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

• Main Author: Mingyu Zhang
• Format: Article
• Language: English
• Published: SpringerOpen 2020-05-01
• Series: Journal of Inequalities and Applications
• Subjects: Compressible Navier–Stokes equations; Dimension reduction; Relative entropy
• Online Access: http://link.springer.com/article/10.1186/s13660-020-02405-w

Abstract 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 ) $\varOmega _{\varepsilon }=I_{\varepsilon }\times (0, 1)$ , I ε = ( 0 , ε ) ⊂ R $I_{ \varepsilon }=(0, \varepsilon )\subset \mathbb{R}$ . We show that the strong solutions in the 2D domain converge to the classical solutions of the limit 1D Navier–Stokes system as ε → 0 $\varepsilon \to 0$ .