Structural stability of steady subsonic Euler flows in 2D finitely long nozzles with variable end pressures

Abstract

This paper is devoted to studying structural stability of steady subsonic Euler flows in 2D finitely long nozzles. The reference flow is subsonic shear flows with general size of vorticity. The problem is described by the steady compressible Euler system. With admissible physical conditions and prescribed pressures at the entrances and the exits of the nozzles respectively, we establish unique existence and structural stability of this kind of subsonic shear flows. Due to the hyperbolic-elliptic coupled form of the Euler system in subsonic regions, the problem is reformulated via Lagrange transformation and then decoupled into an elliptic mode and two hyperbolic modes. The elliptic mode is a mixed type boundary value problem of second order quasilinear elliptic equation for the stream function. The hyperbolic modes are transport types to control the total energy and the entropy. Mathematically, the iteration scheme is executed in a weight Hölder space with low regularity.