The far‐field convergence rates and structural stability of subsonic flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles

Abstract This paper establishes a unified framework for analyzing the far‐field convergence rates and structural stability of subsonic Euler flows with arbitrarily large vorticity and characteristic discontinuities in infinitely long nozzles. The main approach is an Euler–Lagrange transformation that flattens the discontinuities and reformulates the flow as a quasilinear elliptic equation in divergence form, combined with weighted local average energy estimates. This method addresses challenges arising from free boundaries of discontinuities and strong vorticity effects. It is shown that the convergence is governed by the slower of an intrinsic exponential decay and the boundary‐induced decay, without the smallness or convexity assumptions. This yields the first such results for flows with characteristic discontinuities. Structural stability is established for both smooth and discontinuous flows, which have linear dependence respect to the finite boundary perturbations, thereby removing the need for a small‐perturbation assumption. Both results extend naturally to incompressible flows.