Abstract
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.
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Translated from Trudy Instituta Matematiki i Mekhaniki UrO RAN, Vol. 29, No. 2, pp. 115 - 132, 2023 https://doi.org/10.21538/0134-4889-2023-29-2-115-132.
Translated by E. Vasil’eva
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Nikonorova, R.F. Simple Invariant Solutions of the Dynamic Equation for a Monatomic Gas. Proc. Steklov Inst. Math. 321 (Suppl 1), S186–S203 (2023). https://doi.org/10.1134/S0081543823030161
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DOI: https://doi.org/10.1134/S0081543823030161