Dimension reduction for compressible Navier-Stokes equations with density-dependent viscosity

In this paper, we investigate the Navier-Stokes equations describing the motion of a compressible viscous fluid confined to a thin domain omega epsilon=I epsilon x(0,1)}=I_{\varepsilon }\times (0, 1)$\end{document}, I epsilon=(0,epsilon)subset of R=(0, \varepsilon )\subset \mathbb{R}$\end{document}. We show that the strong solutions in the 2D domain converge to the classical solutions of the limit 1D Navier-Stokes system as epsilon -> 0.d