In this paper, we investigate the Navier–Stokes equations describing the motion of a compressible viscous fluid confined to a thin domain Ω ε = I ε × (0 , 1) , I ε = (0 , ε) ⊂ R . We show that the strong solutions in the 2D domain converge to the classical solutions of the limit 1D Navier–Stokes system as ε → 0 .