The Analisys of Instabilities of Generalised Kolmogorov Flows.

Abstract: The treatment of (in)stability of the classical Kolmogorov flow of viscous incompressible fluid on the plane torus T2={(x,y)∈ IR2: x∈ [0, 2π/α], y∈ [0, 2/π]} immediately leads to the analysis of solutions of the Navier-Stokes system in the infinite domain K={(x,y)∈ IR2: -∞ < x < ∞, 0 < y < 2π} as the minimal critical Reynolds number of the loss of stability of the Kolmogorov flow corresponds to α=0. In this paper we demonstrate that under some restrictions on the velocity field the critical eigenvalue is real and hence it is natural to analyze the spatial dynamics of the problem.Note: Research direction:Mathematical problems and theory of numerical method