Singularity Formation for the Multi-dimensional Compressible Degenerate Navier–Stokes Equations

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.