Global Existence Of A Transonic Jet With A Strong Shock In Two-Dimensional Steady Compressible Euler Flows

For steady supersonic flow past a solid corner surrounded by quiescent gas, if the pressure of the upcoming supersonic flow is lower than the pressure of the quiescent gas, there may appear a strong shock to increase the pressure and then a transonic characteristic discontinuity to separate the supersonic flow behind the shock-front from the still gas. In this paper we prove global existence of such flow patterns under suitable conditions on the upstream supersonic flow and the pressure of the surrounded quiescent gas, for the two-dimensional steady complete compressible Euler system. Mathematically it is a global weak solution to a characteristic free boundary problem of hyperbolic conservation laws. The main part of the proof is to reformulate the problem in the Lagrangian coordinates, then solve several typical Riemann problems and obtain estimates for wave interraction/reflection/refraction, and define a Glimm functional using suitable weights, which guarantees that the solution can be constructed by standard front tracking method.