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Linear stability analysis of the Couette flow for the 2D Euler-Poisson system

Xueke Pu, Wenli Zhou, Dongfen Bian

Abstract

This paper is concerned with the linear stability analysis for the Couette flow of the Euler-Poisson system for both ionic fluid and electronic fluid in the domain $\bb{T}\times\bb{R}$. We establish the upper and lower bounds of the linearized solutions of the Euler-Poisson system near Couette flow. In particular, the inviscid damping for the solenoidal component of the velocity is obtained.

Linear stability analysis of the Couette flow for the 2D Euler-Poisson system

Abstract

This paper is concerned with the linear stability analysis for the Couette flow of the Euler-Poisson system for both ionic fluid and electronic fluid in the domain . We establish the upper and lower bounds of the linearized solutions of the Euler-Poisson system near Couette flow. In particular, the inviscid damping for the solenoidal component of the velocity is obtained.
Paper Structure (7 sections, 6 theorems, 118 equations)

This paper contains 7 sections, 6 theorems, 118 equations.

Table of Contents

  1. Introduction
  2. Ion dynamics case
  3. Electron dynamics case
  4. Notations
  5. Analysis for the ion dynamics
  6. Analysis for the electron dynamics
  7. Acknowledgements.

Key Result

Theorem 1.1

Suppose that $(\eta^{in}_{+},\omega^{in}_{+}) \in H^1_x H^2_y$ and that $\psi^{in}_{+} \in H^{-\frac{1}{2}}_x L^2_y$ with $\left(\eta^{in}_{+,a},\psi^{in}_{+,a},\omega^{in}_{+,a}\right)=(0,0,0)$. Let $(\eta_{+},u_{+},\phi)$ be a smooth solution for the system fl:ndu-fl:phi. Then the following estima and

Theorems & Definitions (13)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Theorem 1.4
  • Remark 1.1
  • Remark 1.2
  • Lemma 3.1
  • proof
  • proof : Proof of Theorem \ref{['th:uqp']}
  • proof : Proof of Theorem \ref{['th:que']}
  • ...and 3 more