eng Science and Education Publishing International Journal of Partial Differential Equations and Applications 2376-9556 2017-05-23 5 1 10 18 10.12691/ijpdea-5-1-2 IJPDEA2017512 article Yuriy G. Gubarev gubarev@hydro.nsc.ru 1 Laboratory for Fluid and Gas Vortical Motions, Lavrentyev Institute for Hydrodynamics, Novosibirsk, 630090, Russian Federation The problem on linear stability of stationary spatial flows of an inviscid compressible fluid entirely occupying a certain volume with quiescent solid impenetrable boundary in absence of external mass forces is studied. Applying the direct Lyapunov method, such flows are proved to be absolutely unstable under small three-dimensional (3D) perturbations. Constructive conditions for linear practical instability are obtained. The a priori exponential lower estimate for the growth of the considered perturbations in time is found. http://pubs.sciepub.com/ijpdea/5/1/2/ijpdea-5-1-2.pdf an ideal compressible fluid steady-state spatial flows small 3D perturbations the direct Lyapunov method absolute linear theoretical instability conditions for linear practical instability a priori exponential lower estimate