Global Uniqueness of Subsonic Flows for the Steady Euler-Poisson System

TL;DR

This paper proves the global uniqueness of multidimensional subsonic flows in the steady Euler-Poisson system within a bounded nozzle, using convexity properties and energy estimates.

Contribution

It establishes the uniqueness of solutions without small perturbation assumptions, advancing understanding of subsonic flow behavior in this system.

Findings

Uniqueness holds for multidimensional subsonic flows in a bounded nozzle.

Convexity property of subsonic states is key to the proof.

Energy estimates are used to establish the result.

Abstract

We prove the global uniqueness of multidimensional subsonic flows for the steady Euler--Poisson system in a bounded nozzle in the sense that uniqueness holds without restricting solutions to be small perturbations of a background state. The proof is based on a convexity property of the set of subsonic states and energy estimates.