  We establish the vanishing viscosity limit of the Navier-Stokes equations to
the Euler equations for three-dimensional compressible isentropic flow in the
whole space. It is shown that there exists a unique regular solution of
compressible Navier-Stokes equations with density-dependent viscosities,
arbitrarily large initial data and vacuum, whose life span is uniformly
positive in the vanishing viscosity limit. It is worth paying special attention
that, via introducing a "quasi-symmetric hyperbolic"--"degenerate elliptic"
coupled structure, we can also give some uniformly bounded estimates of
$\displaystyle\Big(\rho^{\frac{\gamma-1}{2}}, u\Big)$ in $H^3$ space and
$\rho^{\frac{\delta-1}{2}}$ in $H^2$ space (adiabatic exponent $\gamma>1$ and
$1<\delta \leq \min\{3, \gamma\}$), which lead the strong convergence of the
regular solution of the viscous flow to that of the inviscid flow in
$L^{\infty}([0, T]; H^{s'})$ (for any $s'\in [2, 3)$) space with the rate of
$\epsilon^{2(1-s'/3)}$. Further more, we point out that our framework in this
paper is applicable to other physical dimensions, say 1 and 2, with some minor
modifications. This paper is based on our early preprint in 2015.
