Geodesic
A planar collapse of a gas with a linear velocity field
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 2, pp. 207-216

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Solutions of gas dynamics equations with a linear velocity field and uniform deformation are considered. The linearity matrix is diagonal nondegenerate with different eigenvalues. The state equation is an equation with separated density. The world lines of motion of gas particles are written for a solution of the state equation for a polytropic gas. The motion of particles describes collapses in two mutually perpendicular planes at different times. The motions of bounded specific volumes of particles are shown. The motions of a sonic surface, characteristics, and the characteristic conoid are described. Approximate formulas are given for calculating the motion of characteristics passing through any given surface. An exact solution with nonhomogeneous deformation is obtained for the linearity matrix of the solution without the conditions of density and pressure invariance.
Keywords: gas dynamics, linear velocity field, homogeneous deformation, inhomogeneous deformation, polytropic gas, collapse, characteristics. 
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L. Z. Urazbakhtina; Yu. V. Yulmukhametova. A planar collapse of a gas with a linear velocity field. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 2, pp. 207-216. http://geodesic.mathdoc.fr/item/TIMM_2023_29_2_a15/