  We investigate the global stability and non-vanishing vacuum states of large
solutions to the compressible Navier-Stokes equations on the torus
$\mathbb{T}^3$, and the main novelty of this work is three-fold: First, under
the assumption that the density $\rho({\bf{x}}, t)$ verifies $\sup_{t\geq
0}\|\rho(t)\|_{L^\infty}\leq M$, it is shown that the solutions converge to
equilibrium state exponentially in $L^2$-norm. Second, by employing some new
thoughts, we also show that the density converges to its equilibrium state
exponentially in $L^\infty$-norm if additionally the initial density
$\rho_0({\bf{x}})$ satisfies
$\inf_{{\bf{x}}\in\mathbb{T}^3}\rho_0({\bf{x}})\geq c_0>0$. Finally, we prove
that the vacuum states will not vanish for any time provided that the vacuum
states are present initially. This phenomenon is totally new and somewhat
surprising, and particularly is in contrast to the previous work of [H. L. Li
et al., Commun. Math. Phys., 281 (2008), 401-444], where the authors showed
that the vacuum states must vanish within finite time for the 1D compressible
Navier-Stokes equations with density-dependent viscosity
$\mu(\rho)=\rho^\alpha$ with $\alpha>1/2$.
