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

[摘要] 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 $\varepsilon \to 0$.

[学科分类] 电力

[关键词] Compressible Navier–Stokes equations;Dimension reduction;Relative entropy