Supersonic flows with a contact discontinuity to the two‐dimensional steady rotating Euler system

We concern 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. We then investigate the structural stability of these background supersonic shear flows with a contact discontinuity under the perturbations of the incoming supersonic flow and the upper and lower nozzle walls. It can be formulated as an initial boundary value problem with a contact discontinuity as a free boundary. The Lagrangian transformation is employed to straighten and fix the contact discontinuity, and the rotating Euler system is reduced to a first‐order hyperbolic system for the Riemann invariants. The key ingredient of the analysis is to obtain the estimates of the solution for the associated linearized hyperbolic system via the characteristic method.