  This paper concerns the structural stability of supersonic flows with a
contact discontinuity in a finitely long curved nozzle for the two-dimensional
steady compressible rotating Euler system. Concerning the effect of Coriolis
force, we first establish the existence of supersonic shear flows with a
contact discontinuity in the flat nozzle. Then we consider the stability of
these background supersonic shear flows with a contact discontinuity when the
incoming supersonic flow and the upper and lower nozzle walls are suitably
perturbed. The problem can be formulated as an initial boundary value problem
with a contact discontinuity as a free boundary. To deal with the free boundary
value problem, the Lagrangian transformation is introduced to straighten and
fix the contact discontinuity. The rotating Euler system is reduced to a first
order hyperbolic system for the Riemann invariants. We design an iteration
scheme and derive some estimates for the solution to the hyperbolic system.
Finally, by using the inverse Lagrangian transformation, we prove the original
free boundary problem admits two layers of smooth supersonic flows separated by
a smooth contact discontinuity.
