Secondary bifurcation of a steady solution into an invariant torus for evolution problems of Navier-Stokes' type

Bifurcation of the solution of Navier-Stokes PDE into a torus when a previous periodic solution becomes unstable is investigated in the case of a process of successive bifurcations of increasing complexity (where the first bifurcation occurs when a steady flow becomes unstable while a characteristic parameter of the problem crosses a first critical value). It is shown mathematically that the bifurcated solution is in general on a two-dimensional torus which is invariant under the dynamical system considered and which is stable (if it exists) while the periodic solution is unstable. The quasi-periodicity of the solution requires further investigation.