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

Journal of Inequalities and Applications

Mingyu Zhang¹ 

[1] School of Mathematics & Information Sciences, Weifang University;

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

DOI  :  10.1186/s13660-020-02405-w

来源: DOAJ

【 摘 要 】

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 $\varepsilon \to 0$ .

【 授权许可】

Unknown