Decomposition of Three-Dimensional Steady Non-isentropic Compressible Euler System and Stability of Spherically Symmetric Subsonic Flows and Transonic Shocks under Multidimensional Perturbations

TL;DR

This paper introduces a decomposition method for the 3D steady compressible Euler system on Riemannian manifolds, demonstrating stability of spherically symmetric subsonic flows and transonic shocks under multidimensional boundary perturbations.

Contribution

It develops a general decomposition technique for the Euler system on Riemannian manifolds and applies it to prove stability of specific flow configurations.

Findings

Decomposition method applicable to general Riemannian manifolds.

Proved stability of spherically symmetric subsonic flows.

Established stability of transonic shocks under boundary perturbations.

Abstract

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 $\mathbb{R}^3$ under multidimensional perturbations of boundary conditions.