Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.1, pp.78-82

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

1999, Volume 2, Number 1, pp.78-82

Global Stability of Systems Related to the Navier-Stokes Equations.
Alexander Rauh

A generalized Lyapunov method is outlined which predicts global stability of a broad class of dissipative dynamical systems. The method is applied to the complex Lorenz model and to the Navier--Stokes equations. In both cases one finds compact domains in phase space which contain the omega-sets of all trajectories, in particular the fixed points, limit cycles, and strange attractors.

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