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Compressible Nonlinearly Viscous Fluids: Asymptotic Analysis in a 3D Curved Domain

  • Richard AndrášikEmail author
  • Rostislav Vodák
Article
  • 30 Downloads

Abstract

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.

Keywords

Navier–Stokes equations Compressible fluids Asymptotic analysis Dimension reduction Curved domains 

Mathematics Subject Classification

35Q30 35Q35 76D05 

Notes

Acknowledgements

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.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no competing interests.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical Analysis and Applications of Mathematics, Faculty of SciencePalacký University OlomoucOlomoucCzech Republic

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