Abstract

The Regular Partially Invariant Submodels of the Rank Three for the Compressible Fluid

A.R.Garifullin (Theoretical Physics Department, Bashkir State Pedagogical University, Ufa, Russia)

e-mail: theorphys@bspu.ru

The gas dynamics model consisting of five first order equations which connects velocity vector, the density, the pressure has been investigated.Our equation of state describes the compressible fluid motion at the large pressure and high temperature. An optimal system of admitted subalgebra is known for such a model. A submodel of the initial model is connected with the every subalgebra of the optimal system. The regular partial invariant submodels of the rank three are generated by the two-dimensional subalgebras. There are three invariants expressed via the independent variables. All functions except pressure may be found from the rest invariants. It was shown that there exist nine similar submodels. The submodels are reduced to a canonical form by special change of the invariants. The canonical form consists of the four equations quasilinear system of the second order and the explicit expression for the pressure. Seven submodels of the stationary type and two submodels of evolution type (time is an invariant) are considered. It was found that subalgebra doesn’t contain the rotation operator in four stationary cases and it is obviously to use the Cartesian coordinates in mentioned situation. The submodels are united and may be represented as one canonical form.

Section : 12