“Simple” solutions of the equations of dynamics for a polytropic gas
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The notion of a “simple” solution of a system of differential equations that admit a local Lie group G of transformations of the basic space is considered as an invariant H-solution of type (0, 0) with respect to the subgroup HυG. Such solutions are attractive since they are described by explicit formulas that provide a clear physical interpretation for them. For gas-dynamic equations with a polytropic gas law, all simple solutions that are not related to special forms of gas flow are listed. Examples of simple solutions are given and the collapse phenomenon, which has been previously studied for barochronic flows, is described.
KeywordsArbitrary Constant Simple Solution Factor System Isothermal Flow Typical Trajectory
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- 3.S. V. Golovin, “Optimal system of subalgebras for the Lie algebra of the operators admitted by the equations of gas dynamics for a polytropic gas,” Preprint No. 5-96, Institute of Hydrodynamics, Sib. Div., Russian Acad. of Sci., Novosibirsk (1996).Google Scholar