  In this paper, the Cauchy problem for the three-dimensional (3-D) isentropic
compressible Navier-Stokes equations with degenerate viscosities is considered.
By introducing some new variables and making use of the "quasi-symmetric
hyperbolic"-"degenerate elliptic" coupled structure to control the behavior of
the fluid velocity, we prove the global-in-time well-posedness of regular
solutions with vacuum for a class of smooth initial data that are of small
density but possibly large velocities. Here the initial mass density is
required to decay to zero in the far field, and the spectrum of the Jacobi
matrix of the initial velocity are all positive. The result here applies to a
class of degenerate density-dependent viscosity coefficients, is independent of
the BD-entropy, and seems to be the first on the global existence of smooth
solutions which have large velocities and contain vacuum state for such
degenerate system in three space dimensions.
