Secondary bifurcation of a steady solution into an invariant torus for evolution problems of NavierStokes' type
Abstract
Bifurcation of the solution of NavierStokes 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 twodimensional torus which is invariant under the dynamical system considered and which is stable (if it exists) while the periodic solution is unstable. The quasiperiodicity of the solution requires further investigation.
 Publication:

Applications of Methods of Functional Analysis to Problems in Mechanics
 Pub Date:
 1976
 Bibcode:
 1976amfa.proc..354I
 Keywords:

 Branching (Mathematics);
 NavierStokes Equation;
 Toruses;
 Turbulent Flow;
 Cauchy Problem;
 Eigenvalues;
 Hilbert Space;
 Operators (Mathematics);
 Perturbation Theory;
 Steady Flow;
 Fluid Mechanics and Heat Transfer