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

Myoungjean Bae, Ben Duan, Chunjing Xie

Abstract

We prove the global uniqueness of subsonic solutions to the steady Euler-Poisson system in a bounded domain. Previous works established the existence and local uniqueness of multidimensional subsonic flows by constructing solutions as small perturbations of one-dimensional background states, where a contraction mapping argument applies in a small perturbation regime. In contrast, the present paper removes the smallness assumption and proves global uniqueness within a class of subsonic solutions satisfying the same boundary data.

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

Abstract

We prove the global uniqueness of subsonic solutions to the steady Euler-Poisson system in a bounded domain. Previous works established the existence and local uniqueness of multidimensional subsonic flows by constructing solutions as small perturbations of one-dimensional background states, where a contraction mapping argument applies in a small perturbation regime. In contrast, the present paper removes the smallness assumption and proves global uniqueness within a class of subsonic solutions satisfying the same boundary data.
Paper Structure (7 sections, 9 theorems, 191 equations)

This paper contains 7 sections, 9 theorems, 191 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem \ref{['theorem-1']}
  3. The existence of a solution
  4. The uniqueness
  5. Proof of Theorem \ref{['theorem-2']}
  6. The existence of a solution
  7. The uniqueness

Key Result

Theorem 1.2

Let $n=2$ or $3$, and suppose that

Theorems & Definitions (18)

  • Theorem 1.2: Euler--Poisson system with self-consistent electric fields
  • Remark 1.3
  • Theorem 1.4: Euler-Poisson system with self-consistent gravitational fields
  • Definition 2.1
  • Proposition 2.2
  • Lemma 2.3
  • Definition 2.4
  • Lemma 2.5
  • proof
  • Proposition 2.6: Convexity of the $\delta$-subsonic set $\mathcal{P}_{\delta}$
  • ...and 8 more