Global stability of supersonic Euler flows in quasi-one-dimensional convergent nozzles

Abstract

In this paper, we investigate the global well-posedness and stability of steady supersonic Euler flows in a quasi-one-dimensional convergent nozzle. First, we show that there exists a critical nozzle length L1, the global well-posedness of steady supersonic flows can be obtained and the explicit solution is given as long as the nozzle length L < L1. Then we prove the global stability of steady supersonic flows under small perturbations of initial-boundary values by wave decomposition.