Structural stability and optimal convergence rates of subsonic Euler flows with large vorticity in infinitely long nozzles

Abstract

In this paper, we establish the structural stability and optimal convergence rates of non-isentropic subsonic Euler flows with large vorticity in two-dimensional infinitely long nozzles. By applying the stream function formulation for compressible Euler equations, Euler equations are equivalent to a quasilinear second order elliptic equation of the stream function for subsonic flow. Then, the key points to prove the structural stability of subsonic flows with large vorticity under small perturbations of nozzle boundaries are the standard estimates of elliptic equations. Furthermore, using the maximum principle and the choice of compared functions, we obtain the optimal convergence rates of subsonic flows at far fields.