We establish the global existence and uniqueness of classical solutions to the
Cauchy problem for the isentropic compressible Navier-Stokes equations in three
spatial dimensions with smooth initial data that are of small energy but possibly
large oscillations with constant state as far field, which could be either vacuum
or nonvacuum. The initial density is allowed to vanish, and the spatial measure
of the set of vacuum can be arbitrarily large; in particular, the initial density can
even have compact support. These results generalize previous results on classical
solutions for initial densities being strictly away from vacuum and are the first
for global classical solutions that may have large oscillations and can contain
vacuum states. © 2012 Wiley Periodicals, Inc