Dimension reduction for compressible Navier–Stokes equations with density-dependent viscosity
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...
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Format: | Article |
Language: | English |
Published: |
SpringerOpen
2020-05-01
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Series: | Journal of Inequalities and Applications |
Subjects: | |
Online Access: | http://link.springer.com/article/10.1186/s13660-020-02405-w |
Summary: | 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 $\varepsilon \to 0$ . |
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ISSN: | 1029-242X |