| Abstract: | We investigate the stability in the large of Couette flow between two cylinders rotating in the same direction. For the case of infinitesimally small perturbations, a sufficient condition for stability of the Couette flow (the Synge condition) was obtained in [1, 2]. In [3] for an investigation of the stability in the nonlinear case, to this condition we must add certain constraints on the initial energy and the angular velocities. In the proposed study, using the second method of Lyapunov, sufficient conditions for stability in the large are obtained, which differ little from the Synge condition. In this case these conditions approach the Synge condition as the distance between the cylinders is decreased. |
