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. 
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     author = {E. V. Makarevich},
     title = {Optimal system of subalgebras admitted by the gas dynamics equations in case of state equation with separated density},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {19--38},
     publisher = {mathdoc},
     volume = {8},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2011_8_a2/}
}
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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/