The chain of embedded invariant submodels for conic motions

Abstract

The equations of continuum mechanics are invariant in relation to the Galilean group generalized by extention. Its 11-dimensional Lie algebra has many subalgebras, which form the optimal system of dissimilar subalgebras. Subalgebras from the optimal system form the graph of embedded subalgebras. There are many chains of subalgebras in the graph. We consider the chain of embedded subalgebras containing operators of space and time translation, the rotation and uniform extension of all independent variables for the models of the continuous medium mechanics. We choose concordant invariants for each subalgebra from the chain. The chain of invariant submodels is constructed in a cylindrical coordinates based on chosen invariants. It is proved that solutions of a submodel constructed on a subalgebra of higher dimension will be part of solutions of submodels constructed on subalgebra of smaller dimensions for the considered chain. Thus, the chain of embedded invariant submodels is constructed by the example of equations of ideal gas dynamics.