Inertial Manifolds and Gevrey Regularity for the Moore-Greitzer Model of an Axial-Flow Compressor

Summary

In this paper, we study the regularity and long-time behavior of the solutions to the Moore-Greitzer model of an axial-flow compressor. In particular, we prove that this dissipative system of evolution equations possesses a global invariant inertial manifold, and therefore its underlying long-time dynamics reduces to that of an ordinary differential system. Furthermore, we show that the solutions of this model belong to a Gevrey class of regularity (real analytic in the spatial variables). As a result, one can show the exponentially fast convergence of the Galerkin approximation method to the exact solution, an evidence of the reliability of the Galerkin method as a computational scheme in this case. The rigorous results presented here justify the readily available low-dimensional numerical experiments and control designs for stabilizing certain states and traveling wave solutions for this model.