Geodesic
Optimal system of subalgebras admitted by the gas dynamics equations in case of state equation with separated density
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 19-38

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We consider the gas dynamics equations with the state equation of separated density. The optimal system of subalgebras for a $12$-dimensional Lie algebra admitted by the gas dynamics equations is given. We use the decomposition of a $12$-dimensional Lie algebra to the semidirect sum of a $6$-dimensional Abelian ideal and a $6$-dimensional subalgebra to construct the optimal system. On the first step we construct the optimal system of projections on $6$ dimensional subalgebra. Then the projections are complemented with elements from Abelian ideal. We propose the compact notation of the optimal system of subalgebras for $12$-dimensional Lie algebra which is constructed with the help of the optimal system for $6$-dimensional subalgebra.
Mots-clés : optimal system of subalgebras
Keywords: gas dynamics equations, state equation of the separated density. 
E. V. Makarevich. Optimal system of subalgebras admitted by the gas dynamics equations in case of state equation with separated density. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 19-38. http://geodesic.mathdoc.fr/item/SEMR_2011_8_a2/
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