  We are concerned with the global existence and vanishing dispersion limit of
strong/classical solutions to the Cauchy problem of the one-dimensional
barotropic compressible quantum Navier-Stokes equations, which consists of the
compressible Navier-Stokes equations with a linearly density-dependent
viscosity and a nonlinear third-order differential operator known as the
quantum Bohm potential. The pressure $p(\rho)=\rho^\gamma$ is considered with
$\gamma\geq1$ being a constant. We focus on the case when the viscosity
constant $\nu$ and the Planck constant $\varepsilon$ are not equal. Under some
suitable assumptions on $\nu,\varepsilon, \gamma$, and the initial data, we
proved the global existence and large-time behavior of strong and classical
solutions away from vacuum to the compressible quantum Navier-Stokes equations
with arbitrarily large initial data. This result extends the previous ones on
the construction of global strong large-amplitude solutions of the compressible
quantum Navier-Stokes equations to the case $\nu\neq\varepsilon$. Moreover, the
vanishing dispersion limit for the classical solutions of the quantum
Navier-Stokes equations is also established with certain convergence rates. The
proof is based on a new effective velocity which converts the quantum
Navier-Stokes equations into a parabolic system, and some elaborate estimates
to derive the uniform-in-time positive lower and upper bounds on the specific
volume.
