Compressible Nonlinearly Viscous Fluids: Asymptotic Analysis in a 3D Curved Domain
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Concerning three-dimensional models, an analytical solution is often impossible and numerical solution can be unduly complicated. Thus, we need to simplify three-dimensional models, when possible, prior to solving the problem. Recently, several lower-dimensional models for dynamics of compressible fluids were rigorously derived from three-dimensional models. We extend the current framework by dealing with nonsteady Navier–Stokes equations for compressible nonlinearly viscous fluids in a deformed three-dimensional domain. The deformation of the domain introduced new difficulties in the asymptotic analysis, because the deformation affects the limit equations in a non-trivial way.
KeywordsNavier–Stokes equations Compressible fluids Asymptotic analysis Dimension reduction Curved domains
Mathematics Subject Classification35Q30 35Q35 76D05
This research was supported by The Ministry of Education, Youth and Sports CZ.02.1.01/0.0/0.0/17_049/0008408 Hydrodynamic Design of Pumps, and by Grant IGA PrF 2016 025.
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Conflict of interest
The authors declare that they have no competing interests.
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