Abstract
This paper studies the stability of the adiabatic unsteady motions of a perfect gas for which the velocity is proportional to the distance to the center of symmetry. The solutions of the gas dynamic equations of such a form and their physical interpretation are considered in [1]. The stability of one of the solutions, which corresponds to the pulsations of uniform gravitating spheres, was studied in paper [2]. The stability of the other solutions (gas motions in the absence of Newtonian gravitation, nonperiodic motions of gravitating gas) has not previously been investigated. The stability of such solutions is investigated in this paper and it is shown that the motions in which gas compression occurs are, as a rule, unstable.
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