Electron. J. Differential Equations,
Vol. 2018 (2018), No. 114, pp. 121.
Rigorous derivation of a 1D model from the 3D nonsteady NavierStokes
equations for compressible nonlinearly viscous fluids
Richard Andrasik, Rostislav Vodak
Abstract:
Problems with threedimensional models lie very often in their large
complexity leading to impossibility to find an analytical solution.
Numerical solutions are sometimes an option, but they can be unduly
complicated in the case of threedimensional models. Frequently,
researchers investigate models where one or even two dimensions are
almost negligible and nothing important is occurring in them.
These models can be simplified and turned into one or twodimensional
models, which is very helpful, because their solutions are easier than
solutions of the original threedimensional models. Since nonsteady
NavierStokes equations for compressible nonlinearly viscous fluids
in a threedimensional domain belongs to the class of models which need
a simplification, when possible, to be effectively solved, we performed
a dimension reduction for this model. We studied the dynamics of a
compressible fluid in thin domains where only one dimension is dominant.
We present a rigorous derivation of a onedimensional model from the
threedimensional NavierStokes equations.
Submitted January 23, 2018. Published May 14, 2018.
Math Subject Classifications: 35Q30, 35Q35, 76D05.
Key Words: NavierStokes equations; compressible fluids; nonlinear viscosity;
dimension reduction; asymptotic analysis.
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Richard Andrasik
Department of Mathematical Analysis and Applications of Mathematics
Faculty of Science, Palacky University Olomouc
tr. 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
email: andrasik.richard@gmail.com


Rostislav Vodak
Department of Mathematical Analysis and Applications of Mathematics
Faculty of Science, Palacky University Olomouc
tr. 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
email: rostislav.vodak@upol.cz

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