Stability of spherically symmetric subsonic flows and transonic shocks under multidimensional perturbations

We develop a method that works in general product Riemannian manifold to decompose the three-dimensional steady full compressible Euler system, which is of elliptic–hyperbolic composite-mixed type for subsonic flows. The method is applied to show stability of spherically symmetric subsonic flows and transonic shocks in space R3R3 under multidimensional perturbations of boundary conditions.