Steady Euler flows with contact discontinuities in infinitely long nozzles with general upstream data

We investigate steady compressible Euler flows in two-dimensional infinitely long nozzles, where the piecewise smooth upstream data at infinity admits a characteristic discontinuity. Except the subsonicity condition, no additional constraints are imposed on the data. We establish the existence and uniqueness of subsonic weak solutions associated with a smooth contact discontinuity curve. The original problem is reformulated into an elliptic equation in divergence form with discontinuous coefficients, such that the contact discontinuity conditions are inherently preserved in the solution of the elliptic problem. We further investigate the downstream asymptotic behavior and show that the convergence rate of the flow matches that of the nozzle walls.