On the compressible Euler dynamics equations in transonic flow

This paper is concerned with the transonic flow in a variable area duct for the full compressible Euler system. We developed a generalized Glimm method to confirm the existence of a solution for the initial–boundary value problem. The stability is resulted from the estimates on the interactions among the classical elementary waves and the perturbations caused by the operator splitting. When the method is applied to the equations, the limit of approximate solutions serves as a BV entropy solution in the cases where the duct has the positive material derivative or small L1L1-norms of derivatives. In particular, both situations are consistent when the duct is expanded.