Building of Mathematical Models of Continuum Media on the Basis of the Invariance Principle

Abstract

The system of differential equations which describes the motion of continuum media of gas, liquid, Reiner-Rievling-type liquid, etc., is considered.

$$ \begin{gathered} {\rho_t} + div(\rho u) = 0; \hfill \\ \rho [{u_t} + (u \cdot \nabla )u] - div\Pi (\nabla u) + \nabla \rho; \hfill \\ {\rho_t} + u \cdot \nabla \rho + G\, div\,u + H\phi = 0. \hfill \\ \end{gathered} $$

Solving the problem of its group classification, we obtained all the state equations which lead to the expansion of the main group Γ₀ assumed by the initial equations under the arbitrary elements Π, G, H.