Stability of transonic jet with strong shock in two-dimensional steady compressible Euler flows

For steady supersonic flow past a solid convex 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 the global existence, uniqueness, and stability of such flow patterns under suitable conditions on the upstream supersonic flow and the pressure of the surrounding quiescent gas, for the two-dimensional steady complete compressible Euler system. Mathematically, a global weak solution to a characteristic free boundary problem of hyperbolic conservation laws is constructed and shown to be unique and stable under the framework of front tracking method.