Rigorous derivation of a 1D model from the 3D non-steady Navier-Stokes equations for compressible nonlinearly viscous fluids
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Problems with three-dimensional 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 three-dimensional 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 two-dimensional models, which is very helpful, because their solutions are easier than solutions of the original three-dimensional models. Since nonsteady Navier-Stokes equations for compressible nonlinearly viscous fluids in a three-dimensional 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 one-dimensional model from the three-dimensional Navier-Stokes equations.
CitationAndrasik, R., & Vodak, R. (2018). Rigorous derivation of a 1D model from the 3D non-steady Navier-Stokes equations for compressible nonlinearly viscous fluids. Electronic Journal of Differential Equations, 2018(114), pp. 1-21.
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