Geodesic
Simple Invariant Solutions of the Dynamic Equation for a Monatomic Gas
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 2, pp. 115-132

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We consider a system of gas dynamics equations with the state equation of a monatomic gas. The equations admit a group of transformations with a 14-dimensional Lie algebra. We consider 4-dimensional subalgebras containing the projective operator from the optimal system of subalgebras. The invariants of the basis operators are computed. Eight simple invariant solutions of rank $0$ are obtained. Of these, four physical solutions specify a gas motion with a linear velocity field and one physical solution specifies a motion with a linear dependence of components of the velocity vector on two space coordinates. All these solutions except one have variable entropy. The motion of gas particles as a whole is constructed for the isentropic solution. The solutions obtained have a density singularity on a constant or moving plane, which is a boundary with vacuum or a wall.
Keywords: gas dynamics equations, projective operator
Mots-clés : invariant solution. 
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     title = {Simple {Invariant} {Solutions} of the {Dynamic} {Equation} for a {Monatomic} {Gas}},
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R. F. Nikonorova. Simple Invariant Solutions of the Dynamic Equation for a Monatomic Gas. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 2, pp. 115-132. http://geodesic.mathdoc.fr/item/TIMM_2023_29_2_a9/