Center manifold of the viscous Moore-Greitzer PDE model

A commonly used mathematical model for jet engines that captures the flow behavior of a compression system, known as the viscous Moore-Greitzer PDE model, consists of a PDE and two ODEs. The PDE describes the behavior of disturbances in the inlet region of the compression system, and the two ODEs describe the coupling of the disturbances with the mean flow. In this paper, we study this full-order model and first show that it is not topologically equivalent to its linearized version near the point where the pressure rise reaches its maximum. We further show that the model features a center manifold near this maximum pressure rise, which makes it possible to translate the study of the behavior of the local flow in the compressor into a study of the flow of two scalar differential equations on the center manifold, which we carry out explicitly in the paper.