Journal of Mathematical Sciences and Applications
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Journal of Mathematical Sciences and Applications. 2015, 3(1), 12-21
DOI: 10.12691/jmsa-3-1-3
Open AccessArticle

On Stability of Steady–State Three–Dimensional Flows of an Ideal Incompressible Fluid

Yuriy G. Gubarev1, 2,

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

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

Pub. Date: September 08, 2015

Cite this paper:
Yuriy G. Gubarev. On Stability of Steady–State Three–Dimensional Flows of an Ideal Incompressible Fluid. Journal of Mathematical Sciences and Applications. 2015; 3(1):12-21. doi: 10.12691/jmsa-3-1-3

Abstract

The problem on linear stability of steady–state three–dimensional (3D) flows of an inviscid incompressible fluid, completely filling a volume with a solid boundary, is studied in the absence mass forces. It is proved by the direct Lyapunov method that these flows are absolutely unstable with respect to small 3D perturbations. The a priori exponential estimate from below, which testifies to growth of perturbations under consideration in time, is constructed.

Keywords:
an ideal incompressible fluid steady–state 3D flows stability small 3D perturbations the direct lyapunov method a priori exponential lower estimate instability

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