Stability of transonic jets with strong rarefaction waves for two-dimensional steady compressible Euler system

Abstract

We study supersonic flow past a convex corner which is surrounded by quiescent gas. When the pressure of the upstream supersonic flow is larger than that of the quiescent gas, there appears a strong rarefaction wave to rarefy the supersonic gas. Meanwhile, a transonic characteristic discontinuity appears to separate the supersonic flow behind the rarefaction wave from the static gas. In this paper, we employ a wave front tracking method to establish structural stability of such a flow pattern under non-smooth perturbations of the upcoming supersonic flow. It is an initial-value/free-boundary problem for the two-dimensional steady non-isentropic compressible Euler system. The main ingredients are careful analysis of wave interactions and construction of suitable Glimm functional, to overcome the difficulty that the strong rarefaction wave has a large total variation. 2010 Mathematics Subject Classification. Primary: 35L50, 35L65, 35Q31, 35R35; Secondary: 76N10.

Two-Dimensional Steady Supersonic Relativistic Euler Flows Past Lipschitz Wedges

“…When the supersonic flow passes through a convex corner surrounded by static gas, and the pressure of the incoming flow is larger than that of the static gas, a large rarefaction wave and a transonic characteristic discontinuity separate the supersonic flow from the static gas. We establish the structural stability of such wave patterns under BV perturbations of the upcoming supersonic flow in [20].…”

“…Chen et al [4] showed the stability of the large rarefaction wave for two-dimensional steady exothermically reacting Euler flows. Ding and Yuan [20] proved structural stability of the composite wave of the large rarefaction wave and transonic characteristic discontinuity under some perturbation of the upstream supersonic flows past a convex corner. Wang and Yin [28] employed Nash-Morse-H örmander iteration scheme to establish local stability of centered rarefaction wave of the three-dimensional steady compressible full Euler flow past a sharp corner.…”

Stability of supersonic contact discontinuity for two-dimensional steady compressible Euler flows in a finite nozzle

“…Recently, the well-posedness theory for the steady supersonic compressible Euler flows through a 2D finitely long nozzle with a contact discontinuity was established in [36]. For other related problems on the steady supersonic contact discontinuity over a wedge with a sharp convex corner, we refer the reader to [14,29,37,[42][43][44]48]. The contact discontinuity in the Mach reflections was also studied in [19][20][21].…”