Instability of Low Density Supersonic Waves of a Viscous Isentropic Gas Flow Through a Nozzle
In this work, we examine the stability of stationary non-transonic waves for viscous isentropic compressible flows through a nozzle with varying cross-section areas. The main result in this paper is, for small viscous strength, stationary supersonic waves with sufficiently low density are spectrally unstable; more precisely, we will establish the existence of positive eigenvalues for the linearization along such waves. The result is achieved via a center manifold reduction of the eigenvalue problem. The reduced eigenvalue problem is then studied in the framework of the Sturm–Liouville Theory.
Weishi Liu was partially supported by NSF grant DMS-0807327 and KU GRF 2301264-003. Myunghyun Oh was partially supported by NSF grant DMS-0708554.
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