered. It is shown that for the initial density allowing vacuum, the strong solution exists globally if the density is bounded from above. Some weighted estimates play a crucial role in the proof.

中文翻译：

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二维可变粘度可压缩纳维-斯托克斯方程柯西问题的延拓原理

考虑了具有可变粘度的可压缩 Navier-Stokes 方程的二维 (2D) 柯西问题的强解奇点的形成。结果表明，对于允许真空的初始密度，如果密度从上方有界，则强解全局存在。一些加权估计在证明中起着至关重要的作用。