The Basic Attractor of the Viscous Moore-Greitzer Equation

The basic attractor of nonlinear partial differential equations is the part of the global attractor that attracts a prevalent set in phase space. We give a qualitative description of the basic attractor of a model for axial compression systems and show that it consists of three types of components, uniform (design) flow, surge and stall. The basic attractor can contain more than one stall component. The existence of these components is proven and their stability explored. Numerical results are presented, showing the shape and evolution of stall cells over large parameter regions. 1 Introduction In recent years a lot of attention has been devoted to the study of air flow through turbomachines. The main reason for this interest is that when a turbomachine, such as a jet engine, operates close to its optimal operating parameter values, the flow can become unstable. These instabilities put a large stress on the engine and in some cases the engine needs to be turned off in order to recover..