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

Yuriy G. Gubarev^{1, 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

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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