Three-dimensional supersonic flows of Euler-Poisson system for potential flow

TL;DR

This paper establishes the unique existence of three-dimensional supersonic potential flows governed by the Euler-Poisson system in a rectangular cylinder, addressing technical challenges specific to three-dimensional cases.

Contribution

It extends previous work to three dimensions, providing a rigorous proof of existence and uniqueness for supersonic solutions of the Euler-Poisson system in this setting.

Findings

Proved unique existence of 3D supersonic solutions

Addressed technical differences in 3D case

Extended previous 2D results to 3D

Abstract

We prove the unique existence of supersonic solutions of the Euler- Poisson system for potential flow in a three-dimensional rectangular cylinder when prescribing the velocity and the strength of electric field at the entrance. Overall, the main framework is similar to [1], but there are several technical differences to be taken care of vary carefully. And, it is our main goal to treat all the technical differences occurring when one considers a three dimensional supersonic solution of the steady Euler-Poisson system.