The existence and monotonicity of a three-dimensional transonic shock in a finite nozzle with axisymmetric exit pressure (Q600631)

The authors study the existence of a solution to the transonic shock problem for the three-dimensional full steady isentropic Euler problem for polytropic gas when the exit pressure is axially symmetric and lies in an appropriate scope. The flow is in a de Laval nozzle; its boundary consists of two curved surfaces, i.e. the converging and the symmetric diverging parts. The diverging part is given by \(x_2^2+x_3^2 = x_1^2\tan^2(\theta_0)\) with small angle \(\theta_0\). The existence and monotonicity of the transonic shock is proved.