R.F. Nikonorova. Simple invariant solutions of the dynamic equation for a monatomic gas ... P. 115-132

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, invariant solution

Received March 3, 2023

Revised April 14, 2023

Accepted April 17, 2023

Renata Fuatovna Nikonorova, Cand. Sci. (Phys.-Math.), Mavlyutov Institute of Mechanics – Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa, 450054 Russia, e-mail: renatanikon@gmail.com

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Cite this article as: R.F. Nikonorova. Simple invariant solutions of the dynamic equation for a monatomic gas. Trudy Instituta Matematiki i Mekhaniki URO RAN, 2023, vol. 29, no. 2, pp. 115–132;  Proceedings of the Steklov Institute of Mathematics (Suppl.), 2023, Vol. 321, Suppl. 1, pp. S186–S203.