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We establish the global existence and uniqueness of classical solutions tothe Cauchy problem for the isentropic compressible Navier-Stokes equations inthree spatial dimensions with smooth initial data which are of small energy butpossibly large oscillations with constant state as far field which could beeither vacuum or non-vacuum. The initial density is allowed to vanish and thespatial measure of the set of vacuum can be arbitrarily large, in particular,the initial density can even have compact support. These results generalizeprevious results on classical solutions for initial densities being strictlyaway from vacuum, and are the first for global classical solutions which mayhave large oscillations and can contain vacuum states.

Global Well-Posedness of Classical Solutions with Large Oscillations and  Vacuum to the Three-Dimensional Isentropic Compressible Navier-Stokes  Equations