Global Convergence and Error Estimates in Infinity-ion-mass Limits for Bipolar Euler-Poisson System
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| Format: | Preprint |
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2022
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| _version_ | 1866910006788489216 |
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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 |
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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 |