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Gubarev, Yu.G., The direct Lyapunov method. The stability of quiescent states and steadystate flows of fluids and gases, Palmarium Academic Publishing, Saarbrücken, 2012 (in Russian).

has been cited by the following article:

Article

On Instability of Steady–State Three–Dimensional Flows of an Ideal Compressible Fluid

1Laboratory for Fluid and Gas Vortical Motions, Lavrentyev Institute for Hydrodynamics, Novosibirsk, 630090, Russian Federation

2Department for Differential Equations, Novosibirsk State University, Novosibirsk, 630090, Russian Federation


International Journal of Partial Differential Equations and Applications. 2017, Vol. 5 No. 1, 10-18
DOI: 10.12691/ijpdea-5-1-2
Copyright © 2017 Science and Education Publishing

Cite this paper:
Yuriy G. Gubarev. On Instability of Steady–State Three–Dimensional Flows of an Ideal Compressible Fluid. International Journal of Partial Differential Equations and Applications. 2017; 5(1):10-18. doi: 10.12691/ijpdea-5-1-2.

Correspondence to: Yuriy  G. Gubarev, Laboratory for Fluid and Gas Vortical Motions, Lavrentyev Institute for Hydrodynamics, Novosibirsk, 630090, Russian Federation. Email: gubarev@hydro.nsc.ru

Abstract

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.

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