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Mechanics
The system of differential equations which describes the motion of continuum media such as gas, liquid and Reiner-Rievling liquid is considered. Solving the problem of its group classification, we obtained all the state equations which lead to the expansion of the main group $Gamma$ assumed by the initial equations under the arbitrary elements: $Pi$, $G$ and $H$. Here $Pi$ is the tensor of viscous tensions; $G$, $H$ are functions depending on the hydrostatic pressure and the density of the continuum medium considered.
The J.L. Ericksens problem of constitutive equations cite{Bytev:Tr} is solved for the continuum medium considered cite{Bytev:Anin,Bytev:By,Bytev:And}. Thus, we not only get the general representations on the stree tensor and the corresponding state equation, but the more wide groups continuous transformations which are assumed by the motion equations in every particular case of tensor $Pi$ and functions $G$, $H$ specialization as well. In other words, the group $Gamma_i$ corresponds to every three elements $Pi_i$, $G_i$, $H_i$.
As it good knows, the traditional approach to the building the mathematical models of continuum mechanics is the overlapping of the requirement for tensor of viscous tensions invariance relative to the action of $SO_3$ group cite{Bytev:Tr}. But as it has been shown cite{Bytev:And}, the rotation transformation are not include into equivalence transformation group. It is for this reason that one and the same continuum medium can be isotropic or anisotropic depending on movements type. As example, the Stokeses and Naviers-Stokeses liquids is obtained.
This work was supported in part by the Russian Foundation for Basic Research (the grant 04-01-00130).
Note. Abstracts are published in author's edition
Last update: 06-Jul-2012 (11:52:45)