Abstract:
The equations of ideal hydrodynamics are considered with the state equation in the form of the pressure represented as the sum of density and entropy functions. Some twelve-dimensional Lie algebra corresponds to the admissible group of transformations. Basing on the two-dimensional subalgebras of the Lie algebra, we construct the rank 2 invariant submodels of canonical form and evolutionary type. The form is refined of the rank 2 invariant submodels of canonical form and evolutionary type for the eleven-dimensional Lie algebra admitted by the gas dynamics equations with the state equation of the general type.
Keywords:
equations of ideal hydrodynamics, state equation, admissible subalgebra, representation of invariant solution, invariant submodel, submodel of evolutionary type, canonical form of a submodel.
Citation:
D. T. Siraeva, “The canonical form of the rank 2 invariant submodels of evolutionary type in ideal hydrodynamics”, Sib. Zh. Ind. Mat., 22:2 (2019), 70–80; J. Appl. Industr. Math., 13:2 (2019), 340–349