Abstract:
The treatment of (in)stability of the classical Kolmogorov flow of viscous incompressible fluid on the plane torus T<sup>2</sup>={(x,y)∈ IR<sup>2</sup> : 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)∈ IR<sup>2</sup> : -\infty < x < \infty , 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.
Fulltext:
https:/.../preprint.asp?id=1995-126&lg=r