Nonresonant case of intersection of bifurcation curves in the Couette–Taylor problem

The nonresonant case (Res 0) of the motion of a viscous incompressible fluid between rotating coaxial cylinders in a small neighborhood of a bifurcation point of codimension 2 is considered, where the amplitude system has only essential resonant terms. Existence and stability conditions are obtained for its solutions which correspond to various periodic and quasiperiodic solutions of the Navier–Stokes equations. In a small neighborhood of some points of the resonance Res 0, the regions of existence and stability of these solutions are determined.