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.
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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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Andrášik, R., Vodák, R. Compressible Nonlinearly Viscous Fluids: Asymptotic Analysis in a 3D Curved Domain. J. Math. Fluid Mech. 21, 13 (2019). https://doi.org/10.1007/s00021-019-0412-y
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DOI: https://doi.org/10.1007/s00021-019-0412-y