This article is cited in 3 papers

Research papers

Group-theoretical solutions to gas dynamic equations generated by threedimensional Lie subalgebras

A. A. Cherevko

M. A. Lavrent'ev Institute of Hydrodynamics

Abstract: We study group-theoretical solutions to the dynamic equations of polytropic gas. We give a complete list of invariant and partially invariant solutions generated by $3$-dimensional subalgebras of symmetry Lie algebra $L_{13}$. There are $146$ different invariant solutions, $61$ partially invariant solutions, and $12$ types of barochronic solutions in this list. This result is applicable in gas dynamics, aerodynamics, and physics of atmosphere.

UDC: 533, 517.958

MSC: 35L60, 58J70, 76N15

Received November 26, 2007, published December 25, 2007

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