Abstract: In this talk, we discuss the well-posedness theory of compressible subsonic jet flows for two dimensional steady Euler system with general incoming horizontal velocity and suitably large flux. We show the stream function formulation for two dimensional compressible steady Euler system enjoys a variational structure even when the flows have nontrivial vorticity, so that the jet problem can be reformulated as a domain variation problem. Then we adapt the framework developed by Alt, Caffarelli and Friedman to study this Bernoulli type free boundary problem, and obtain the existence and uniqueness of the compressible subsonic jet flows for two dimensional steady Euler system. Finally, based on a compactness argument, we prove that there is always a subsonic jet attached with the nozzle at its orifice as long as the incoming mass flux is larger than a critical value. This is a joint work with Wenhui Shi, Lan Tang and Chunjing Xie.