Global Convergence and Error Estimates in Infinity-ion-mass Limits for Bipolar Euler-Poisson System

Fuente: arXiv
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Main Authors: Li, Yachun, Wang, Shihao, Zhao, Liang
Format: Preprint
Published: 2022
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author Li, Yachun
Wang, Shihao
Zhao, Liang
author_facet Li, Yachun
Wang, Shihao
Zhao, Liang
contents This paper is concerned with the global-in-time convergence from bipolar Euler-Poisson system (BEP) to unipolar one (UEP) through the infinity-ion-mass limit by letting the ratio of the mass of ion $m_i$ over that of electron $m_e$ goes to infinity. The global convergence of the limit is obtained for smooth solutions sufficiently close to constant equilibrium states. Furthermore, by applying the stream function method and taking advantage of the anti-symmetric structure of the error system, one obtains the corresponding global-in-time error estimates between smooth solutions of (BEP) and (UEP). It is worth mentioning that due to the strong coupling through the Poisson equation in bipolar system, stream functions for ions and electrons equations should be constructed separately based on asymptotic expansions of solutions, which is very different from the case of unipolar system.
format Preprint
id arxiv_https___arxiv_org_abs_2211_16436
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Global Convergence and Error Estimates in Infinity-ion-mass Limits for Bipolar Euler-Poisson System
Li, Yachun
Wang, Shihao
Zhao, Liang
Analysis of PDEs
35B25, 35L45, 35L60, 35Q35, 35Q60
This paper is concerned with the global-in-time convergence from bipolar Euler-Poisson system (BEP) to unipolar one (UEP) through the infinity-ion-mass limit by letting the ratio of the mass of ion $m_i$ over that of electron $m_e$ goes to infinity. The global convergence of the limit is obtained for smooth solutions sufficiently close to constant equilibrium states. Furthermore, by applying the stream function method and taking advantage of the anti-symmetric structure of the error system, one obtains the corresponding global-in-time error estimates between smooth solutions of (BEP) and (UEP). It is worth mentioning that due to the strong coupling through the Poisson equation in bipolar system, stream functions for ions and electrons equations should be constructed separately based on asymptotic expansions of solutions, which is very different from the case of unipolar system.
title Global Convergence and Error Estimates in Infinity-ion-mass Limits for Bipolar Euler-Poisson System
topic Analysis of PDEs
35B25, 35L45, 35L60, 35Q35, 35Q60
url https://arxiv.org/abs/2211.16436