Subsonic Euler flows with damping in two-dimensional expansion nozzles

In this paper, we use the steady isentropic Euler system with linear damping to describe Chaplygin gas flow in a two-dimensional expansion nozzle. Firstly, the unique existence of subsonic and supersonic solutions of the damped radial isentropic Euler flow in a two-dimensional expansion and contraction nozzle are established. Then take the radial subsonic solution in a expansion nozzle as the background solution, the structural stability problem of the background solution under small perturbations of the inlet Bernoulli function, inlet velocity ratio, and outlet density is transformed into the unique existence problem of the solution to the boundary value problem of a nonlinear hyperbolic-elliptic coupled system. After performing a Lagrange transformation on the decoupled system, we transform it into a fixed boundary problem, linearize it, and construct a suitable iteration set and a iteration scheme. Finally the existence of a unique fixed point can be proved, which yields the structural stability of the background solution.