Bifurcation of the Kolmogorov flow with an external friction

Abstract

We consider Kolmogorov's problem of stationary flows in a thin layer with a bottom friction. Using the Lyapunov-Schmidt theory, we construct bifurcating solutions of this problem in the case where the linearized equations have simple eigenvalues. Compared with the previous paper [7], where we did not take account of the bottom friction, we find some interesting properties of bifurcation curves.