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

中文翻译：

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具有密度相关粘度的可压缩Navier–Stokes方程的降维

在本文中，我们研究了Navier–Stokes方程，该方程描述了可压缩粘性流体的运动，该流体局限于一个薄域$ \ varOmega _ {\ varepsilon} = I _ {\ varepsilon} \ times（0，1）$，$ I_ { \ varepsilon} =（0，\ varepsilon）\ subset \ mathbb {R} $。我们显示2D域中的强解收敛于极限1D Navier–Stokes系统的经典解，即$ \ varepsilon \ to 0 $。