Summary: A FINITE DIMENSIONAL ATTRACTOR OF THE
MOORE­GREITZER PDE MODEL \Lambda
BJ ¨
ORN BIRNIR y AND H ¨
OSKULDUR ARI HAUKSSON z
Abstract. The Moore­Greitzer PDE model with viscosity is presented and the equations rewrit­
ten as an evolution equation on a Hilbert space. It is proven that the model has a unique global
solution which is smooth in space and time. Furthermore it is proven that there exists a global
attractor, i.e a compact set which attracts all bounded sets. Finally it is shown that the attractor
has a finite fractal dimension.
Key words. Moore­Greitzer equation, jet engine model, existence and uniqueness of solutions,
global attractor, Hausdorff dimension, fractal dimension
AMS subject classifications. 34D45, 34K15, 35B40, 35K55
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
original operation. For this reason jet engines are currently operated away from their
optimal operating parameter values.

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

Collections: Mathematics