  We consider the compressible Navier-Stokes system describing the motion of a
viscous fluid confined to a straight layer
$\Omega_{\delta}=(0,\delta)\times\mathbb{R}^2$. We show that the weak solutions
in the 3D domain converge strongly to the solution of the 2D incompressible
Navier-Stokes equations (Euler equations) when the Mach number $\epsilon $
tends to zero as well as $\delta\rightarrow 0$ (and the viscosity goes to
zero).
